Carbon Chain Molecules:
Production and Spectroscopic Detection
Inaugural-Dissertation
zur
Erlangung des Doktorgrades
der Mathematisch-Naturwissenschaftlichen Fakultät
der Universität zu Köln
vorgelegt von
Guido W. Fuchs
aus Polch
UNIVERSITÄT
ZU KÖLN
Köln 2002
Berichterstatter:
Prof. Dr. G. Winnewisser
Prof. Dr. J. Jolie
Tag der mündlichen Prüfung:
18.2.2003
Abstract
In this work the production and detection of carbon chain molecules in laboratory and
interstellar space are presented. The work is divided into three parts.
Part I, the production of reactive molecules. The availability of efficient molecular
sources are of great importance for absorption and emission experiments. Hence, their
characterization and optimization is indispensable for the success of these kinds of experiments. Molecular sources can be very specialized concerning the species produced.
The excimer laser ablation source used in Cologne is highly efficient in the production
of pure carbon molecules, i.e. carbon clusters. However, the carbon cluster yield in the
range from C10 to C60 is still not satisfactory. For an improvement of the production
rates new methods have to be tested. In the course of this thesis a excimer laser ablation is compared with Nd:YAG laser ablation. For that purpose a quadrupole mass
spectrometer has been used to characterize the Nd:YAG laser ablation source. Investigations on a slit nozzle discharge source have been performed. This type of molecule
source is able to produce pure carbon clusters but was originately developed for the
production of hydro-carbon molecules. Both kinds of molecule sources, i.e. laser ablation as well as slit nozzle discharge sources, produce a plasma which causes significant
problems when recording mass spectra. Therefore, a mass spectrometer specially designed for plasma applications in combination with the discharge slit nozzle was tested
in Lichtenstein/Balzer. Cations as well as anions could be detected but no signal of
discharge related neutrals were found. In addition to the mass spectroscopic studies also
infrared (IR) absorption experiments have been performed. In the course of this thesis
the Cologne carbon cluster experiment has been rebuild. In particular, the preceding
IR diode laser spectrometer has been replaced by a new one which has been largely
improved by using a liquid nitrogen dewar for the laser diode, new detectors for the
2000 cm−1 frequency region, stable optical setup and the development of new data acquisition and calibration software. First measurements are presented.
Part II, measurements of Cn N radicals. At the Harvard Laboratory Astrochemistry
Group measurements have been performed on mono-substituted C3 N isotopomers (cyanoethynyl) in a supersonic molecular beam using Fourier transform microwave spectroscopy. A detailed spectroscopic characterization of 13 CCCN, C13 CCN, CC13 CN and
CCC15 N including their hyperfine spectra is given in this work. The rotational and leading centrifugal distortion constants were determined to high accuracy by using microwave data between 9.5 - 38.4 GHz and previously measured millimeter data. The Fermi
contact b(14 N), dipole-dipole c(14 N), and the nitrogen quadrupole hyperfine coupling
constants for 13 CCCN, C13 CCN, and CC13 CN have been determined and the previously published b(13 C) and c(13 C) values were stated more precisely [McCarthy et al.,
J.Chem.Phys. 103, 7820 (1995)]. The magnetic hyperfine coupling constants of the presented 13 C isotopic species of C3 N differ from those of the isoelectronic chain C4 H, but
are fairly close to those of the isoelectronic C2 H, indicating a rather pure 2 Σ electronic
ground state. The CCC15 N b and c magnetic hyperfine constants follow the expected
ii
values derived from the 14 N species. In addition two new cyano radicals, linear C4 N and
C6 N were analyzed. C4 N, C6 N are linear chains with 2 Π electronic ground states and
both have resolvable hyperfine structure and Λ-type doubling. At least four transitions
in the lowest-energy fine structure component Ω =1/2 were measured between 7 and 22
GHz and, at most, 9 spectroscopic constants were required to reproduce their spectra
to a few parts in 107 . Although the strongest lines of C6 N are more than five times
less intense than those of C5 N, owing to large differences in the ground state dipole
moments, both new chains are more abundant than C5 N. Searches for C7 N have so far
been unsuccessful. The absence of lines at the predicted frequencies requires that the
product of the dipole moment times the abundance (µ · Na ) to be more than 60 times
smaller for C7 N than for C5 N, suggesting that the ground state of C7 N may be 2 Π, for
which the dipole moment is calculated to be small.
Part III, Cn N radicals in the interstellar space. Astrophysical investigations of C3 N
isotopomers are compared with laboratory data presented in this work. Possible misassignments of 13 CCCN lines towards IRC+10216 are investigated. Finally, a search for
C2 N has been performed towards the envelope of the late-type star IRC+10216 using the
IRAM 30m telescope at Pico Veleta, Spain. Three lines in the frequency bands at 154,
224 and 248 GHz have been detected at transition frequencies of C2 N and preliminary
assigned to C2 N as a carrier. Thus, a rotational temperature as well as a column density
of C2 N could be estimated. The results are in agreement with estimations deduced by
previous observations (Guèlin & Cernicharo [74] ). Further astronomical measurements
are necessary to confirm this tentative detection.
Kurzzusammenfassung
In der vorliegenden Arbeit werden die Produktion und die Messung von Radikalen im
Labor sowie im Weltraum an ausgesuchten Beispielen vorgestellt. Die Arbeit ist in drei
Teile gegliedert. Teil 1 befaßt sich mit der Charakterisierung von Molekülquellen. Die in
Köln verwendete Excimer-Laserablationsquelle ist hoch effizient in der Erzeugung von
reinen Kohlenstoffmolekülen, sog. Kohlenstoff Clustern. Zunächst wird eine ExcimerLaserablation mit einer Nd:YAG- Laserablation verglichen. Dabei wurde ein QuadrupolMassenspektrometer zur Charakterisierung der Nd:YAG-Ablationquelle eingesetzt. Desweiteren wurde eine Schlitzdüsen-Entladungsquelle untersucht die neben der Produktion
von Kohlenwasserstoffen und anderer kohlenstoff-basierter Moleküle auch reine Kohlenstoffcluster erzeugen kann. In beiden Molekülquellenarten entsteht ein Plasma, daß zu
erheblichen Schwierigkeiten bei der Aufnahme von Massenspektren führt. Ein speziell für
Plasmen vorgesehenes Massenspektrometer wurde in Lichtenstein/Balzer mit Hilfe der
Schlitzdüsen-Entladungsquelle getestet. Erste Ergebnisse werden vorgestellt. Zusätzlich
wurde am Kölner Kohlenstoff Cluster Experiment das vorhandene IR-Dioden Spektrometer erneuert. Wesentliche Verbesserungen wurden erreicht durch den Einsatz eines
Flüssigstickstoff-Dewars für die Kühlung der Laserdioden, nachweisempfindlichere Detektoren für den Frequenzbereich um 2000 cm−1 , einen stabileren optischen Aufbau,
iii
sowie die Entwicklung neuer Meß -und Kalibrationssoftware. Erste Meßungen werden
vorgestellt.
In Teil 2 dieser Arbeit werden Messungen an einfach-substituierten C3 N Isotopomeren sowie Untersuchungen an C4 N und C6 N vorgestellt. Die Messungen an 13 CCCN, C13 CCN,
CC13 CN und CCC15 N führten zur detailierten spektroskopischen Charakterisierung der
Radikale und wurden an einem Fourier Transform Mikrowellen Spektrometer der Harvard Laboratory Astrochemistry Group vorgenommen. Die linearen, mit 13 C und 15 N
substituierten C3 N Moleküle wurden mittels einer elektrischen Entladungsquelle mit anschließender adiabatischen Expansion hergestellt. Mit den gemessenen Mikrowellendaten
zwischen 9.5 und 38.4 GHz und den zuvor bekannten Millimeterwellen-Daten konnten
die Rotations- sowie die führenden Zentrifugalverzerrungsterme sehr genau ermittelt,
die Fermikontakt- sowie die Dipol-Dipol Wechselwirkung der 13 C-Isotope präzisiert und
die magnetische Wechselwirkung der 14 N bzw. 15 N-Isotope erstmals ermittelt werden.
Zusätzlich wurden zwei neue Cyan-Radikale, lineares C4 N und C6 N, untersucht. Basierend auf Messngen der Ω=1/2 Zustände zwischen 7 und 22 GHz [121], wurden die
Molekülparameter der sich im 2 Π elektronischen Grundzustand befindenden Radikale
ermittelt. Beide Spezies zeigen eine Hyperfeinstrukturaufspaltung und Λ-Verdopplung.
Die in dieser Arbeit bestimmten neun Molekülparameter je Radikal ermöglichen eine
Reproduktion der Spektren bis auf wenige kHz Genauigkeit.
In Teil 3 werden astrophysikalische Untersuchungen an linearen C3 N Isotopomeren mit
den in dieser Arbeit gewonnenen Labordaten verglichen. Eigene Arbeiten umfassen die
Suche nach C2 N in der Sternenhülle von IRC+10216 mit Hilfe des IRAM 30m Teleskops
am Pico Veleta, Spanien. Es wurden drei Linien in den Frequenzbändern um 154, 224
und 248 GHz beobachtet, die mit Rotationsübergängen von C2 N übereinstimmen und
eine vorläufige Zuordnung dieser Linien zu C2 N erlauben. Weitere astrophysikalische
Messungen sind jedoch notwendig um eine eindeutige Detektion von C2 N in IRC+10216
sicherzustellen.
iv
”Jedermann sieht die Grenzen seiner eigenen Vision als
die Grenzen der Welt an.”
by Arthur Schopenhauer (1788 - 1860)
For my parents Agnes and Werner Fuchs
Contents
Abstract / Kurzzusammenfassung
i
Zusammenfassung
ix
1 Introduction
1
I
7
Characterization of Radical Sources
2 Molecule Source Characterization
2.1 Ablation Technique . . . . . . .
2.1.1 Excimer Laser Ablation
2.1.2 Nd:YAG Laser Ablation
2.2 Discharge Plasma . . . . . . . .
2.3 Conclusions and Prospects . . .
3 The
3.1
3.2
3.3
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9
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Cologne Carbon Cluster Experiment: The New Setup
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The Cologne Carbon Cluster experiment . . . . . . . . . . . . . . . . . . 34
The New Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Conclusions and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . 37
II C3 N Isotopomers, C4 N, and C6 N
39
4 Experimental Setup
4.1 The Production of Cn N Radicals
4.1.1 The Precursor Gases . . .
4.1.2 The Discharge Nozzle . . .
4.2 Adiabatic Expansion . . . . . . .
4.3 The Fourier Transform Microwave
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5 Linear Cn N, Cyanide Radicals
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Spectrometer
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69
vi
Contents
6 Theoretical Considerations
6.1 Pure Rotation of Linear Molecules . . . . . . . . . . .
6.1.1 Selection Rules . . . . . . . . . . . . . . . . .
6.2 Fine Structure . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Hund’s Coupling Cases a) and b) . . . . . . .
6.2.2 Λ-type Doubling, and l-type Doubling . . . .
6.3 Hyperfine Structure . . . . . . . . . . . . . . . . . . .
6.3.1 Magnetic Hyperfine Structure . . . . . . . . .
6.3.2 The Electric Quadrupole Interaction . . . . .
6.4 Matrix Representation of the Hamiltonian . . . . . .
6.4.1 The Matrix Representation of the 2 Π-Radicals
7 Measurements and Analysis
7.1 The C3 N Mono-Substituted Isotopomers
7.1.1 CCC15 N . . . . . . . . . . . . . .
7.1.2 13 CCCN, C13 CCN and CC13 CN .
7.2 C4 N and C6 N . . . . . . . . . . . . . . .
7.3 The Search for C7 N . . . . . . . . . . . .
7.4 Conclusions and Prospects . . . . . . . .
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123
123
III Linear Cn N Chains in Space
8 Cn N Chains in Space
8.1 The Search for Interstellar C2 N .
8.1.1 Observation . . . . . . . .
8.1.2 Data Analysis . . . . . . .
8.1.3 Discussion . . . . . . . . .
8.1.4 Conclusions and Prospects
125
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127
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IV Appendix
143
A Linear Cn H
145
B The HQ Matrix Elements
147
C Molecular Constants of C13 CCN and CC13 CN
151
D Tables: Interstellar C3 N ,C5 N, and C3 N Isotopomers
153
Bibliography
157
List of Figures
173
Contents
vii
List of Tables
175
Acknowledgments
177
Beglaubigung
179
Publication List
179
Curriculum Vitae
181
viii
Contents
Zusammenfassung
Interstellares Gas, sowie von kalten Sternen ausgestoßenes Gas, zeigt eine große Vielfalt
an beobachteten Molekülen, in der Kohlenstoff als viert häufigstes Element im Universum eine zentrale Rolle spielt. In der vorliegenden Arbeit werden die Produktion und
die Messung von Radikalen im Labor sowie im Weltraum an ausgesuchten Beispielen
vorgestellt. Insbesondere wird die Produktion von kohlenstoffhaltigen Radikalen wie reine Kohlenstoffcluster Cn oder Moleküle der Form Cn N erläutert. Die Anwendung der
hier vorgestellten Techniken kann aber auch zur Produktion anderer Moleküle eingesetzt
werden, z.B. von Sin Cm , NCn N, HCn H, HCn N, etc. .
Effiziente Molekülquellen sind von zentraler Bedeutung für die Entdeckung und Strukturbestimmung neuer Moleküle mit Hilfe der Emissions- und Absorptionsspektroskopie.
Die Charakterisierung und Optimierung von Molekülquellen ist daher wichtig in Hinblick auf zukünftige Erfolge auf diesem Gebiet der Forschung. Die in Köln verwendete
Excimer-Laserablationsquelle ist hoch effizient in der Erzeugung von reinen Kohlenstoffmolekülen, sog. Kohlenstoff Clustern, und ermöglichte die Entdeckung von linearem
C8 und C10 [61, 14]. Die Detektion von größeren Clustern erscheint jedoch zunehmend
schwieriger, sodaß einer Erschließung neuer Produktionstechniken eine wachsende Bedeutung zukommt. In dieser Arbeit wurde zunächst eine Excimer-Laserablation mit einer
Nd:YAG- Laserablation verglichen. Der seperate Aufbau einer Testapparatur erlaubte
den Einsatz eines Quadrupol-Massenspektrometers zur Charakterisierung der Nd:YAGAblationquelle. Desweiteren wurde eine Schlitzdüsen-Entladungsquelle untersucht die
neben der Produktion von Kohlenwasserstoffen und anderer kohlenstoff-basierter Molekülen auch reine Kohlenstoffcluster erzeugen kann. Bei beiden Quellen, d.h. bei Entladungs- sowie bei Ablationsquelle, entsteht ein Plasma, das zu erheblichen Schwierigkeiten bei der Aufnahme von Massenspektren führt. Diese lassen sich jedoch durch
Verwendung geeigneter Energiefilter beheben, wie Testmessungen an einem Plasmamonitor der Firma Inficon AG gezeigt haben. In dem Entladungsplasma konnten dann
Kationen sowie Anionen nachgewiesen werden. Neutralteilchen sind allerdings wesentlich schwieriger nachzuweisen.
Neben der Optimierung der Quellen ist eine gesteigerte Nachweisempfindlichkeit der
verwendeten Spektrometer essentiell. Wesentliche Verbesserungen des vorhandenen IRDioden Spektrometers wurden durch den Einsatz eines Flüssigstickstoff-Dewars zur
Kühlung der Laserdioden erreicht. Die Verwendung von InSb-Detektoren statt der bisher verwendeten HgCaTe Detektoren führt im Frequenzbereich um 2000 cm−1 ebenfalls
zu einem Gewinn im Signal-Rausch-Verhältnis. Ein stabilerer optischer Aufbau, sowie
die Entwicklung neuer Meß -und Kalibrationssoftware führten zu einer Verbesserung der
x
Zusammenfassung
Systemstabilität sowie zur präzisen Frequenzzuordnung der Mess-Signale. Erste Messungen belegen dies auf eindrucksvolle Weise.
Desweiteren werden spektroskopische Untersuchungen an Kohlenstoffkettenmolekülen
mit einer Nitrilgruppe Cn N im cm-Wellenlängenbereich vorgestellt. Im einzelnen sind
dies vier C3 N Isotopomere sowie die Kettenmoleküle C4 N und C6 N.
Die Messungen an 13 CCCN, C13 CCN, CC13 CN und CCC15 N führten zur detailierten
spektroskopischen Charakterisierung der Radikale und wurden an einem Fourier Transform Mikrowellen Spektrometer der Harvard Laboratory Astrochemistry Group vorgenommen. Die linearen, mit 13 C und 15 N substituierten C3 N Moleküle wurden mittels
einer elektrischen Entladungsquelle mit anschließender adiabatischen Expansion hergestellt. Mit den gemessenen Mikrowellendaten zwischen 9.5 und 38.4 GHz und den zuvor
bekannten Millimeterwellen-Daten konnten die Rotations- sowie die führenden Zentrifugalverzerrungsterme sehr genau ermittelt, die Fermikontakt- sowie die Dipol-Dipol
Wechselwirkung der 13 C-Isotope präzisiert und die magnetische Wechselwirkung der 14 N
bzw. 15 N-Isotope erstmals ermittelt werden. Die magnetischen Kopplungskonstanten der
13
C enthaltenden C3 N Radikale unterscheiden sich von denen der isoelektronischen C4 H
Ketten, liegen aber nahe an denen von C2 H bekannten Werten und lassen somit auf einen
fast reinen 2 Σ Grundzustand schließen. Die CCC15 N magnetischen Hyperfeinkonstanten
folgen den von den 14 N-Radikalen theoretisch abgeleiteten Werten.
Zusätzlich wurden zwei neue Cyan-Radikale, lineares C4 N und C6 N, untersucht. Basierend auf Messungen an jeweils vier Rotationsübergängen im unteren Ω=1/2 Zustand
zwischen 7 und 22 GHz [121], wurden die Molekülparameter der sich im 2 Π elektronischen Grundzustand befindenden Radikale ermittelt. Beide Spezies zeigen eine Hyperfeinstrukturaufspaltung und Λ-Verdopplung. Die in dieser Arbeit bestimmten 9 Molekülparameter je Radikal ermöglichen eine Reproduktion der Spektren bis auf eine Genauigkeit von ca. 107 . Obwohl die stärksten Linien von C6 N etwa 5 mal schwächer sind
als die entsprechenden C5 N Linien, was auf einen großen Unterschied im Grundzustandsdipolmoment zurückzuführen ist, liegen beide neuen Kettenmoleküle in einer größeren
Häufigkeit als C5 N vor.
Es wurde im Verlaufe dieser Arbeit auch versucht C7 N spektroskopisch nachzuweisen.
Trotz guter Vorhersagen konnte jedoch keine der in den beobachteten Spektren enthaltenen Linien auf C7 N zurückgeführt werden. Das Fehlen der erwarteten Linien setzt
vorraus, daß das Produkt aus Dipolmoment und Häufigkeit (µ · Na ) mehr als 60 mal
kleiner für C7 N als für C5 N ist, sodaß C7 N wahrscheinlich nicht im 2 Σ sondern im 2 Π
Grundzustand vorliegt. Berechnungen ergeben, daß das zum 2 Π Grundzustand gehörige
Dipolmoment sehr klein ist.
Cn N Radikale sind auch im Weltraum schon nachgewiesen. In Teil 3 werden astrophysikalische Untersuchungen an linearen C3 N Isotopomeren mit den in dieser Arbeit gewonnenen Labordaten verglichen. Eigene Arbeiten umfassen die Suche nach C2 N in
der Sternhülle von IRC+10216 mit Hilfe des IRAM 30m Teleskops am Pico Veleta,
Spanien. Es wurden drei Linien beobachtet, die mit Rotationsübergängen von C2 N
übereinstimmen und eine vorläufige Zuordnung dieser Linien zu C2 N erlauben. Die
Säulendichte konnten abgeschätzt werden und steht in Einklang mit theoretischen Vor-
xi
hersagen von Millar & Herbst [132]. Weitere astrophysikalische Messungen sind jedoch
notwendig um eine eindeutige Detektion von C2 N in IRC+10216 sicherzustellen.
xii
Zusammenfassung
1 Introduction
“ I ask you to look both ways. For the road to a knowledge of
the stars leads through the atom; and important knowledge of the
atom has been reached through the stars. ”
Sir Arthur Eddington (1882 - 1944), Stars and Atoms
Interstellar gas and gas ejected into space by cool stars are known to contain a rich
collection of molecules [123]. After Hydrogen, Helium and Oxygen, Carbon, the fourth
abundant element in space with its plurality of possible bondings unclose a whole zoo
of different carbon bearing molecules, ions and radicals. An important feature of the
carbon atom is that it easily builds long carbon chain molecules. Many of the organic
compounds are familiar to the terrestrial chemist and can be found in a standard chemical
stockroom like formaldehyde, ethanol, and methyl formate but a large part of the known
interstellar molecules, as seen in Tab. 1.1, are entirely new species. A closer look on
these species reveals that while two-thirds of the diatomic molecules and one-third of
the triatomics are inorganic there exists no inorganic molecule detected in space with
more than 5 atoms indicating that future discoveries of large molecules are likely to
exclusively comprise organic compounds.The particularity of the carbon chains found
in space is that most of them are highly unsaturated and therefore represent a form of
matter which is explosively unstable through polymerization even at moderate densities
and difficult to study on earth. It is for this reason that laboratory detection lagged
behind the astronomical discoveries of new radicals for a long time. There are two
different types of carbon chains: those which carry a permanent electric dipole moment
and those that are nonpolar. Most of the molecules found in space are polar compounds
which can be detected with radio- or microwave techniques. Today, modern laboratory
spectrometers like FTMW spectrometers or advanced mm-wave to THz-spectrometers
can achieve a high sensitivity and frequency accuracy of 2 kHz in the 10 GHz region up to
50 kHz in the 1 THz region. Application of these powerful spectrometers on supersonic
molecular beams in the mid 1990’s resulted in an avalanche of new detected molecules
most of which are candidates of future astronomical discovery like long carbon chains,
chains attached to rings, silicon-carbon rings, and protonated molecular ions. In the gas
2
1 Introduction
phase, rotational transitions and low lying bending vibrations can be observed and yield
in an unambiguous identification of molecules. Large telescopes with a high signal-tonoise ratio can achieve frequency accuracies of one part in 107 [179]. This connection
between laboratory spectroscopy and radioastronomy yielded already results in the early
1960’s with the detection of the hydroxyl radical [192] in ’63, followed by ammonia [39]
and water [40] 5 years later. In principal an unambiguous identification of molecules
in space is also possible in the optical or UV frequency region like it happened for CH,
CH+ and CN in the early 1940’s [195]. The majority of discoveries, however, have been
made in the frequency region between 100 and 300 GHz (1-3 mm region). Nonpolar
species which are equally important for astrochemistry than polar molecules have no
pure rotational spectrum and can therefore not be detected by radio astronomy. This
shortcoming has been partially overcome by the onset of infrared astronomy. Molecules
such as CO2 , C2 H2 , CH3 , C3 or even C5 have been identified in this frequency region by
ro-vibrational absorption or by emission from hot gas as for example in the case of H2
[50]. Beside asymmetric stretching modes in the mid-infrared region many carbon chain
molecules exhibit infrared active, low-energy bending vibrations. All pure carbon chain
molecules Cn with n > 2 are expected to display bending vibrations in the range 30 150 cm−1 , i.e. in the far-infrared region. C3 for example has already been detected in
the interstellar space by KAO (Kuiper Airborne Observatory) near 2 THz [59]. Further
spectroscopic data in these frequency region will be essential for future missions, such
as SOFIA (Stratospheric Observatory For Infrared Astronomy) and Herschel, a 3 m
telescope space mission. Because of the success in detecting more than 120 molecules so
far and the prospect of finding many more, the interest in carbon bearing molecules is
stronger than ever.
Considering a spiral galaxy like our Milky Way, the interstellar medium consists about
75% of hydrogen and 24% of helium which leaves only 1% of the total interstellar mass
for all other chemical elements [179]. ”It is one of the paradoxes of interstellar chemistry
that unsaturated carbon should be so conspicuous in a regime where hydrogen is the
dominant chemically active element by more than three orders of magnitude” ([123],
p.178). A hydrogen-helium chemistry by its own is very poor, however, 80% of the
remaining gas is consisting of C, N, and O which have a reach chemistry. Following this
argument it comes as no surprise that molecules containing C, H and N like HCn N, Cn H
or Cn N play a key role in the chemistry of molecular clouds or circumstellar envelopes,
as can be seen in Tab. 1.1. 73% of the detected interstellar molecules contain carbon,
66% hydrogen, 34% nitrogen and 28% oxygen. It is a remarkable fact that in certain
sources in space a large number of reactive organic compounds often exist in comparable
abundances with stable compounds of the same size.
Although big progress has been made in theoretical astrochemistry, this science is still
heavily dependent on pure fact gathering. New chemical models like those of Millar &
Herbst [131] or Doty et al. [48] include as much as 407 molecules, ions and radicals
connected by 3851 reactions [132], and most of these species are still not detected in
space.
It can be seen as disadvantage of modern chemical network models, though, that they de-
3
pend on such large numbers of parameters and reaction coefficients which are not always
known to high precision and which in turn allow for a certain flexibility in predictions.
By new astronomical measurements, these parameters can be refined and the models can
be tested. Radicals like Cn or Cn N which play an important role in the production or
depletion of cyanopolyynes are a sensitive probe for such models. To make spectroscopic
work contribute optimally to astrophysics, it is advantageous to examine molecules of
small or medium size which contain C, H, or N. Therefore in this thesis radicals like
linear isotopic C3 N, C4 N and C6 N, have been investigated and first measurements on
C7 N and C8 N have been started but did not result in any detection so far.
The main task of laboratory spectroscopy concerning its contribution to astrophysics
is to make accurate frequency predictions available for species yet undetected. Under
this considerations a spectroscopic characterization is said to be complete when it provides either measured transitions to high precision or calculated transitions from the
derived spectroscopic constants to an accuracy similar to measurements. For open shell
molecules as presented in this work not only the rotational and leading centrifugal distortion constants have to be determined but also several constants which characterize
the hyperfine structure as well as the Λ-doubling caused by the unpaired electron. However, the first detection of linear C3 N in the gas phase has not been done in laboratory
but with a radio telescope by Guélin and Thaddeus [78, 79] in 1977. Today, the study of
the HC3 N-C3 N pair is of great importance to test and refine photochemical models e.g.
of carbon-rich stars like IRC+10◦ 216 [38]. C5 N has first been measured in laboratory
by Kasai et al. [99] and then in the dark cloud TMC-1 by Guélin et al. [77]. A detailed
study of the electronic structure of C3 N is also worth undertaking because this radical
is isoelectronic with C4 H, a well-studied molecule in which an extremely low-lying A2 Π
electronic state strongly interacts with the X 2 Σ+ ground state [121]. Owing to large
zero-order mixing between the two states, the 13 C hyperfine coupling constants of C4 H
at each substituted position along the chain [37] differ significantly from those of the
closely related chain CCH [120]. Determination of the analogous constants for isotopic
C3 N should provide an unambiguous comparison of the electronic structure and chemical
bonding for these two isoelectronic radicals.
Even-membered Cn N chain radicals may play important roles in interstellar chemistry
and soot formation [48, 81]. So far, CCN is the only member of this group that has
been detected in the gas-phase. Like CN, the electronic spectrum of CCN was observed
more than twenty-five years [128] before its pure rotational spectrum was measured [142].
Laboratory detection of longer C2n N radicals has proven to be difficult because they, like
CCN, are expected to have 2 Π electronic ground states and small dipole moments [144].
Non of the Cn N molecules with n even have yet been detected in space. Recently, the
feasibility of C2 N detection in space was proposed by Mebel & Kaiser [127]. Therefore,
in the course of this work a search for linear C2 N towards the late-type star IRC+10216
has been performed.
If it is said that the distribution of more complex and reactive molecules in space remains
largely unknown and that many have been observed in only a single or few sources, the
same is true for the terrestrial ”sources” of these species. For a long time, production of
4
1 Introduction
highly reactive molecules in laboratory was a main obstacle in their detection. So far,
only application of sensitive spectrometers in combination with supersonic molecular
beams seem to be particular effective for the study of reactive carbon chains. Here the
rotational spectra of the radicals are greatly simplified at low rotational temperatures of
a few degree Kelvin which can easily be achieved in supersonic expansions. In this work,
different kinds of production methods have been investigated (Chapter 2). Excimer
laser ablation sources achieve high production rates of pure carbon molecules Cn or
silicon-carbon molecules Sin Cm . The Cologne carbon cluster experiment consists of a
highly sensitive IR tunable diode laser spectrometer (Chapter 3). Radicals like linear C8
and C10 have been observed with this spectrometer for the first time [61, 14]. Another
method to produce radicals is the usage of discharge nozzles. In this work, two kinds
of discharge nozzles have been applied, a slit nozzle and a pinhole nozzle. The first one
has been used to examine a discharge plasma by the usage of a plasma monitor and
the latter one was needed for the production of C4 N, C6 N and C3 N isotopomers. The
complete production method as well as the FTMW spectrometer used for the detection
of the Cn N radicals is decribed in Chapter 4. Chapter 5 provides a brief introduction
of spectroscopic properties of Cn N radicals known so far. Main aspects of the theory of
radical spectroscopy are summarized in Chapter 6. Measurements and analysis of the
C3 N isotopomers, C4 N and C6 N radicals are discussed in Chapter 7. The role of Cn N
chains in the interstellar medium and their detections so far as well as the search for C2 N
towards IRC+10216 performed in the course of this thesis is described in Chapter 8.
5
Table 1.1: Known Interstellar and Circumstellar Molecules (Dec
Number of Atoms (2-7)
2
3
4
5
6
H2
C3
c-C3 H
C5
C5 H
AlF
C2 H
l-C3 H
C4 H
l-H2 C4
AlCl
C2 O
C3 N
C4 Si
C 2 H4
C2
C2 S
C3 O
l-C3 H2
CH3 CN
CH
CH2
C3 S
c-C3 H2
CH3 NC
+
CH
HCN
C2 H2
CH2 CN
CH3 OH
+
CN
HCO
CH2 D ?
CH4
CH3 SH
CO
HCO+
HCCN
HC3 N
HC3 NH+
CO+
HCS+
HCNH+
HC2 NC
HC2 CHO
+
CP
HOC
HNCO
HCOOH NH2 CHO
CSi
H2 O
HNCS
H2 CHN
C5 N
+
HCl
H2 S
HOCO
H2 C 2 O
l-HC4 H
KCl
HNC
H2 CO
H2 NCN
NH
HNO
H2 CN
HNC3
NO
MgCN
H2 CS
SiH4
+
NS
MgNC
H3 O
H2 COH+
NaCl
N 2 H+
NH3
OH
N2 O
c-SiC3
PN
NaCN
CH3
SO
OCS
SO+
SO2
SiN
c-SiC2
SiO
CO2
SiS
NH2
CS
H+
3
HF
H2 D
SH
SiCN
HD
AlNC
FeO
Number of Atoms (8-13)
8
9
10
11
12
CH3 C3 N
CH3 C4 H
CH3 C5 N
HC9 N
C 6 H6
HCOOCH3
CH3 CH2 CN (CH3 )2 CO
CH3 COOH? (CH3 )2 O
C7 H
CH3 CH2 OH
H2 C 6
HC7 N
CH2 OHCHO C8 H
l-HC6 H
2002), [31]
7
C6 H
CH2 CHCN
CH3 C2 H
HC5 N
HCOCH3
NH2 CH3
c-C2 H4 O
CH2 CHOH
13
HC11 N
6
1 Introduction
Part I
Characterization of Radical Sources
2 Molecule Source Characterization
“ ...one or two atoms can convert a fuel to a poison, change a
color, render an inedible substance edible, or replace a pungent
odor with a fragrant one. That changing a single atom can have
such consequences is the wonder of the chemical world.“
P. W. Atkins, ”Molecules”
In this thesis, it will be shown how radicals can be produced and detected by different
high resolution spectroscopic tools like IR spectroscopy and FTMW spectroscopy. The
aim is to determine as many molecular properties as possible like moment of inertia,
electronic structure, vibrational motions, hyperfine interactions, etc. Well known production methods in combination with spectrometers of extreme high sensitivity allow
for the detection of molecules and radicals up to linear C13 , HC13 H or HC17 N [62, 123].
However, detection of more complex radicals or molecules of even larger sizes seem to be
impaired by the effectiveness of the production methods. For example, for the detection
of C13 with a vibrational dipole moment of ∼2 Debye, a particle density of ≈ 1010 cm−3
is required to record the rotationally resolved IR spectrum of an asymmetric stretching
mode. In future, molecular sources have to produce even higher yields to allow for the
detection of molecules with smaller dipole moments or unfavorable partition functions.
For the same reason, it is advantageous to produce molecules with low rotational temperatures because the spectra simplify and gain intensity of low lying transitions. Another
important requirement of molecular sources is the stability of their production yield.
When spectrometers work at their limit of sensitivity the signal has to be integrated
many times in order to increase the signal-to-noise ratio. Therefore, it is apparent that
conditions have to be stable over the whole integration time. Furthermore, the characterization of available molecule sources is an important step towards the development of
new production techniques.
Out of many techniques to produce radicals, two particularly important methods have
been chosen which are the laser ablation and the discharge nozzles technique. Both are
applicable to the Cologne IR-Carbon Cluster experiment but due to advantage of laser
ablation sources to only produce pure carbon molecules Cn this technique is predominantly used. It has resulted already in a number of first detections of linear carbon
2 Molecule Source Characterization
relative Scale
10
Frequency [nm]
Figure 2.1: Spectra of C2 at 516 nm measured in Basel. A laser ablation source (top)
and and discharge nozzle (bottom) was used to produce the C2 radicals.
clusters like C8 and C10 [61]. The detection of C13 [62] has shown that even higher
members of linear Cn chains can be detected with this type of ablation source. This
molecule source is particularly valuable for the production of iso-atomic molecules like
Cn , Sin or Men with n=2,3,4,... but also for other species like Cn Sim when using appropriate target materials. The Cologne IR experiment will be described in Chapter 3. The
used ablation source is in principle similar to the Smalley type ablation source [169, 41].
However, important improvements have been done to adapt this technique to laser spectroscopical needs which led to a tremendous success in the production of radicals. The
improved design has been described in [186, 58, 14]. Details will be discussed further
down. So far an excimer laser with 25-50 ns pulses and typical pulse energies of 270 mJ
was used as a strong laser light source at repetition rates of 50 Hz. It is evident that
longer pulses with higher energies increase the amount of ablated material. However,
the main question is whether the ablated material is available in a molecular form or
whether it immediately builds grains and soot. For molecular spectroscopic reasons it
is desirable to have a broad mass distribution of ablated material in a molecular form
with high abundances of particles containing between 3 and 30 atoms. As an alternative
to the excimer laser, a Nd:YAG laser was used with pulse energies up to several Joules
and pulse lengths of 0.1 to 1 ms. A new experimental setup was built to characterize
the ablated material by means of quadrupole mass spectroscopy (QMS).
11
Figure 2.2: C60 optimized mass spectrum. a) mainly small carbon clusters are produced.
By changing the flow rate of the buffer gas larger clusters were produced (b). For
certain laser and source conditions the production of C60 can drastically be enhanced
(c). [80]
Laser ablation is not unique in producing radicals or iso-atomic molecules. There are
several other techniques like sputtering, electric arcs, the use of ovens, etc. which could in
principle as well be used but which have proved in praxis to be less efficient. Considering
these alternatives the discharge nozzle technique appears to be quiet comparable to the
laser ablation technique and was therefore also taken into account in the experiment.
The applied discharge slit nozzle was developed by the Basel group [111, 135]. The
conceptual design of a discharge nozzle will be described in more detail in Section 2.2
as well as in Chapter 4.1.2. Between each of the described production methods, there
are principle differences concerning the conditions under which the molecules can be
detected, i.e. pressure, temperature, chemical composition, jet boundaries and layers.
Properties of molecular beams, i.e. supersonic jets, will be discussed in Chapter 4.2.
As an example, two spectra of C2 are shown in Fig. 2.1 which were recorded using two
different molecular sources. Both sources are able to produce C2 in sufficient amounts
for cavity ringdown spectroscopy in the visible region but the rotational temperatures
12
2 Molecule Source Characterization
of the molecules are different for both techniques. The laser ablation spectrum has a
rotational temperature of about 10-20 K whereas for the discharge spectrum, Trot is in
the order of 100 K. For an extended spectroscopic analysis of molecules it is important
to produce molecules under different physical conditions, e.g. different temperatures
which is possible by using the appropriate molecule source. A detailed understanding of
different types of production methods is thus indispensable.
For this purpose, a diagnostic tool is needed that focus on yield and relative mass distribution of molecules or radicals produced by different types of molecule sources rather
than their structure or other intrinsic properties. Mass spectrometers, for example,
have an extremely high sensitivity compared to other spectrometers but do not allow
for any information beyond pure mass-per-charge distribution. Beside this restriction,
they can provide valuable information on chemical reaction mechanisms. Broad scans
covering molecules of nearly every size allows for source controlling which can support
the production of certain species. A famous example is the discovery of the Buckminster
fullerene C60 in 1985 by Smalley, Curl, and Kroto [108, 41, 169] 1 . For this, a laser
ablation source was monitored by a mass spectrometer so that experimental conditions
could successfully be varied in order to yield C60 in huge amounts (see Fig. 2.2).
1
In 1996, Kroto, Smalley, and Curl have won the Nobel prize in Chemistry for their discovery of C60 .
2.1 Ablation Technique
13
Liquid
100
Liquid−Vapor
Triple Point
Pressure (ATM)
10
Solid
1
Vapor
0.1
3400
3600
3800
4000
4200
4400
4600
4800
Temperature (K)
Figure 2.3: Pressure-temperature diagram of graphite [106, 155].
2.1 Ablation Technique
Laser ablation can be described as removal of material by applying an intense light pulse
of high energy onto a target in order to vaporize solid or liquid materials. Under atmospheric pressure graphite is solid and has a transition to the gas phase at temperatures
higher than 4000 K, see Fig. 2.3. Laser ablation can achieve high temperatures and
high gas phase carbon densities and is therefore an ideal tool for spectroscopy on carbon
clusters and other carbon bearing radicals.
The effect of intense laser light on solid material such as graphite results in lattice vibrations, electronic excitations or direct ionization which causes bonds to break. Depending
on the laser power irradiated, the material vaporizes or liquefies. With beam intensities
higher than 108 W/cm2 , more material is vaporized while consequently less is liquefied
[86]. The produced vapor does not condense immediately on the surface but flows off
thus perturbing the conditions of a local thermodynamic equilibrium. The number of
ablated carbon atoms depends on the irradiated laser wavelength, laser power and the
evaporation heat of graphite. Only a small fraction of the radiation is directly absorbed.
If n denotes the real and κ the imaginary part of the complex refraction index, than
2 +κ2
reflectance R for a perpendicular irradiation on graphite is R = (n−1)
. The value of R
(n+1)2 +κ2
14
2 Molecule Source Characterization
cap
plasma
pulsed helium
supply
rotating
graphite
rod
reaction channel
jet
vacuum
He
10 bar
GV
graphite
plasma
UV−puls
adiabatic
expansion
excimer
UV−pulse
248 nm
Figure 2.4: The Cologne Laser Ablation Source
is between 0.1 and 0.5, depending on the orientation of the light in respect to the graphite
structure [18], yielding a fraction A ≡ 1 − R of absorbed radiation. However, the power
of the laser light is also an important factor in the absorption process [70, 86]. If the laser
power exceeds a threshold value of 108 W/cm2 , a plasma is built on the graphite surface
which almost completely absorbs the laser power and partially transfers the energy to the
material. This energy transfer takes place due to radiation in the visible and ultraviolet
spectral range [86] or via compression waves [70] where the plasma pressure can easily
achieve 100 kbar. For the ablation source discussed here, typical ablations of 30-50 ng
carbon per pulse are achieved, which corresponds to roughly 1.5 · 1015 carbon atoms [7].
A graphite rod of 1 cm in diameter was used as target which consisted to more than
99.5% of 12 C at a density of 2.25 g/cm3 (Goodfellow/Cambridge). While being exposed
to the laser beam, the graphite rod is slowly rotated to ensure a stable and uniform
ablation process.
2.1.1 Excimer Laser Ablation
The standard technique to produce pure carbon clusters at the Cologne IR experiment
is to use a pulsed excimer laser beam at 248 nm wavelength which is focused onto a
rotating graphite rod. Thereby, a plasma consisting of carbon particles is produced
which accelerates the ablation process. Helium at a backing pressure of 10 bar flushes
the vaporized graphite in an adiabatic expansion into the vacuum chamber causing fast
condensation of single atoms to small carbon clusters. Within a few µsec the temperature
of the carbon vapor drops down from several thousand Kelvin plasma temperature to a
few Kelvin rotational temperature of the condensed clusters. A total amount of 1013 –1014
clusters of different sizes are produced with every single laser pulse [58]. A two stage
roots blower unit and a vacuum rotary pump keep the chamber pressure below 10−1
mbar. Carbon clusters with up to 13 atoms have been produced in sufficient amounts
for infrared absorption detection [60].
Carbon clusters seeded in a flow of buffer gas usually readily separate down stream, most
likely due to differing formation times. It is thus possible to clearly distinguish between
clusters of different sizes, i.e. small clusters come first while larger ones come later.
2.1 Ablation Technique
15
Figure 2.5: Jet produced by excimer laser ablation technique. The molecular probe
region for spectroscopy is 1-2 cm downstream the source exit. Left: Side view of the
ablation jet with a sketch of the source. The jet dimensions are roughly 17 cm both
in height and length. A compression zone caused by the edge next to the source is
visible at the lower boundary of the jet. Right: Top view of the jet. Jet width is
roughly 1-3 cm.
For the Cologne IR experiment, a KrF excimer laser (Lambda Physics, LPX200) is used.
This laser can operate at repetition rates of up to 50 Hz with pulse lengths of 25-50 ns
and pulse energies up to 500 mJ. For the production of carbon cluster pulse energies of
200 mJ result in an optimal yield. The evaporation heat of graphite is λ = 716.9 kJ/mol
[155], i.e. the maximal number of particles that can be ablated is 1.7 · 1017 , assuming
a total absorption of laser power in the vaporization process. The excimer laser has a
’square’ beam profile. When the light is focused by a MgF2 lense (f=50cm), the beam
has a size of 0.45 x 0.05 mm2 on the surface of the graphite rod (see Fig. 2.8). Energy
densities of 1 · 109 W/cm2 are therefore achievable. The laser ablation source is made
of stainless steel and consists of two parts, the main body and the cap, as can be seen
in Fig. 2.4 (left). At the rear side, a solenoid valve can be attached and a hole of 2 x 2
mm2 allows for inflow of buffer gas. The gas preexpands into a cross sectional area of 12
mm x 1mm at the graphite rod. The visible graphite rod area at the channel surface is
70mm2 . The source exit consists of a slit like reaction channel sized 12mm x 0.9mm in
cross section and 8mm in length. The excimer pulse enters the ablation source through
the exit slit. The square form of the UV beam profile results in a line focus at the
graphite rod. After several hours of operation the reaction channel is clogged by soot
and has to be cleaned. The laser ablation process with subsequent adiabatic cooling is
shown in Fig. 2.4 (right). First, the valve is opened and a buffer gas (e.g. He) with a
backing pressure of 10 - 15 bar flows through the nozzle. During this flow, an excimer
pulse is released which causes the formation of a dense plasma of vaporized carbon atoms
16
2 Molecule Source Characterization
C3
C9
C13
density of
particles nρ
[#/cm3 ]
2.3 · 1012
4.2 · 1010
9.9 · 109
particles NC
per pulse
13
≈ 10
≈ 1.7 · 1011
≈ 4 · 1010
mass
[ng]
0.6
0.03
0.01
rel. abundance
Ci / C3
1
1/55
1/230
Table 2.1: Particle numbers of C3 , C9 and C13 using excimer laser ablation
and ions. For each individual measurement, the time delay between the opening of the
valve and the excimer pulse has to be adjusted to achieve optimal jet conditions. In
case of an incorrect time delay the molecule yield drops because of insufficient cooling.
The reason for this is that the hot atomic carbon vapor is cooled by the buffer gas at
room temperature and additionally small molecules can form via three-body collisions
in an endothermal process. The formation of molecules and radicals mainly happens in
the reaction channel where the density and pressure is high enough for a condensation
process. The most efficient cooling process is adiabatic expansion of the gas into the
vacuum chamber where the molecules are then available for spectroscopic detection (see
Fig. 2.5).
From IR measurements on linear carbon clusters [58] it has been shown that mainly small
molecules are produced in the excimer jet (see Tab. 2.1). C3 is found to be much more
abundant than C9 and C13 . It is remarkable however, that long carbon chains like C13
are also produced in sufficient amounts for IR detection. So far, only linear carbon chains
[189] or silicon-carbon clusters [188, 187] have been found. Interest in the detection of
molecules with cyclic, polycyclic or cage like structure which probably correspond to
larger species is increasing, though. There has never been a mass spectroscopic analysis
of the here introduced Cologne laser ablation source and there is no information at hand
whether larger molecules are formed in the excimer jet or not 2 . These facts led directly
to the question whether it is possible to change conditions in a way to increase the yield
of medium sized to large molecules (e.g. C10 - C60 ).
Murray et al. [138, 197] employing material research experiments investigated the effect
of lasers with different wavelength on graphite targets. They compared pulsed laser
depositions of carbon films using a KrF excimer laser at wavelength 248 nm with pulse
lengths of 15 ns with those of a Q-switched Nd:YAG laser at 1064 nm, also having
a pulse length of 15 ns. The fluence of the excimer laser at the pyrolytic graphite
target was 3 J/cm2 while that of the Nd:YAG was 2.7 J/cm2 . In a time-of-flight (TOF)
mass spectrum positive ions ejected from the target were investigated3 . In the Nd:YAG
spectrum, many peaks corresponding to carbon clusters C+
n of size 1 ≤ n ≤ 27 appeared
+
+
with most intense peaks for C11 and C15 . Contrary to that, the TOF mass spectrum
2
Fullerenes can also be produced in a laser ablation source [169, 41] but their production has not yet
been proved in the case of the Cologne laser ablation source.
3
No buffer gas was applied.
2.1 Ablation Technique
17
pulsed
Nd:Yag @ 1064 nm
IR beam
vacuum
chamber
skimmer / orifice
Quadrupole
Jet
ion detector
quadrupole mass filter
pulsed
ionization chamber / ion optics
amplifier
Figure 2.6: QMS experimental setup
+
for the excimer laser ablation only had significant peaks at C+
2 and C3 . Murray et al.
concluded that “the ejected species [...] are dependent upon the laser wavelength” [138].
Since these results are in agreement with the investigations for the Cologne excimer laser
ablation shown in Tab. 2.1, application of a Nd:YAG laser rather than an excimer laser
appeared to be useful for the production of medium sized and large carbon clusters.
2.1.2 Nd:YAG Laser Ablation
For the characterization of a Nd:YAG ablation it seemed desirable to directly investigate
the mass spectrum. For this reason, a new experimental setup had to be build (see Fig.
2.6). The Nd:YAG laser (Baasel BLS 700) used for this work operates at a wavelength
of 1064 nm with pulse energies of up to 15 Joule. The laser has no option of Q-switching
and thus has pulse widths from 0.1 to 1 ms instead of 25 - 50 ns. Important technical
data of the Nd:YAG and the excimer laser are given in Tab. 2.2. As detection device, a
quadrupole mass spectrometer was applied that works in two modes, the first of which
has a mass range of 1 - 100 amu with high mass resolution while the second works
between 100 - 400 amu. This mass spectrometer had previously been used to analyze
the electric arc spectrum of graphite and is described in [58]. It is designed to detect
neutral species and contains an electron impact ionizer, a quadrupole mass filter and an
18
2 Molecule Source Characterization
ion detector. The ion source works with an adjustable emission current between 0.04
and 5 mA and electron energies of ∼ 90 eV. The ionized molecules are mass selected in
a mass filter which consists of four rods with 4 mm diameter and 200 mm length. Field
radius of the latter is 3.45 mm 4 . Mass resolution m/∆m at mass 100 is better than
100 for the first modus (1 - 100 amu) and 50 for the second modus (10 - 400 amu) 5 .
A multiplier is used as ion detector with an output current between 10−6 and 10−12 A
which is subsequently amplified and transformed into a voltage signal which is then send
to a computer.
The first question to answer was whether a 0.1 -1 ms Nd:YAG laser pulse ablation onto
a graphite target without the use of buffer gas results in a similar mass spectrum as
reported by Murray et al. [138], i.e. can clusters of the size C11 and C15 be found or
not? Murray et al. had looked for the ionic species and found that C+
n clusters produced
by Nd:YAG laser ablation have kinetic energies less than 5 eV. In a plasma the mean
kinetic energies of neutral species is usually well below those of the corresponding ions.
The potential settings - which are important for the guiding of the ions through the
quadrupole - were well adjusted for particles with kinetic energies of less than 1 eV but
could not be adjusted to arbitrary potentials. A mass spectrum of a Nd:YAG ablation
is shown in Fig. 2.7. The hydro-carbon molecules in the spectrum originate from the
interaction with the rest gas, i.e. with H2 O. Other species like OH and O are produced by
fragmentation processes in the electron impact source due to the high electron energies.
Since ionization potentials of pure carbon chains Cn with n=3-25 are between 7 - 12 eV
[189] a mean kinetic electron energy Ee of 20 eV would probably have been sufficient.
Nevertheless, Ee was kept at 90 eV. A lot of soot was produced during the experiment
and a protection glass in front of the IR mirror became polluted very quickly 6 . Therefore
the vacuum chamber had to be opened regularly. As a consequence, it was not possible
to let the vacuum chamber be evacuated over a longer time, e.g. several weeks, to
achieve background pressures below 10−8 or 10−9 mbar which would have been useful to
avoid interaction of the ablated material with the rest gas during measurements. The
measurements reveal the predominance of atomic C while C2 was less abundant by a
factor of 10 and C3 was already close to the detection limit. Larger clusters could not
be detected. The relative abundance C:C2 :C3 was found to be 100:6.6:2.4.
A comparison of different kinds of carbon cluster sources reveals significant differences
concerning the amount and distribution of produced carbon molecules as can be seen
in Tab. 2.3. Typically, usage of laser ablation sources results in a broad distribution of
cluster sizes in the lower mass region from C1 to C10 [11, 107] with abundances that
allow for absorption spectroscopy.
Gas aggregation sources like thermal vaporization of graphite (vaporization in an oven)
[193, 53, 198] or the Langmuir-method (surface method, electric arc) [89, 168, 54] produce
4
The field radius denotes half the distance between the rods.
The mass resolution is dependent on the operation frequency and dc- and ac voltage of the mass filter.
As a first approximation it can be said that the better the mass resolution the lower the sensitivity.
Details are given in [58]
6
Mirrors can be protected with a Helium flow but this feature was not implemented.
5
2.1 Ablation Technique
19
excimer (KrF),
Nd:YAG, Baasel BLS 700
Lambda Physics LPX 200 (not Q-switched)
wavelength
248 nm
1.064 µm
pulse duration
25 - 50 ns
0.1-1 ms
repetition rate
single pulse - 50Hz
single pulse - 100 Hz
pulse energy
max. 500 mJ
max. 15 Joule
aver. power
max. 8 W
max. 50 W
2
beam diameter/size 5-12 x 23 mm
6 mm
beam divergence
1-3
≤ 6 mrad
(full angle)
mode
multi mode
multi mode
Table 2.2: Technical data of applied ablation lasers.
soot in large abundances but nearly no small carbon molecules (see Tab. 2.3).
Using these schemes, the Nd:YAG laser ablation process resembles more a thermal or
electric arc process than an typical laser ablation process. This can be explained by the
following considerations. Nd:YAG laser can produce long laser pulses with high pulse
energies which increase the ablation rate while the intensity, i.e. the power per area,
decreases. If a laser does not exceed an intensity of 108 W/cm2 , the ablation process is
not dominated by direct sublimation but rather by melting-vaporization processes. Qswitched Nd:YAG or excimer laser have pulse widths of 15-50 ns and thus high intensities
at the focus point. The target material absorbs the energy during a time interval that
does not allow for heat conduction effects. Thus, most of the energy is directly used
for sublimation. If the pulse width of the laser is increased, heat conduction dominates
the energy transfer and melting occurs. The intermediate step through a liquid phase
can be very efficient in terms of ablation yield, however, most of the material is ejected
as soot rather then in molecular form. To gain more insight into these processes, the
ablated material was investigated under a microscope (see Fig. 2.8 and 2.9). Aluminum
has been used to determine the focus size of the Nd:YAG laser beam. The beam focus
area is about 3 · 10−5 cm2 in the case of the Nd:YAG laser and roughly 2 · 10−3 cm2 in
the case of the excimer laser. If a pulse energy of 200 mJ with a pulse length of 100 µs
is applied, maximum intensity at the target can reach 7 · 107 W/cm2 which is still below
the threshold value of 108 W/cm2 . If instead the excimer laser with a 200 mJ pulse
energy is applied, the intensity is 1.8 · 109 W/cm2 . As Fig. 2.8 (e,f) and 2.9 (e,f) show,
melting of graphite is much more emphasized by using a Nd:YAG laser compared to an
excimer laser. This indicates that much more soot is produced using a Nd:YAG laser
instead of an excimer laser. However, meltings occur in both cases as the small carbon
blebs indicate. Graphite is difficult to analyze under an optical microscope because of
its low contrast and strong light absorption in the visible frequency range. Therefore,
differences concerning ablation processes can better be investigated if silicium or glass
are used as target materials rather than graphite. The melting zone of an silicium wafer
20
2 Molecule Source Characterization
Figure 2.7: Mass spectrum of Nd:YAG laser ablated graphite rod. Background pressure
was 1.4 · 10−5 mbar.
after being exposed to a Nd:YAG laser pulse is clearly visible in Fig. 2.9(d) whereas the
same energy applied by an excimer laser shows no sign of melting.
Ablation of graphite without the use of buffer gas is of no use for absorption spectroscopy
since the molecule yield is not high enough for that purpose. Therefore, as a next step the
Nd:YAG laser irradiation had to be combined with a buffer gas flow in order to achieve
high molecule production rates. The attempt to record a mass spectrum of an ablation
jet by using a Nd:YAG laser together with Helium as buffer gas failed completely. This
can be explained by two reasons. 1) If no buffer gas is used, the pressure in the vacuum
chamber (about 10−4 - 10−5 mbar due to the use of a turbo molecular pump with 1500
l/s) changes to maximal 10−3 mbar which can still be handled by the mass spectrometer
without the need of using a skimmer 7 . If a buffer gas is used, even at moderate backing
pressures of 1 bar a skimmer is absolutely necessary to avoid damage of the secondary
electron multiplier (or channeltron) as well as to avoid collisions and interactions of
the ions in the mass filter. Furthermore, a skimmer is needed to avoid turbulences of
the gas flow in front of the hole. Turbulences cause collisions and thus a change in
the chemistry of the jet which is undesired. On the other hand, the introduction of a
skimmer brings in certain difficulties and disadvantages. For example, the skimmer has
7
This type of experiment resembles more a drift experiment in which the ablated species have time to
interact with the rest gas in the vacuum chamber before they are ionized and detected. Therefore,
also species like C2 H and C2 H2 can be found (Fig. 2.7).
2.1 Ablation Technique
C-Cluster
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
21
Laser
thermal
electric arc
[11] [107] [175] [53]
[89]
[168]
[168]
37.0
56.0
99.0 22.2
35
100.0
100.0
31.4
35.0
74.4 62.5
13
20
35-48
100.0 100.0 100.0 100.0
100.0
61
7-10
2.13
2.5
14.5
3.8
.
.
0.6-1.0
7.9
1.6
31.6
5.7
.
.
.
0.413
.
26.1
.
.
.
.
1.11
.
34.7
.
.
.
.
0.19
.
11.0
.
.
.
.
0.11
.
0.9
.
.
.
.
0.32
.
.
.
.
.
.
Table 2.3: Relative C-cluster concentration of different production techniques. Values
of 100.0 in each column indicate clusters with largest abundance whereas all other
entries were set in relation to those. [133]
to be perfectly aligned with respect to the molecule flow and the ionization chamber of
the mass spectrometer. Since the opening diameter of the skimmer has to be chosen
small, i.e. of the order 100 -200 µm this can be very difficult. In addition to that, the
supersonic gas flow is not stable, i.e. might have slightly different shapes or internal
structures. Therefore, proper alignment is not easy. In first approximation, loss of
intensity due to usage of a skimmer is primarily determined by a 1/r2 law with r the
distance between skimmer and ionizer. Thus r should best be a few mm to cm 8 . In the
experimental setup described here the distance between skimmer and ionization region
could not be reduced below 15 cm. This results in a loss of signal intensity of two orders of
magnitude. 2) If a buffer gas is used to form a supersonic expansion, the plasma spreads
far beyond the focus point of the laser ablation. Although a plasma in its entireness
is neutral, it can cause significant electrical interferences even through a skimmer. A
typical problem was that for masses < 1 a huge artificial signal occurred but no signal
was recorded at other masses. The main goal to characterize a supersonic ablation jet
with the help of a mass spectrometer could therefore not be achieved. It has to be stated
that the mass spectrometer used in the experiment, i.e. the mass filter and ion detector,
worked perfectly. Also, laser ablation did not cause principal problems, although there
happened to appear soot depositions on the diagonal mirror. What seemed to be more
critical for the experiment was the device consisting of skimmer and ionizer which was
used to extract the molecules and radicals out of the ablation jet as well as to ionize
them. However, this device serves as a mediator between molecule source and molecule
detection. Consequently, this part of the setup had to be rearranged and optimized. For
the optimization process it is advantageous to have a stable supersonic molecular flow.
Laser ablation technique as it was implemented in this specific setup was not able to
8
It seems to exist an optimum distance between skimmer and ionization region as can be read in [165].
22
2 Molecule Source Characterization
serve this purpose.
As a consequence, a slit nozzle discharge source was used in further experiments to
produce molecules and radicals in a supersonic jet. Although the discharge jet was
stable and easy to apply, disturbances very similar to those of Nd:YAG laser ablation
appeared. As a result, it was not possible to record mass spectra with the current
experimental setup. Further improvements were necessary.
2.1 Ablation Technique
23
Figure 2.8: Excimer laser ablation of different kinds of material. a) and b) show
ablations on aluminum foil (thickness 10 µm). In a) the whole area of ablation is
shown for which 16 shots at 150 mJ were needed to produce the hole. In b) one shot
at 450 mJ results in a very sharp edge, no signs of melting are visible. In c) an ablated
glass sheet (thickness 2 mm) is shown. The laser was applied 30 sec at 50 Hz with a
pulse energy of 400 mJ. Bubbles (diameter 17 - 40 µm) indicate a melting phase. In
d) a silicium wafer after one shot of a 330 mJ laser pulse is shown. For pictures e)
and f) a laser was applied to a graphite rod over a period of 10 sec at 50 Hz repetition
rate with a pulse energy of 400 mJ. Left side of e) shows the ablation hole with an
estimated width of 190 µm; the bright vertical stripe (44 µm in width) indicates the
edge of the ablation hole. f) shows the ablation edge in more detail which marks the
border line of the melting zone to the unperturbed region. The blebs and bubbles
indicate a liquid phase during ablation process close to the ablation hole.
24
2 Molecule Source Characterization
Figure 2.9: Nd:YAG laser focused on different kinds of material. Photos a) and b)
show ablations on aluminum foil (thickness 10 µm). On the right hand side of a) the
effect of a single laser shot (200 mJ during 100 µs) is demonstrated. The hole on the
left side of a) is caused by the same laser light applied 50 times. In b), 100 shots of a
1 ms (230 mJ) laser pulse were applied. In the lower left corner it can be seen that
the ablation hole is surrounded by a melting zone and a transition zone which has an
outer border wall towards the unperturbed aluminum. In c), an ablated glass sheet
(thickness 2 mm thick) is displayed. The dark zone at the lower right corner indicates
the melting zone of the center ablation region. Picture d) shows an ablated silicium
wafer. The square structure in the upper region can be interpreted as focus region of
the laser pulse (1 shot, 100 µs, 330 mJ). A segment line in the lower left area marks
the border between melting region and unperturbed silicium structure. Pictures e)
and f) show an ablated graphite rod. In e), melting of graphite can clearly be seen.
In f), 50 laser pulses (1 ms) with an energy of 330 mJ were applied. Small blebs (8-11
µm in diameter) surround the edge of the ablation hole.
2.2 Discharge Plasma
25
enlargement
slit (30 x 0.25 mm 2 )
expansion
applied potential
grounded
metal plate
insulator
(−600 to −1200 V)
discharge
pulsed valve
gas
gas
Figure 2.10: Discharge slit nozzle
2.2 Discharge Plasma
Discharge nozzles are of great importance for the investigation of molecular species and
can by applied in many spectroscopic fields, see Fig. 2.11. The discharge slit nozzle
used for the mass spectroscopic analysis of the described experiment was developed at
Basel by Linnartz et al. [111, 135] and is a versatile tool concerning the production of
molecules, radicals and ions. It has been shown that pure carbon clusters can be formed
in such a device (see Fig. 2.1) [113, 136] as well as hydro-carbons of many kinds [110]
and ions [112]. In Fig. 2.10, a cross section of the molecule source is shown. The orifice
of the slit consists of an insulator, a metal plate, a second insulator and two sharp plates
which form the actual slit (30mm x 250 µm, 60◦ exit angle). A solenoid valve is used
for the inflow of buffer gas and precursor gas with a backing pressure of 2-5 bar and a
mass flow between 15 and 30 sccm (standard cubic cm per minute). A stable discharge
can be achieved by applying a voltage of 400 - 1000 V (300-400 µs) to the jaws during
the gas flow. The discharge strikes to the inner metal plate which is grounded 9 . During
this process, the flow is heated up which causes fragmentation of the precursor gas, and
thus new species start to form. During the subsequent expansion the gas is cooled down
and can reach temperature as low as 100 K (see Chapter 4.2).
The investigation of the discharge mass spectrum was performed at Balzers/Lichtenstein
in November 2000 using a Plasma Monitor PPM 422 (Inficon AG). For this purpose,
the electric discharge nozzle, a gas mixing device and precursor gases were implemented
into a setup as shown in Fig. 2.12. The plasma monitor (PM) operates in the mass
range between 1 - 512 amu. It is optimized to detect ions in a plasma but is also able
to detect neutrals. The PM consists of an entrance orifice, ion optics, an ion source,
energy analyzer, intermediate focus, mass filter and an ion counter. In this test setup
9
If the outer plate is grounded and the negative voltage is applied to the inner plate the discharge is
instable and arcing to the solenoid valve occurs.
26
2 Molecule Source Characterization
Figure 2.11: Jets produced by a discharge slit nozzle. The molecular probe region
for spectroscopy is 1-2 cm downstream the source exit. Left: Angular view of the
discharge jet. Right: Top view showing a broad zone with two diverging areas of
high density. In the Cologne Carbon Cluster experiment the IR laser probes the jet
parallel to the slit. The resultant absorption length (4-5 cm) is larger than in the case
of the laser ablation source (Fig. 2.5).
the discharge (500 - 600 V) nozzle was used with repetition rates of 1-2 Hz and gas
pulses of 1 ms. Discharge duration was less than 300-500 µs. If the PM is used in a
pulsed operation mode as it is described here, a 103 CPS (counts per second) signal at
the PM corresponds to a sensitivity of 106 CPS in a cw plasma. The average pressure
in the vacuum chamber was ∼ 3 · 10−3 mbar (N2 equivalent) during operation. An
electrically isolated extraction orifice10 instead of a skimmer was used as entrance hole
to the PM and placed 2-3 cm apart from the front of the discharge nozzle. Ions are
more easily detected than neutrals because they are guided into the PM by an electric
field, and alignment of the PM orifice with respect to the jet is less crucial. Thus a large
extraction volume can be probed. The detected mass distribution of ions is not effected
by any ionization process as it would be the case for neutral species and fragmentation
processes are negligible. Kinetic energies of ions in a plasma are in the order of a few to
hundred eV. A quadrupole without any energy filter can only handle ions with a certain
energy distribution. It is therefore necessary to first determine the energy distribution
of the ions with an energy analyzer (± 500V) and then to select the species of a certain
10
Could be pos. and neg. biased or on floating potential.
2.2 Discharge Plasma
27
Vacuum
Chamber
Plasma−Monitor
Discharge
Source
Sample Gas
Jet
Ion Detector
Quadrupole Mass Filter
Energy Filter
Ionization Chamber / Ion Optics
24.0
23.9
Mass Flow
Controller
Voltage
Multi Channel
Figure 2.12: Experimental setup for mass spectrometry on a molecular beam at
Balzer/Lichtenstein, Nov 2000
energy range. For example, if neutral He is ionized in the PM (ion source 70 eV, 1 mA),
the energy distribution is Emean = 98 eV with ∆E = 2-4 eV (see Fig. 2.13). If necessary,
the PM potentials can be set appropriate to Emean so that even high energy ions (± 500
eV) can be detected. The energy filter can select ions within a certain energy range ∆E
for a further mass selection in the mass filter. If only nitrogen was used in the discharge
slit nozzle, Emean was found to be 4.40 eV. In Fig. 2.14 (top), cations of the N2 discharge
have been investigated and nitrogen complexes N+
n with a broad mass distribution have
been found. The mass resolution m/∆m at mass 55 amu was 23. Acetylene (C2 H2 )
diluted in a buffer gas is a precursor for the production of many radicals and ions like
Cn H, HCn H, H2 Cn ,... . Fig. 2.14 (bottom) shows a 20 sec scan of a discharge using
0.5% C2 H2 in Ar. The mean kinetic energy of the ions was 4.40 eV. In the lower mass
+
+
+
regions, ions like C2 H+
2 , Ar , ArH3 and C4 H2 could be found but the corresponding
count rates of max. 80 CPS are rather sobering. The signal-to-noise ratio of the ions is
between 6 - 17 and the ion signals are well resolved. In a second experiment anions have
been detected. The measurements showed that anions are less abundant than cations.
In both cases the detected ion signal was far from being satisfying. Nevertheless, mass
spectra of positive and negative ions could be obtained.
For measurements on neutral species a multi-channel analyzer was used to allow for
integrations over the relevant time intervals when the discharge was switched on, thereby
reducing the noise. Again, the detection of even the faintest rest gas molecules worked
28
2 Molecule Source Characterization
Figure 2.13: Energy distribution of He+ produced in the ion source of the plasma
monitor, ∆E = 2-4 eV.
perfectly but no correlated discharge signal could be recorded. The reason for this failure
might be that the PM was optimized for ion detection and hence no skimmer was used
since this is less important for ions than it is for neutral species. This lack of a skimmer
clearly lowered the chance of detecting neutrals. Another reason may be that the ion
optic precedes the ion source in the PM setup. Therefore, the ion source has a distance
of 3-4 cm to the orifice which corresponds to an intensity decrease in the order of 101 -102 .
2.2 Discharge Plasma
29
Figure 2.14: Mass spectra of a molecular beam. Top: Discharge on N2 molecules (E=-4.4
eV). Bottom: Measurement of cations on a discharge of 0.5% C2 H2 in Ar (E=-4.4 eV).
30
2 Molecule Source Characterization
2.3 Conclusions and Prospects
Detection of ions and neutrals in a supersonic jet makes high demands on mass spectrometers. This is especially true if one considers that the use of a mass spectrometer
is intended to monitor conditions within the jet during optimization processes, i.e. with
integration times of max. 5 min or less. The main challenge is the development of an
effective extraction device to probe molecules and ions of a few mbar pressure gas flow.
The most important region to probe the jet is 1 - 3 cm downstream the nozzle exit.
Depending on the backing pressure of the buffer gas and the type of nozzle used, pressures
up to 10 mbar may occur in regions where the extraction orifice or skimmer is placed.
In this experiment the pumping speed is not high enough to reduce the mean vacuum
pressure below 10−1 -10−2 mbar during operation with 50Hz discharge/ablation repetition
rates. Mass filter usually require operation pressures of 10−4 - 10−5 mbar. The use of a
single pressure reduction stage can not be sufficient to achieve this pressure drop. To use
a mass spectrometer at high repetition rates a second stage pressure reduction is required.
The Distance d between the two orifices (or skimmer and orifice) of the reduction stage
should be much smaller than the mean free path of the incoming particles. The exact
distance d depends on the Knudsen characteristics of the extracted beam [165].
It has been shown that there is a difference between the detection of ions and that of
neutrals. Ions require no further ionization process and can be guided by electric or
magnetic fields. Nevertheless it is important to place the ion optics very close to the
extraction orifice to enhance the yield. If the focus is on neutral detection, an ionization
source has to be placed right behind the skimmer (or orifice). Hence it is clear that a
mass spectrometer can only be optimized on either ions or neutrals. Displacement of
the ionization source or of the ion optics result in a significant decrease of the signal
intensity.
In a pulsed experiment with pulse lengths of a few µs up to several hundred µs, a mass
spectrometer which intrinsically works in a pulsed mode, like a TOF mass spectrometer
is advantageous, i.e. a better duty cycle can be achieved by using a TOF instead of a
quadrupole mass spectrometer. This is because a TOF records all masses simultaneously
whereas a quadrupole can only detect one species at a time. If a mass scan from 1 to 400
amu is desired, the effectiveness of the TOF relative to a quadrupole is 400. Another
principal disadvantage of a quadrupole is that the mass range is usually limited, e.g.
from 1 - 400 amu in the here described experiment. TOF have no such mass limits. It
is the mass resolution that decreases for higher masses and thus limits the TOF mass
range. A quadrupole mass spectrometer needs an energy filter to detect species with high
energies or broad energy distributions. This is not needed if a TOF mass spectrometer
is used. The use of an energy analyzer provides additional information on the plasma
conditions. In most cases this information is less important, and TOFs usually make no
use of this possibility because it restricts the mass spectrum to species within a certain
energy range.
For measurements on less stable molecular beams and supersonic jets, i.e. when fluc-
2.3 Conclusions and Prospects
31
tuations between peak times of a beam occur, the use of an additional ion storage
quadrupole device can be advantageous. Independent on the kind of mass filter which
is used (i.e. quadrupole or TOF), this device can collect ions for a certain time, e.g. for
a time slightly longer than the duration of the plasma pulse, before they are released to
the mass filter section. A precise timing is therefore not as crucial as without using this
device.
Mass spectrometers can be used to optimize experimental conditions or they can serve
as monitoring devices for experiments which require time consuming searches for certain
species or long integration times. They can also be applied to develop new molecular
sources. Although the nowadays available molecule sources are very efficient, it is very
likely that the production of larger radicals or reactive molecules in their gas phase, e.g.
molecules with a carbon chain backbone between C20 and C60 , will only be possible if
new production techniques are developed and tested. This can be of great importance for
the understanding of grain growth or for the identification of larger cyclic or polycyclic
molecules. It seems that even the limits for the detection of linear species can be pushed
further away to allow discoveries beyond molecules like C13 , HC17 N, HC13 H, H3 C12 N,
C14 H, ... [61, 123].
32
2 Molecule Source Characterization
3 The Cologne Carbon Cluster
Experiment: The New Setup
Good name in man and woman, dear my lord,
Is the immediate jewel of their souls:
Who steals my purse steals trash; ’tis something, nothing;
’Twas mine, ’tis his, and has been slave to thousands;
But he that filches from me my good name
Robs me of that which not enriches him
And makes me poor indeed.
William Shakespeare (1564 - 1616), “Othello”
Molecules like pure carbon clusters Cn or other species with no permanent dipole moment can only be observed due to their vibrational or electronic properties. C3 and
C5 have been astrophysically detected towards the late-type star IRC+10216 [87, 13].
The knowledge of the ro-vibrational transitions of small carbon clusters in the IR region is therefore important for future astronomical detections of these species. The
Cologne carbon cluster experiment combines an effective excimer laser ablation source
(see Chapter 2.1.1) with a sensitive, high resolution infrared tunable diode laser (TDL)
spectrometer. TDL’s provide a fairly monochromatic beam which guarantee high spectral resolution and high sensitivity, with detection of absorbance as low as 10−6 -10−7 .
Radicals like linear C8 and C10 have been observed with this spectrometer for the first
time [61, 14]. The experimental setup has previously been described in the work of
Berndt [14], Giesen [60] and Winnewisser et al. [194].
TDL’s are not well suited for large scans over wide frequency ranges. Thus spectral
searches for the asymmetric stretching modes of gas-phase carbon molecules is essentially
guided by the infrared vibration spectra of cold matrix isolated carbon clusters (see e.g.
Shen et al. [166]) and their assignment to asymmetric stretching modes by ab initio
calculations (e.g. Martin et al. [115]). In the recent years the group of Prof. J.P. Maier
from Basel has developed a novel matrix isolation technique that allows to deposit mass
selected carbon clusters. The infrared spectra of such a matrix can undoubtedly be
34
3 The Cologne Carbon Cluster Experiment: The New Setup
Figure 3.1: The Cologne carbon cluster experiment.
assigned to a cluster of a certain size. Once the vibrational bands of the radicals are
known an aimed search for ro-vibrational transitions in the gas phase can be conducted.
3.1 The Cologne Carbon Cluster experiment
Fig. 3.1 shows the new experimental setup of the Cologne carbon cluster experiment.
A TDL spectrometer with a spectral resolution better than 5×10−4 cm−1 is used to
record the rotationally resolved spectra of asymmetric stretching modes of small carbon
clusters. Using a number of different diode lasers the spectral region between 1750
– 2100 cm−1 , where most of the carbon clusters are predicted to have characteristic
IR active vibrational bands, can be covered. The IR laser beam intersects the pulsed
cluster jet of a laser ablation source (see Chapter 2.1.1 for details of the source) 10 mm
downstream from the nozzle. An increase in sensitivity is gained by using a multi-pass
optics of Herriott type to obtain 24 passes through the jet. Since most of the diode
lasers have multi-mode laser performance, a monochromator with 1 cm−1 resolution has
to provide sufficient mode separation. The exiting IR beam is focused on a HgCdTe
photo-conductive detector. A fast AC-coupled amplifier allows time resolved detection
of the weak absorption signal on a pair of gated boxcar integrators before storing the
data by a PC. Part of the IR beam is used to monitor the absorption spectrum of a
3.2 The New Setup
35
Figure 3.2: Sensitivity of IR detectors [97]. In this experiment InSb (J10D) detectors
are used in the 5 µm region.
reference gas and fringes of a germanium etalon simultaneously with the cluster signal.
The 1m reference cell is used to record Doppler limited lines of a reference gas at low
pressures. Frequency calibration of the data is accomplished by referencing the lines to
the fringe spectrum of the etalon with a free spectral range of 0.016 cm−1 .
3.2 The New Setup
Measurements of the linear radicals C13 , C10 and C8 have revealed that for the detection
of higher members of the Cn chain further improvements in the sensitivity of the spectrometer are needed. The main problems occurred from the use of a cold head system
for cooling the laser diodes, mechanical instabilities in the optical system and electrical
interference of the IR signal with the excimer pulse signal. In the course of this thesis a
completely new experimental setup was build. Important improvements have been done
including:
• Laser diodes mounted in a liquid nitrogen dewar instead of using a cryogenic cold
head
36
3 The Cologne Carbon Cluster Experiment: The New Setup
Figure 3.3: Frequency calibration using CCCS and Calib. The TDL laser was frequency
modulated at 5kHz.
• The use of InSb detectors for the 2000 cm−1 frequency region instead of HgCdTe
detectors
• Enhancement of mechanical stability
• Setting up a new optical system to avoid astigmatism
• Reduction of electrical interferences
• Development of new calibration software
With the new setup a better signal-to-noise can be achieved and the sensitivity is increased in the frequency region of 2000 cm−1 where vibrational bands of C10 and C8
occur. In the new setup the laser diodes are mounted in a liquid nitrogen dewar instead
of a cryogenic cold head using closed cycle technique. Mechanical shocks are completely
avoided and baseline fluctuations are significantly smaller. The frequency of the TDL
3.3 Conclusions and Prospects
37
diodes is tuned by temperature and current. In the new setup the minimal temperature
of the diodes can not drop below 77 K so that special diodes are required. The laser
power of these diodes is between 0.1 and 10 mW as it was the case with the previously
used diodes at temperatures of . 4K. The spectral line widths of these lasers are about
30 MHz. A new laser control device and complete new electrical connections of the
electronic devices reduced electrical interference with the Excimer pulse significantly.
The optical system has been improved by using stable mountings for the optic components and by mounting both optics and vacuum chamber on the same optical bench.
The arrangement of the optic components is chosen to minimize astigmatism and loss
of signal.
The HgCdTe detectors for the reference and etalon signal were replaced by InSb photovoltaic detectors for the measurements at 5 µm wavelength (i.e. at 2000 cm−1 ). In Fig.
3.2 it can be seen that HgCdTe (J15D12, Judson) detectors have their peak sensitivity
between 10-11 µm whereas InSb (J10D, Judson) detectors peak at 5 µm.
Reference and etalon signal can be modulated in two modes. Mode one (M1) uses a
chopper wheel with a modulation frequency at 1.2 kHz whereas mode two (M2) modulates the frequency of the TDL laser (up to 6 kHz). M1 is used for measurements
with the laser ablation source. M2 can be used for fast and high precision frequency
calibration where the lock-in amplifiers operate in the second derivative mode.
The new calibration software CCCS (Carbon Cluster Control Software) is based on the
linux operating system using the in-house program dada as program language. CCCS
receives and converts the data into ascii format and displays the measurement on the
monitor screen. The program is nearly self explaining and comprises of help functions.
With an additional program Calib the data can be immediately frequency calibrated,
see Fig. 3.3.
Test measurements on C3 have been performed. Fig. 3.4 shows the R(28) transition of
C3 .
3.3 Conclusions and Prospects
High resolution absorption spectroscopy is one of the most powerful tools to characterize small gas-phase molecules. The Cologne carbon cluster experiment has provided
highly accurate data on asymmetric stretching transitions of small linear carbon clusters
during the last few years. With the new setup even more challenging problems can be
approached. At first, searches for hitherto undetected linear chains like C11 and C12 can
be started. The vibrational spectra of cyclic C6 and C8 trapped in a cold matrix have
been found by Graham et al. [190, 191]. It is thus most likely to find these species in the
gas-phase with the Cologne infrared spectrometer. The infrared spectra of combination
bands also provide good predictions for the low bending modes of carbon clusters, which
are as low as 1 - 4 THz.
38
3 The Cologne Carbon Cluster Experiment: The New Setup
Figure 3.4: Rovibrational transition of C3 at 2067 cm−1 (left line). The line at the right
hand side is probably due to a hot band transition of C3 .
Part II
C3N Isotopomers, C4N, and C6N
4 Experimental Setup
“ The principle of science, the definition almost, is the following:
The test of all knowledge is experiment. Experiment is the sole
judge of scientific ’truth’. But what is the source of knowledge?
Where do the laws that are to be tested come from? Experiment,
itself, helps to produce these laws, in the sense that it give us hints.
But also needed is imagination to create from these hints the great
generalizations - to guess at the wonderful, simple, but very strange
pattern beneath them all, and then to experiment to check again
whether we made the right guess. ”
Richard P. Feynman, ”The Feynman Lecture on Physics”
The rotational spectra of the molecules presented here were detected in a supersonic
molecular beam by a Fourier Transform Microwave (FTMW) experiment carried out at
the Harvard-Smithsonian Laboratory, Cambridge MA/USA. This spectrometer (Fig.4.1)
has been used to detect over 80 new reactive molecules during the past six years [179]
and the experimental setup has previously been described in McCarthy et al. [118, 122].
The basic principle of the spectrometer is as follows. A pulsed supersonic molecular
beam of an organic precursor gas heavily diluted in an inert gas is produced by an commercial solenoid valve (General Valve Co.). Reactive molecules of many kinds are made
by applying a small electrical discharge in the throat of the supersonic nozzle, prior to
expansion of the gas into the large Fabry-Perot cavity of the spectrometer. As the molecular beam traverses the cavity the molecules are irradiated by a short (1 µs) microwave
pulse at frequency ν0 . The microwave pulse induces polarized resonant transitions of the
molecules, ions or radicals. At that time the molecules are under far different conditions
than they were prior to the expansion. Important properties which have to be considered
are the translational, rotational and vibrational temperatures, as well as the pressure,
and density of the molecules. After the polarizing pulse is switched off the polarized gas
coherently emits at its resonant frequencies. This free-induction decay (FID) is detected
time resolved by a superheterodyne receiver and subsequently Fourier transformed to
42
4 Experimental Setup
give the spectrum in the frequency domain. The spectrometer operates from 5 to 40
GHz and is fully-computer controlled to the extent that, in spite of the small spectral
coverage of each setting of the Fabry-Perot (< 0.5 MHz), automated scans covering wide
frequencies and requiring many hours of integration, can be conducted. Rotational lines
of known molecules are routinely monitored for calibration.
The experimental part can be divided in three main sections, i.e. the production of the
radicals (see Chap. 4.1) using a gas flow controller and a discharge nozzle, their cooling
in an adiabatic expansion (see Chap. 4.2) and the subsequent detection in the FTMW
spectrometer (see Chap. 4.3).
43
.
70 cm
liquid
Nitrogen
Fabry−Perot cavity
Gas
input
5
4
ν + δ
o
ν
o
Pulsed discharge
nozzle
Signal
antenna
Polarization
pulse
antenna
3
Vacuum chamber
PIN
switch
+30dB
6
Diffusion pump
trigger
PIN
switch
Mirror
36 cm
2
30 MHz
9
1
ν − 30 MHz
o
ν + δ
o
.
30 MHz
source
Frequency
synthesizer
ν − 30 MHz
o
30 MHz
Bandpass
δ + 30 MHz
7
+20dB
0 to +90 dB
filter
δ
Low−pass
filter
8
Figure 4.1: Block diagram of the FTMW low band system, 5 - 25 GHz with supersonic
jet. (1) The control computer sets the synthesizer frequency (5 - 26.5 GHz) to νo -30
MHz. (2) The output is mixed (single sideband modulator) with a 30 MHz signal
which results in a frequency of νo and is amplified (’drive’ amplifier) (3) A 1 µs pump
pulse triggered by a ’polarization’ PIN switch enters the FP-cavity via an antenna
and (4) polarizes the incoming molecules in the vacuum chamber. The TE00q mode of
the radiation field is indicated by the dotted lines between the mirrors. At this stage
the molecules have undergone significant cooling due to the adiabatic expansion in the
supersonic jet and rotational temperatures of a few Kelvin can be achieved. (5) During
the relaxation process the molecules emit signals at certain transition frequencies νo +δ
During this process the ’polarization’ PIN is switched off to suppress noise from the
drive amplifier. (6) The Free Induction Decay (FID) signal of the molecules is received
at the signal antenna and amplified (front-end amplifier). (7) It passes a second PIN
switch and is then mixed with a νo -30 MHz signal from the synthesizer. The image
rejection mixer has an internal amplifier (+20dB). (8) The resulting δ+30 MHz signal
passes a bandpass filter which discriminates the broadband noise and a second mixer
transfers the signal down to the 1-MHz video band using a 30 MHz signal. (9) The
computer records the filtered and amplified signal in the time domain.
44
4 Experimental Setup
4.1 The Production of CnN Radicals
Radicals can be produced in many ways [58], e.g. by laser ablation, cw glow discharge,
and pulsed discharge followed by a supersonic expansion. In the present work the latter
method was used and the production of the radicals consisted mainly of two steps. (1) To
find and produce the appropriate stable precursor gases, which are then mixed through
a gas flow controller (see 4.1.1). (2) To choose and build an effective discharge nozzle
and optimize the conditions for a maximum radical yield (see 4.1.2).
4.1.1 The Precursor Gases
To achieve an efficient way of producing long carbon chain molecules like HCn N, CH3 Cn N,
H2 Cn , and even for open-shell molecules like Cn N with n≥3 it is advantageous to use
moderately large organic precursors (e.g. cyanoacetylene and diacetylene), rather than
commercially available gases such as acetylene (C2 H2 ) and nitrogen (N2 ).
Cyanoacetylene (HC3 N) was used for the production of C4 N and C6 N as well as for the
production of all 13 C isotopic species of C3 N (in this case 13 C isotopic acetylene had to
be added).
An appropriate synthesis of HC3 N has been described in Murahashi et al. [137] and
Moravec [134] together with suggestions for further readings. HC3 N can be stored at
-5◦ C for several months without evidence of polymerization and a vacuum distillation
process prior to use was not required. The sample can be produced to a purity of more
than 98% as has been shown by 1 H NMR spectroscopy [66].
Once the precursor gases are produced they are heavily diluted in an inert gas like
argon or neon which is necessary to maintain a steady gas discharge and to achieve low
rotational temperatures of 3 K in the adiabatic expansion following the discharge, (see
Fig.4.2).
In general there seems to be no ready made recipes for the optimum mixing ratio of
precursors to yield a certain radical in sufficient amounts; the work has nearly always to
be done by trial and error. In the case of Cn N chains the pioneering work was already
done by Gottlieb et al. [66, 121] and Ohshima et al. [142] and had only slightly to be
changed. A good mixture for supersonic expansions proofed to be quit different from
mixtures used in gas flow cells (see Gottlieb et al. [66]). The best results for C3 N
production in a glass tube using a glow discharge where achieved by using HC3 N and
N2 or He with an equal molar mixing ratio at 3.3·10−5 bar (3.3 Pa). For experiments
using a supersonic expansion the best conditions were found to be the following:
13
C-isotopic C3 N: In this work the strongest lines of the 13 C-isotopes of C3 N were obtained with a mixture of 0.02% HC3 N and 0.07% 13 C-enriched acetylene in Ne.
The 13 C-enriched acetylene is a 50% H13 CCH, 25% H13 C13 CH and 25% HCCH
mixture produced by hydrolysis of Li2 C2 containing an 1:1 mixture of 12 C and 13 C
that was prepared by the NIH Stable Isotope Resource at Los Alamos National
4.1 The Production of Cn N Radicals
45
Laboratory [121]. For speed and convenience all measurements on isotopic species
were done with enriched samples and in the case of the 13 C isotopic species an
enhancement of the signal by a factor of 2-3 was achieved.
An other, but less effective, way to produce isotopic cyanoacetylene is to use a
C2 H2 /13 CO/inert gas mixture. For the CC13 CN species a lot of energy is needed
to break the strong C≡N bond in the HC3 N precursor. This problem can be
circumvented by using HCC13 CN as precursor which can be produced using chemical reactions like K13 CN + H3 PO4 → H13 CN + other and H13 CN + C2 H2 →
HCC13 CN + other.
CCC15 N: For the production of CCC15 N only a mixture of 0.2-0.3% CH3 C15 N (Acetonitrile) in Ne was used and for the strongest lines a 6 times stronger signal than
those of the 13 C isotopic species was observed.
C2 N: Ohshima et al. [142] used a 0.15% CH3 CN or CCl3 CN mixture diluted in Ar
where the CCl3 CN/Ar sample produced a two times stronger signal. 1
C4 N and C6 N: For the C4 N and C6 N production it was sufficient to take 0.05% HC3 N in
Ne. The relation of the signal intensity between CCCN and C4 N is ∼15 and under
optimized experimental conditions, the absorption intensities of the strongest lines
of the C6 N are only two times weaker than those of C4 N.
The total mass flow which entered the vacuum chamber was 14 sccm (standard cubic
cm per minute) for C4 N and 32 sccm for isotopic C3 N and C6 N.
1
C2 N can also be produced in a glass tube experiment using a microwave discharge of CF4 with
CH3 CN as Kakimoto & Kasuya have shown in [98].
46
4 Experimental Setup
.
4.3 cm
teflon
insulation
Mirror
Discharge
Source
copper electrode
3mm thick
Sample Gas
Jet
30 sccm
gas
5−6 mm
.
Vacuum chamber
24.0
hot
trigger
23.9
Discharge
Mass Flow
Controller
Voltage
1100−1250 V
time
Voltage
trigger
on/off
.
H13 CCH
2.4%
HC 3 N
Ne
2.1%
95.5%
Current
oscilloscope
Figure 4.2: The Production of Cn N radicals. On the left: precursor gases (H13 CCH,
HC3 N) are mixed with a buffer gas (Ne) and fed to a pulsed discharge nozzle before
it adiabatically expands into the vacuum chamber. On the top right: the discharge
nozzle as it is used for the production of intermediate sized radicals. On the bottom
right: The discharge voltage and current is monitored. In most cases an efficient
radical production is indicated by a fine fringed current line. The dashed vertical
cursor which frame the current line within the 2ms voltage supply marks a separation
of 1-1.5 ms.
4.1 The Production of Cn N Radicals
47
.
.
copper
electrodes
5 − 10 mm Teflon
spacer
Gas
copper
electrodes
10 − 20 mm Teflon
spacer
Gas
.
.
.
Pulsed
nozzle
Teflon
spacers
.
Pulsed
nozzle
Teflon
housing
.
10 mm Teflon
spacer
Teflon
housing
.
Figure 4.3: Nozzle for the production of molecules and radicals. On the left: Discharge
nozzle optimized for the production of radicals like C4 N. On the right: Discharge
nozzle for the production of molecules like HC17 N. The left part on each figure is a
solenoid valve with an orifice of 1mm.
4.1.2 The Discharge Nozzle
Discharge nozzles similar to the ones used for the here presented experiments were first
described by Schlachta et al. [164] in 1991. Since then many other work groups used
discharge nozzles of the same type to produce radicals and molecules. The first long
carbon chain molecule of astrophysical interest was the cyanopolyyne HC9 N observed
in the laboratory by Iida et al [92] in 1991. The same group showed that also reactive molecules which previously were detected in glow discharges in glass tubes (e.g.
C3 N, C4 H [66], and C6 H [146]) can also be effectively generated in supersonic expansion
discharge nozzles.
The basic geometry of the discharge nozzles which were used for this work is as follows.
A solenoid valve through which the sample gas enters the nozzle is mounted on a Teflon
housing which contains a Teflon spacer (5-18 mm in length), two oxygen-free highconductivity copper electrodes (1mm thick) separated by a spacer (4-10 mm) of the same
dielectric. In some cases a third spacer is added to function as a reaction channel but this
is usually only the case if long closed-shell molecules are to be studied. The dimensions of
the electrodes and the insulators are quite critical for the efficient formation of discharge
products. Applying a short pulse discharge in a small region between the electrodes
where the pressure of the flow gas is still high and a subsequent expansion of the gas
in a supersonic free jet, where almost no collision occurs, generates a relatively high
concentration of transient species. These conditions are very different to a dc discharge
in a flow gas cell system which is far inferior in terms of the plurality of radical production
as known so far. This emphasizes the importance of the right discharge conditions, such
as dimension of the discharge unit, the applied discharge voltage, discharge timing, and
as already discussed the composition of the sample gas.
48
4 Experimental Setup
.
Pin 1
2
3
4
5
6
7
8
solenoid
valve
gas
11 mm
i.d. 3 mm
1 mm
copper
4 mm
teflon
discharge
zone
reaction
channel
ground
−HV
Figure 4.4: Test nozzle to optimize the geometry of the discharge nozzle. Eight electrodes
(PIN) give the possibility to freely choose the distances of the electrodes in use, i.e.
the discharge zone can be varied by just reconnecting the electrodes from outside the
vacuum chamber. Also the length of the reaction channel is adjustable from 0-30mm.
Highly reactive molecules as well as long carbon chain molecules like HC17 N can be
produced with this nozzle.
Restricting oneself to the here described geometry of the nozzle there is a possibility to
systematically vary the length of the discharge zone and of the reaction channel during
the operation of the nozzle. As part of this thesis a test nozzle as seen in Fig.4.4 was
build to study the most effective electrode and reaction channel positions and lengths.
Two electrodes were used at a time which could be chosen freely out of the 8 electrodes
of the test nozzle. The region between cathode and the grounded electrode is called
the ’discharge zone’ which is followed by the ’reaction channel’, i.e. the space left until
the flow exits the nozzle. With this nozzle many different combinations of discharge
zone lengths and reaction channel lengths can be tested and in-situ electrode changing
during an experiment can be done from outside the vacuum chamber which ensures
similar conditions for each electrode setting in terms of mass flow, valve opening times
and gas mixing. The testing and optimization usually works by monitoring the signals of
known species; starting with easily to produce ones like HC5 N or C3 N and then refining
with more rare species of the same type. There seems to be a principal difference in the
production of stable and unstable molecules. In the case of the closed-shell molecules
like HC9 N [141] and HC2n+1 N with n=5-8 [118] which have been generated from simple
molecules such as (CN)2 and HC4 H (or CH2 CHCN and C2 H2 as used in [141]) more
collisions are required to form longer carbon chains. This might explain why for such
molecules a nozzle with an additional reaction channel is favorable. Once an optimum
setting of ’discharge zone’ and ’reaction channel’ lengths is found an easier to assemble
and to clean nozzle can be build (see Fig. 4.3, right and Fig. 4.7). For highly reactive
species such as open shell free radicals it is important to avoid any quenching process on
the surfaces of electrodes, insulators (spacers) and other molecules. Collisions apparently
4.1 The Production of Cn N Radicals
49
drive the hydrocarbon chemistry to the more stable closed-shell polyynes [118]. The
optimal production conditions for the Cn N chains were achieved by using no reaction
channel 2 and a 10 mm discharge zone in the test nozzle. This corresponds to a short
nozzle as shown in Fig. 4.3 (left) 3 . This nozzle was used with a low-current dc discharge
of 1100-1300 V synchronized with a 300-480 µs long gas pulse at a total backing pressure
of 2.5 bar and a total gas flow of 30-32 sccm. The discharge current (see Fig. 4.2 bottom
right) was typically 10-100 mA and lasted from 1 - 1.5ms per pulse corresponding to
an energy per pulse of the order of 100mJ. For the production of open-shell molecules
the first (inner) electrode was used as the cathode and the second (outer) electrode was
grounded, whereas long closed-shell carbon chains were obtained by using the second
(outer) electrode as cathode. The strength of rotational lines can decrease by a factor
of 2-4 when the polarity of the electrodes is reversed [118]. For radicals the loss factor
can be much higher by changing the polarity. The short discharge nozzle was used for
the measurements of C4 N, C6 N and the C3 N isotopomers (see Fig. 4.5 and Fig. 4.6) and
it is also described in [37].
2
3
except the tip of the nozzle
These conditions were found to be similar to those that optimize production of the acetylenic free
radicals Cn H.
50
4 Experimental Setup
Figure 4.5: The short ’radical’ nozzle during a discharge. This nozzle was used for the
measurements of C4 N, C6 N and the C3 N isotopes.
Figure 4.6: The supersonic jet expansion of the short nozzle. The picture was taken
in Cologne using a pure He discharge at 5 bar stagnation pressure and 10−1 mbar
background pressure. The straight line in the middle of the picture marks the center
line of the gas flow. The jet boundary is indicated by the upper line which arises
from the nozzle exit at an angle of roughly 23◦ with respect to the exit plummet. The
dashed line indicates the barrel shock. On the right hand side the vacuum chamber
window limits the further view on the still expanding jet.
4.1 The Production of Cn N Radicals
51
Figure 4.7: The long nozzles during a discharge. The pictures were taken in Cologne
using pure He discharges at 5 bar stagnation pressure and 10−1 mbar background
pressure. The discharge nozzle has a total length of 55mm (with tip), both electrodes
were separated by a spacer (13mm length, 5mm hole diameter) and the last electrode
has a distance of 29mm from the nozzle exit. At the top: The first (on the very left
which can hardly be seen) electrode was grounded and the second (the dark, vertical
stripe in the middle of the nozzle) on a negative high voltage. Bottom picture: The
first electrode (left to the bright discharge zone) had a negative high voltage and the
second (in the middle of the nozzle) was grounded. This kind of nozzle is mainly used
in the mode shown in the upper picture and is very effective in the production of long
carbon chain molecules with an electronic close shell structure, e.g. HC17 N.
52
4 Experimental Setup
4.2 Adiabatic Expansion
After the precursor gases have passed the discharge region the particles in the gas undergo an adiabatic expansion into the vacuum chamber, i.e. they form a molecular
beam. Spectroscopy on a pulsed molecular beam is used in a number of laboratories because the low rotational temperature of the molecules within the beam allows interesting
experiments in the field of Van-der-Waals complexes, clusters and radicals. Compared
with experiments in glass tubes under room temperature and medium low pressure 4
the spectra of stable and unstable molecules in a beam are very simple since they are
usually free of high rotational and highly excited vibrational states.
Although the primal interest is in the molecules created in the discharge the first and
main part of this section deals with the buffer gas atoms which usually contribute to
more than 98% of the flow particles and which set constraints on the flow conditions
in which the molecules of interest are seeded. In the last part of this section the focus
is on the interaction of the buffer gas with the molecules and radicals and the spectral
behavior in a supersonic expansion of the latter. The problem is mainly approached in
a theoretical way to clarify the basic prosseses. It has to be mentioned that deviations
from experiment are known but that up to now no theory comprising jet properties,
chemical reactions and spectroscopic properties of certain molecular species is available.
The experiment described here is set up in a pulsed mode with repetition rates of 2
Hz which requires smaller and less expensive pumping systems than a cw mode. In this
experiment a 35cm diameter diffusion pump (Varian) backed by a dual-stage mechanical
pump is used to maintain a background pressure of 2.7·10−9 bar (0.27 mPa). Typical
peak pressures at 2 Hz repetition rate of the nozzle are 6.7·10−8 bar (6.7 mPa).
Assuming a perfect adiabatic process one could argue that the properties of the molecules
are mainly determined by the adiabatic equations, like
T
=
T0
p
p0
γ−1
γ
(4.1)
with T0 ≈ 300 K the stagnation temperature, p the background pressure during the
expansion 5 and p0 = 2.5 bar the stagnation pressure result in a minimum temperature
of Ta & 1.2 K. This however does not consider that the adiabatic expansion happens as a
’free jet’, i.e. a supersonic flow which can show complicated features as seen in Fig. 4.8.
Free jets have been investigated by many authors and the main reference for this section
is the ’new classic’ book edited by Scoles ’Atomic and Molecular Beam Methods’ [165],
the work of Balle & Flygare [6], and McClelland et al. [124].
Molecular beams with pulses longer than 100µs in a vacuum chamber of 1m length are
technically rather ”gated” or ”modulated” than pulsed (R. Gentry in [165], p.54), i.e the
4
5
usually in the µbar - mbar region
This is not necessarily the mean background pressure but the lower limit can be set to the achieved
pressure if there is no gas load.
4.2 Adiabatic Expansion
53
Background Pressure P b
Compression
Waves
M>1
Reflected
Shock
Expansion
Fan
P0 ,T0
M<<1
M=1
Mach Disc Shock
Zone of
Silence
M>>1
M<1
Flow
Slip Line
M>1
Barrel Shock
Jet Boundary
Figure 4.8: Continuum free-jet expansion [165].
mean free path of molecules moving at a speed of typically 800-1000 m/s is larger than
the dimension of the vacuum chamber itself. In the further discussion the molecular
beam although pulsed is treated as a continuum free-jet for the time between 500 - 1100
µs after the valve has opened and released the gas because in that time it is assumed that
the beam exposes all important features which characterize a continuum free jet. A gas
expansion from an region with a stagnation pressure p0 into an area with a background
pressure pb becomes supersonic if the equation
p0
>G≡
pb
γ+1
2
γ
γ−1
= 2.05 using γ =
5
3
for atoms
(4.2)
is fulfilled. G is less than 2.1 for all gases and in this experiment the requirement of
Eq. 4.2 is easily achieved. A supersonic flow increases velocity as the gas expands and
the Mach number M , with
v
M≡
(4.3)
vs
where v is the flow velocity and vs is the speed of sound, is a measure of this, i.e the
beam is supersonic if M ≥ 1. Eq. 4.2 ensures that the pressure at the source exit or
nozzle ’throat’ is well above the background pressure and the flow is said to be ’underexpanded’. In the subsequent expansion the gas is accelerated so strongly that M can
be much larger than 1, e.g. 40 or even larger which means that the particles in the beam
have a higher velocity than the local speed of sound. On the other hand information
can only propagate at the speed of sound 6 . This means that for a certain region in the
flow, the so called ’zone of silence’ (ZOS), the particles in the flow are not influenced by
6
Here, information refers mainly to the pressure and density distribution in the vacuum chamber or
the molecular flow.
54
4 Experimental Setup
any external conditions imposed on them like the ambient pressure pb which they have
to meet downstream. The jet over-expands with M continuously increasing in the ZOS.
Of course at some point the supersonic flow is adjusted to the boundary conditions via
shock waves, which are regions between the ZOS and the rest of the vacuum chamber
that are very thin non-isotropic regions of large density, pressure and temperature. The
re-compression usually happens as a barrel shock at the sides and the Mach disc shock
at the normal to the centerline of the flow, see Fig. 4.8. In this regions the flow becomes
subsonic (M < 1) and can react on the background pressure, walls or other obstacles.
Assuming that only background gas reacts on the flow the distance nozzle exit - mach
disc location xM is given by
r
xM
p0
= 0.67
(4.4)
d
pb
where d is the nozzle diameter. This formula together with a similar one for the width of
the barrel shock has proved to give results which are in fair agreement with observations
at the Cologne Cluster Experiment. In this experiment a laser ablation or alternatively a
discharge is used where many molecules are optically excited which make the jet visible.
In the Cologne Cluster Experiment p0 is 10 bar and pb is of the order 5·10−2 mbar with
a clearly visible jet of ca. 17 - 20 cm length within the vacuum chamber which agrees
well with Eq. 4.4. On the contrary because of the very low background pressure as it
occurs in the here described FTMW experiment the location of the Mach disc would
be far beyond the walls of the vacuum chamber. The main constrains on the jet are
therefore the walls and mirrors of the vacuum chamber.
The shock wave thickness is of the order of the mean free path λ and for the centerline
region it can be estimated using
kB T (x)
λ(x) = √
2σp(x)
(4.5)
with kB the Boltzmann constant, T (x) the temperature at the position along the centerline axis x, p(x) the pressure and σ the hard sphere collision cross section of the buffer
gas. The distance between the mirrors where the free jet can expand is 70 cm and to
estimate the shock front position xS which limits the free jet in the x-direction a detailed
knowledge of the flow properties is necessary.
Scoles ([165], p.23, Tab. 2.2) gives numerical formulas for the Mach number M as a
function of (x/d), with x the downstream coordinate along the centerline axis, assuming
an isentropic, compressible flow of an ideal gas 7 (see Fig. 4.9). For a pin nozzle and
with (x/d) 1 and gases with γ = 5/3 like He, Ne, Ar, etc. this formulae 8 reduces to
x 23
M = 3.232 ·
(4.6)
d
This equation is independent of the background pressure and is only valid in the ZOS
where M > 1. Once the Mach number is known in that region all the other important
7
8
It is also assumed that there are negligible viscous and heat conduction effects.
[165], p.23, Tab. 2.2
4.2 Adiabatic Expansion
55
flow properties can be calculated if the stagnation values like T0 , p0 , n0 (particle density)
are given and the following equation
−1
T
γ−1 2
(4.7)
= 1+
M
T0
2
together with the adiabatic equations, e.g. Eq.4.1, are used, see Fig.4.9.
To get an idea of the numbers involved in the flow process a simple model is applied
to calculate some flow properties, see Fig. 4.10, and a small program was written 9 to
calculate the Mach number, temperatures, pressure, velocity, collision numbers, etc. at
various points downstream the flow axis. The discharge is not explicitly included in the
model but is assumed to correspond to a higher stagnation temperature T0 .
In the simple model the gas pre-expands into the discharge nozzle so that the pressure
drops from the stagnation pressure p0 to the pressure at the nozzle exit pn ∼ 2 mbar 10 .
This pressure drop can be estimated by assuming a constant mass flow rate ṁ = ρvA,
with ρ the density, v the one-dimensional flow speed, and A the cross-sectioned area of
the flow which then can be used to calculate the increase of the flow velocity, i.e the
Mach number via ([165], p.19, Eq. 2.9)
(γ+1)/2(γ−1)
1
2
γ−1
An
2
=
1+
M
A0
M γ+1
2
(4.8)
where An is the flow area at the nozzle exit and A0 the flow area at the valve exit.
According to that the flow gains already ca. 97% of is final speed in the discharge nozzle
and the temperature drops to ∼20K.
It follows a free expansion into the vacuum chamber. For the calculation of the free jet
properties, as it is summarized in Tab.4.1, the discharge nozzle was now not included
and the free jet starts directly behind the valve orifice 11 . The expansion is split into
3 zones. The first is the region of continuum flow where all particles can interchange
energy via collisions and one parameter, the Mach number, characterizes all important
properties at each point along the flow axis, e.g. the isotropic equilibrium Boltzmann
distribution of the velocity. Because the density of the gas decreases rapidly in the expansion the collision frequency cannot maintain continuum flow and a smooth transition
to free-molecular flow begins (zone 2). The low background pressure in this experiment
causes this transition to happen without any conspicuous continuum shock structure. A
measure of this transition is the point xF at which only one collision Z ' 1 is left for each
particle to interact during the rest of the expansion. Usually one collision is sufficient to
achieve a transitional relaxation but beyond xF the particles remain in their states and
the temperature TF of the flow does not change after the transition to a free molecular
flow so that TF is the lowest possible temperature which can be achieved during the
9
based on the formulas [165], Eq. 2.3, 2.4-2.6, Tab. 2.2, and [124], Eq. 4
assuming the input values of Tab. 4.1
11
This means that the distances xi given in the Tab.4.1 have no direct meaning to the experimental
setup but are included to estimate the order of magnitude.
10
56
4 Experimental Setup
Figure 4.9: Top: Mach number along the centerline axis of a free expansion. Bottom:
Temperature along the centerline axis of a free expansion.
4.2 Adiabatic Expansion
57
x F beginning
transition zone
.
.
.
.
discharge
nozzle
2
gas
tube
TF
A0
.
. 5.
free jet
Tn , p n , v n
A nozzle
discharge
energy
.
.
.
.
..
..
.
.
.
background
.
.
. gas
.
.
.
.
T0 , p 0
.
.
4
3
1
.
.
.
free−molecular
flow
.
.
.
.
.
.
.
.
. . .
.
TS . . . .
.
.
.
.
.
.
.
x S begin of shock zone
Figure 4.10: Model of flow development. 1. The stagnation region (tube and solenoid
valve). 2. The gas enters the discharge nozzle. The pressure drops to pn (Eq. 4.8)
A0 is the entrance nozzle area and Anozzle the exit area. Because of the boundary
conditions enforced by the walls the expansion is strictly speaking not adiabatic but
this fact is neglected here. To calculate the temperature drop Eq. 4.1 is used and
Tn is the temperature at the nozzle exit. The gas pre-expands in the nozzle and is
gaining flow speed. When a discharge is applied the energy of the flow increases to
Tn,d . 3. Free jet. Isentropic flow region. Many collisions occur. 4. At xF transition to
free-molecular flow. The translational temperature is ’frozen’. 5. Shock waves appear
at xS and re-thermalize the flow gas.
expansion. Because of the walls or mirror a shock wave will appear at xS which marks
the transition to zone 3. Unwanted collisions with molecules scattered by the surfaces
in front of the expansion re-thermalize or broaden the velocity distribution, i.e heat the
beam, in terms of an effective temperature.
Assuming T0 = 300 K xS can be estimated to be ≈ 58 cm because the mirror distance
is 70cm and at that point the mean free path is of the order of 12cm. The highest
possible mach number would still be M (xF ) ≈ 43, so that a translational temperature
of Ttrans = 0.47K should be achievable. Because the translational temperature changes
along the x-axis the mean temperature between the mirrors should be slightly larger
than 0.5 K.
An alternative approach to estimate the translational temperature based on experiments
with iodine in seeded supersonic beams is given in McClelland et al. [124] where the
terminal Mach number can be estimated by
Mt = F (γ)
Kn
− γ−1
γ
(4.9)
58
4 Experimental Setup
with F (γ) = 2.03 for γ = 5/3 and Kn = λ0 /d the Knudsen number, λ0 the mean free path
in the stagnation zone 12 , and the ’maximum fractional change in the mean random
velocity per collision’ ( (H2 , He) = 0.02, (Ar) = 0.25, and (N e, D2 , N2 , CO, . . . ) =
0.1 − 0.5, [124]). In the case of Ne this results in a minimum translational temperature
of 0.1 - 0.3 K depending on which is taken 13 .
The precursors are heavily diluted in the buffer gas and can usually be neglected by the
calculations of the flow properties. From Table 4.1 it can be seen that there are large
discrepancies between the different kind of estimations of the translational temperature
of a free jet, i.e. 30% between TF (xF ) (using Eq. 4.6) and Tt (xt ) (using Eq. 4.9)14 . The
buffer gases can not be detected by the Fourier transform spectrometer and an direct
verification of the here presented flow values is not possible. Instead the translational
velocity of polar species (precursors or radicals which are created in the discharge, see
Section 4.3) can be measured and compared to the theoretical results as seen in Tab. 4.1,
e.g. a velocity of 840 m/s was measured for a molecule which was cooled by Ne atoms
in a supersonic jet. If this molecule was in thermal equilibrium with Ne a stagnation
temperature of 343 K has to be assumed, see Tab. 4.1. Because the Ne as well as the
precursor gases were used at room temperature it has to be concluded that it was the
discharge that heated the gas to ca. 50◦ C prior to the adiabatic expansion.
12
In McClelland et al. [124] the formula is described with a mean free path at the nozzle throat, which
in Balle & Flygare [6] is interpreted as stagnation value. To calculate λth with the pressure at the
nozzle throat p0 has to be replaced by p0 /G, ([165], p.15) which yields higher temperatures of a
factor 2.
13
T0 was assumed to be 300 K. For Ar and He the results are T(Ar)=0.6 K and T(He)=7.3 K respectively.
14
For comparison also the values Ta derived by using the pure adiabatic equation 4.1 are given in Table
4.1. Because Trot (molecule) > Ttrans (molecule) and Ttrans (molecule) ≥ Ttrans (N e) it is clear that
for Trot (molecule) less or equal 0.5K (see Fig. 4.11) Ta can not be ∼ Ttrans (N e). Therefor Ta does
not correctly describe the physical conditions of the buffer gas in the jet.
4.2 Adiabatic Expansion
59
Table 4.1: Free jet flow properties for Ne
Experimental / particle parameters
γ
5/3
∼0.2 - 0.5
mN e [amu]
20.18
σN e−N e [nm2 ]
0.24
T0,1 [K]
293.15
p0 [bar]
2.5
T0,2 [K]
∼ 343
pb [mbar]
2.7·10−6
T0,3 [K]
500
pb,load [mbar]
6.7·10−5
gas mass flow [sccm]
30
repetition rate [Hz] 2
d [mm]
1
D [mm]
5
18
Under standard conditions there are ≈ 6.7·10 particles per pulse.
Jet properties at
xF [mm]
M (xF )
TF (xF ) [K] ≈ Ttrans,min
Tt (xt ) [K] ≈ Ttrans,min
TZ<5 [K] & Trot,min
Ta [K]
p(xF ) [mbar]
v(xF ) [m/s]
vt [m/s]
ρ(x = 350) [1/cm3 ]
T0 (293.15 K), p0
49
48.4
0.5
0.1-0.3
1.1
1.2-4.3
2.3·10−4
776.5
777.1
∼ 1014
T0 (300 K),p0
44
47.8
0.47
0.1-0.3
1.68
1.2-4.4
2.4·10−4
785
786
T0 (343 K), p0
42
44
0.6
0.18-0.4
2.13
1.4-5.1
3.1·10−4
839.7
840.5
Jet boundaries
xM [m]
>4
∅barrel shock [m]
>2
γ = cp /cv the heat capacity ratio, from [124] p.950-951, mN e atomic mass of Ne, σN e−N e
hard sphere collision cross section of Ne [5], T0,i stagnation temperature i, p0 stagnation
pressure, pb = background pressure without gas load, pb,load background pressure with
gas load, d diameter of valve orifice, D diameter of nozzle exit,
x distance from nozzle exit, xF freezing point with Zr,binary (xF ) ' 1, xt point where
terminal Mach number is reached [124], M is taken from [165], the following temperatures T are all translational temperatures, TF (xF ) temperature at freezing point, Tt (xt )
temperature corresponding to Mt with Mt as in [124], TZ<5 temperature at point where
only less than 5 collision remain per particle (a rotational relaxation needs less than
5 collisions), Ta as in Eq. 4.1 using pb (first value) and pb,load (second value), p pressure at xF [165], xM location of Mach disk, ∅barrel shock diameter of the barrel shock,
v flow velocity at x, vt terminal velocity, ρ density at x. It should be xF ≈ xt and
T (xS ) < T (xF ) ≈ T (xt ) < Ta .
60
4 Experimental Setup
Molecular collision rates are important for the translational, rotational and vibrational
relaxation process as well as for chemical reactions and cause the most important deviations from ideal predictions based on the continuum properties. Two-body collision rates
scale with p0 d, whereas three-body collisions required to build molecules out of atoms
scale with p20 d. This means that any chemical reaction takes place in the discharge nozzle
or shortly after the particles enter the vacuum chamber (x/d) ∼ 1 15 where the density
of the flow is still high. After the radicals have formed kinetic processes, such as energy
exchange for cooling of internal states, first decrease and finally ’freeze’, i.e. terminate.
The effectiveness of such cooling processes depends on the number of collisions experienced by each particle. The total amount of binary collisions Ztot can be calculated by
integrating the collision rates Z(x) from x = 0 to x = ∞ and is typically of the order of
102 (pin nozzle) to 103 (slit nozzle) collisions. From this number the number of collisions
Zr remaining in the expansion at a given point x along the flow axis can be calculated
and gives a measure of the positions of the ’transition zones’ where an average particle
will not experience enough collisions to achieve translational or rotational equilibrium.
In the case of the translation relaxation only a few collisions Z ' 1 are required and this
transition often occurs beyond the point where the velocity ratio v(x)/v∞ ∼ 0.98 [165]
16
, see Tab.4.1 (xF ).
Rotational relaxation of small molecules like C3 N need slightly more collisions Z . 5.
Simple diatomic molecules may require ca. 104 for the vibrational relaxation. The needed
vibrational collision number for large polyatomic molecules and the rotational collision
number of most diatomic molecules are of the order 10 to 100 so that the vibrational
modes of diatomic do not participate in the expansion [165].
It is not only the collision number which determines the effectiveness of cooling but also
the cross section σ of the energy transfer (e.g. Erot → Etrans , Evib → Etrans ) compared
with Etrans → Etrans . Usually it is
σ(Etrans → Etrans ) > σ(Erot → Etrans )
> σ(Evib → Etrans )
(4.10)
so that the rotational energy is smaller than the vibrational energy but higher than
the translational energy. In most cases is σ(Erot → Erot ) > σ(Etrans → Etrans ) and
an equilibrium within the rotational levels is achieved with a temperature Trot . The
population of the vibrational levels usually do not follow a Boltzmann distribution but it
is nevertheless standard to speak of a vibrational temperature Tvib which is a temperature
corresponding to a Boltzmann distribution which has been approximated to the real
distribution. After the expansion the gas has usually the following order of temperatures:
Ttrans < Trot < Tvib [43].
The Ttrans , Trot , Tvib values depend on the expansion parameters and are typically
Ttrans < 5 K, Trot < 10 K, Tvib < 100 K (Demtröder et al. [43], 3 bar Ar with 5%
NO2 with a d=50 µm nozzle.). Grabow et al. [69] who did measurements on the SO
15
16
see [165], p. 25, Fig. 2.10
For this experiment v(x)/v∞ ∼ 0.99 .
4.2 Adiabatic Expansion
61
radical (with X3 Σ− ) reported that the effectiveness of the cooling by a beam expansion
depends inversely on the heights of the energy levels to be cooled. Rotational transitions with energy differences of only a few cm−1 are cooled much more effective, i.e. the
rotational temperatures Trot can be as low as a few degree Kelvin, whereas vibrational
states where found to have Tvib of a few hundred K.
If for the rotational relaxation only 3 or less collisions are required the rotational temperature Trot is expected to be between 0.2 - 2.1 K 17 . In Fig. 4.11 a measured C4 N
spectrum is plotted together with a theoretical spectrum corresponding to 0.5 K 18 .
In the work of Grabow et al. [69] molecules in a beam expansion without a discharge
are found to have transitions with low vibrational energies, e.g. OCS, SO2 or SO,
which become much stronger in intensity when the discharge is turned on within the
nozzle orifice. This is in agreement with Schlachta et al. [164] who studied a variety of
diatomic radicals like OH, NH, CN, and C2 and report rotational temperatures of 5-50
K, depending on the expansion parameters, and in many cases vibrational temperatures
of several thousand Kelvin when applying a discharge.
The main advantages for the analysis of the spectrum due to the cooling of the molecules
in the jet can be seen by the formula describing the number of molecules in a certain
state νi , Ji
−Evib
−Erot
N0 Y
)
(
) (
N (νi , Ji ) =
(2Ji + 1)e kTrot e kTvib
(4.11)
Z i
, where νi is the vibrational quantum number of the vibrational mode i and Ji the
rotational quantum number within the vibration νi , and Z the overall partition function:
• The population number N (νi , Ji ) reduces to a few ro-vibrational levels, so that the
number of the absorption lines decreases drastically.
• Because the absolute number N0 remains constant the population of the lower
levels increase and instead of many weak lines a few strong lines are conceived in
the spectrum, see Fig.4.11
17
18
see Table 4.1 with Tt (xt ) = 0.2 K and TZ<5 = 2.1 K.
It is however not unproblematic to make a straight forward comparison between the measured and
the calculated intensities. Some people including myself believe that to estimate the rotational
temperature of a molecule measured with a FTMW spectrometer the effect of the Q-factor (see
section 4.3) has to be considered. The result including this effect would be a rotational temperature
of 0.2K.
62
4 Experimental Setup
Figure 4.11: Theoretical intensities of the C4 N rotational transitions corresponding to
0.5K together with the measured lines as discussed in Chapter 7.2.
4.3 The Fourier Transform Microwave Spectrometer
63
4.3 The Fourier Transform Microwave Spectrometer
The Fourier Transform Microwave (FTMW) Spectrometer at the Harvard/DEAS Spectroscopy Laboratory exists since 1995 and was build following the classical experiment
from Balle & Flygare [6, 29] published in 1981. At the moment the FTMW spectrometer
operates in two modes, the low band mode between 5 and 25 GHz and the high band
mode between 25-40 GHz. Both modes were used for the measurements of the radicals
presented in this work. A block diagram of the used FTMW spectrometer in its low
band operational mode is shown in Fig. 4.1. A schematic diagram of the FTMW was
already published in [122] but Fig. 4.1 reflects some rearrangements which were done
since then and it also shows the cooling of the mirrors. Between 1997 and 2000 the
sensitivity could be improved by more than an order of magnitude and the results were
published in [118].
The spectrometer can only be used within resonant frequencies ν of a TEMmnq mode of
the Fabry-Perot (F.-P.) resonator 19
"
#
1 (m + n + 1)
ν = ν0 (q + 1) +
(4.12)
π cos(1 − Rd )
with ν0 = c/2d, d the distance between the mirrors, R radius of curvature of both
spherical concave mirrors, c speed of light. The experiment is set up in a confocal
arrangement of the mirrors (R=d) with d=70cm and the TEM00q modes which are the
dominant modes are therefore
1
ν = ν0 (q + 1) +
(4.13)
π
and separated by ν0 =214 MHz. One of the mirrors, the ’drive’ mirror, can be moved
and allows the frequency tuning of the spectrometer. To change the resonance frequency
from ν1 to ν2 = ν1 + ∆ν by moving the drive mirror from position 1 with d1 to position
2 with d2 = d1 − ∆d the Eq. 4.12 transforms to
c 1
1
d d2 ≈d2 c(q + 1) ∆d
∆ν =
−
(q + 1) 1 =
2 d1 d2
2
d2
yielding
∆d =
c∆νd2
c(q + 1)
.
(4.14)
At 20 GHz Eq. 4.13 results in (q + 1) ≈ 90 half wavelength between the mirrors and if a
frequency search with step sizes of ∆ν = 500 kHz is desired Eq. 4.14 yields a separation
∆d for each step of ca. 20 µm 20 .
19
20
nomenclature and formulas of the following section are mainly taken from Balle & Flygare [6]
This means that also mechanical vibrations can vary the cavity resonant frequency and thereby
contributes to the low frequency noise.
64
4 Experimental Setup
Using separate antennas, i.e the ’drive’ antenna to connect the F.-P. cavity to the oscillator injecting the 1µs pulse and the ’signal’ antenna to couple the electric field of
the resonator to the detector circuit, which can be tuned externally and independently
critically coupling can be obtained. Both antennas are ’L’ shaped and can have different
geometrical dimensions (varying from 0.5 to 2 cm) depending on the frequency range
they are used for. Various antenna separations from the mirror surface were tested.
During the measurements for the Cn N chain molecules two equal antennas specified for
9.5 GHz were used and both were separated from the mirror surface by 0.08 mm to yield
an optimum coupling.
An important parameter of the experiment is the Q factor (quality factor) which is
defined as
Q = ωW/P
(4.15)
where ω = 2πν is the angular frequency of the radiation, W is the total energy stored
in the cavity and P is the power dissipation, i.e. the energy loss per time −dW/dt. In a
quasi-optical treatment of a resonator there are mainly two reasons for the power inside
the cell to dissipate. (1) The power can be dissipated by diffracting on the mirrors. This
problem can be made arbitrarily small by increasing the radius of the mirrors a. The
a2
Fresnel number F ≡ λR
with F&1 is a measure of the Fresnel diffraction and making
√
F=1, i.e. a = Rλ insures a good Q because the mirror captures more than 95% of the
wave amplitude at any point [6]. The spectrometer has mirrors with radii a of 36 cm
which cause a cut-off frequency at ∼5 GHz, see Fig. 4.13. A general discussion of this
problem is given in the classical work of Boyd & Gordon [21] and Kogelnik & Li [105]
21
. The upper limit at about 40 GHz is not due to diffraction but is imposed by cut-offs
in amplifiers and the high-band PIN switch. (2) Ohmic losses in the metallic mirrors.
Based on the assumption that the dissipations are only due to ohmic losses a theoretical
Qth can be calculated with
d
Qth =
(4.16)
2δ
where δ is the skin depth, i.e. the distance in the conductor at which the amplitude of an
electromagnetic wave has decreased to 1/e of its value at the surface. In this experiment
the mirrors are made of aluminum which has a δ of 8.5·10−5 cm at 10 GHz thus resulting
in a Qth ≈ 4.1·105 . The resonant cavity mode has a Lorentzian line shape and the full
width ∆νc at half height is given by
νc
νc
∆νc =
, or Q =
(4.17)
Q
∆νc
The decay time constant τc of the energy W in the cavity can be obtained by considering that the energy W decays at a rate proportional to W and 1/τc defined as the
proportionality constant
W · (1/τc ) = −
21
dW
(4.15) 2πνc W
≡P =
, thus following
dt
Q
τc =
Q (4.17) 1
=
. (4.18)
2πν
2π∆νc
Storm et al. [171] describe a way to circumvent this problem by using a cylindrical resonator to
operate in TE01q modes instead of TEM00q as used in the spectrometer described here.
4.3 The Fourier Transform Microwave Spectrometer
65
power
ν
Q= ∆ν
Q2 > Q1
Lorentzian
line
shape
signal
1 MHz
band width Fabry−Perot
Q1
Q2
polarization
ν
400 kHz
νo
νpol
Figure 4.12: Cavity mode Lorentzian line shape. The quality factor Q is a measure of
the full width ∆ν at a given frequency ν of the cavity mode. Different Q’s result in
different power values for a given frequency. If the mirrors are adjusted for a cavity
mode center frequency νo of 10 GHz the bandwidth of the Fabry-Perot is ∼ 1 MHz.
The polarization pulse has a 400 kHz offset from the expected molecule emission
frequency.
In this experiment high-quality factors (Q up to ∼ 104 ) have been obtained over much
of the centimeter-wave band. The highest unloaded Q0 22 now achieved is 2·105 , which
is close to the above calculated theoretical limit of about 4·105 . When the cavity is
critically coupled, the loaded QL 23 is about 105 . For a cavity with Q=104 at νc = 10
GHz the decay time τc is 0.16 µs which corresponds to a cavity band width ∆νc of 1 MHz,
see Fig. 4.12. This means that in praxis the maximum frequency region which can be
recorded at a time is of the order <1 MHz, i.e. 500-600 kHz. After this frequency region
is examined a new frequency can be set and a computer moves the mirrors appropriately
to match the desired center frequency with the cavity mode.
Line intensities I are sensitive to the cavity Q. In [6], Eq.(40), a relation between the
emitted electric field in the cavity and the Q factor is given in form of a proportionality
E(r, t) ∼ Q, so that I ∼ Q2 . However the measurable Qef f , in which also influences
of the detection circuit are considered, is no smooth function of the frequency ν and
can vary rapidly between adjacent frequency regions so that measured intensities can
differ strongly from theoretically predicted. During this thesis many new Q-values cor22
23
The unloaded Q, Q0 , accounts for power dissipation in ohmic losses
The sum of all dissipative elements defines the loaded Q, QL , i.e diffraction, antenna coupling, etc..
66
4 Experimental Setup
Figure 4.13: Measured Qef f and calculated Qth for the Fabry-Perot cavity. Set 1 - 4
are effective Q values including effects of the electrical detection circuits measured by
Sam Palmer (April 1998). Set 5 was measured during this work. Between 6 and 13
GHz the Q-value can change rapidly by stepping to an nearby frequency which is best
seen in Set 5. Therefore a comparison between absolute intensities of even close lying
emission lines is nearly impossible. ’s=1.3mm’ and ’d=203µm’ means that the signal
antenna was separated by 1.3mm from the mirror surface and the drive antenna by
203µm.’L=1.9cm’ is the length of the antenna and the frequency in brackets is the optimum coupling frequency for that antenna. The theoretical Q values were calculated by
√
Sam Palmer using the formulae Q = 2πd νc α1 , with αref lectiv = 4π λδ = 1.43 · 10−4 νGHz ,
a2
δ the skin depth and αdif f ractiv = 16π 2 F e−4πF = 23.79νGHz e−1.893νGHz , F = λd
the
Fresnel number in cgs units.
4.3 The Fourier Transform Microwave Spectrometer
67
responding to the used antenna set and frequencies of interest were determined and used
as reference values, see Fig. 4.13.
The essential cavity optics and first-stage amplifier are cooled with liquid nitrogen,
thereby reducing the noise equivalent system temperature from 800 K to about 200 K,
which is nearly a factor of four better sensitivity 24 . Above 10 GHz diffraction losses in
the open resonator are negligible, and roughly two-thirds (110 K) of the receiver noise
is from the cold amplifier and one-third from the 77 K mirrors. Below 10 GHz diffraction from the open resonator contributes significantly to the cavity Q, and the system
temperature rises to about 400 K. The cooling is done separately for each mirror by continuously flowing liquid nitrogen through a copper coil soldered to a copper disk making
good thermal contact with the mirror’s back surface. Thermal isolation of the mirrors
is achieved by suspension on epoxy strips. Condensation of gas from the supersonic jet
does not appreciably degrade the reflectivity of the cold mirrors.
The supersonic molecular beam is oriented parallel, rather than perpendicular as described in [6], to the Fabry-Perot axis and can be removed via a gate valve assembly to
service the discharge nozzle even when the spectrometer is operated at 77 K.
The transition lines measured by this spectrometer appear Doppler shifted, see Fig. 4.14.
The Doppler separation is a measure of the relative speed ±vmolecule of the incoming
molecules with regard to the back and forward traveling microwaves and is symmetric
with respect to the rest frequency νo of the molecules.
∆ν
vmolecule
2
=
,
νo
c
Hz/2
Here 0.107M
· c = 840.45 ms = speed of the molecule. see Fig. 4.14. The line separation
19083.2M Hz
and thus the speed of the molecules can differ due to their size or charge, i.e ions are
faster than neutral species.
24
”The sensitivity of the present liquid-nitrogen-cooled FTM spectrometer is far from the fundamental
limits. Liquid helium cooling of the optics and the first stage of receiver amplification might improve
the sensitivity by nearly an order of magnitude. ” [179]
68
4 Experimental Setup
time domain
E
t /µ s
ν o = 19083.2139 MHz
signal
/ µV
11 kHz
Doppler
∆ν = 107 kHz
frequency ( 400 kHz − ν o )
Figure 4.14: Time and Frequency Domains. The computer receives a FID signal in the
time domain and Fourier transforms it into the frequency domain. The molecules
emission frequency νo is the mean value of the two doppler shifted lines. These originate from the el.mag. waves which travel back and forth in the FP-cavity relative to
the molecule’s flight direction. The Fourier transform FID is displayed as a frequency
offset from the pump frequency νpolarization . The plotted line is an unidentified line
measured during a 13 CCCN survey.
5 Linear CnN, Cyanide Radicals
“ The important thing in science is not so much to obtain new facts
as to discover new ways of thinking about them. ”
Sir William Bragg
Cn N are open shell molecules, radicals in the technical sense of the term, and therefore
paramagnetic. All members of the even numbered radicals are found in the 2 Π electronic
ground state through theory [144] and experiment (e.g. this work) whereas in the case
of odd membered cyanide radicals there is an expected change from 2 Σ to 2 Π ground
state for increasing n [99, 144]. Dipole moments have not been measured for any of the
Cn N chains discussed here, see Tab. 5.1 and 5.2 but instead ab initio calculations have
been performed [144, 20]. In each series the dipole moment is found to increase steadily
with chain length; given that the radicals have the same ground state.
Other carbon chains like Cn H and HCn N which both are readily detected in space are
of great importance regarding the Cn N chains. The first ones, Cn H (or Cn CH, with
CH playing the role of N), is isoelectronic to the Cn N chains and in this work is often
used for references and comparison of molecular constants and properties like magnetic
hyperfine constants or electronic energy separations, see Appendix A. The second ones,
the cyanopolyynes HCn N are interesting because mainly of two reasons. (1.) The role of
Cn N chains in the production and depletion of interstellar cyanopolyynes, see Chapter 8.
(2.) On a theoretical point of view the odd Cn N chains can be thought of daughter
molecules of acetylenic HCn N by removal of the terminal hydrogen atom which results
in an π 4 σ 1 2 Σ electronic state for the cyanide radicals with the radical electron localized
at the terminal carbon [144]. An electron transfer from a π orbital into the half-filled σ
orbital will cause a shift in the charge distribution and generates a nonpolar or in praxis
nearly nonpolar 2 Π state radical which is close in energy, (see Fig. 5.1 top and bottom
right). This causes a principle difference between Cn N chains with odd n or even n. The
electron configuration of even Cn N chains can be explained by adding the electrons of
an extra C atom to an odd numbered Cn N chain after the π → σ electron transfer, (see
Fig. 5.1 bottom).
70
5 Linear Cn N, Cyanide Radicals
In the following part a brief introduction to the Cn N molecules known so far is given.
The odd numbered Cn N (n=1,3,5,...,13) members:
CN Emissions of CN in the violet band first measured in the 1920’s were later (1937 by
Adel [2], 1941 by McKellar [126]) rediscovered in the tails of comets (see Herzberg
[85]) and in absorption towards the star ξ Ophiuchi (in 1941 by Adams [1]).
The exploration of the µm-wave spectrum of the CN radical was widely promoted
by radio astronomical observations. Here CN was first measured by Jefferts et
al. [94] in 1970 towards Orion A and W51 and Penzias et al.[149] and Turner &
Gammon [184] were able to determine the hyperfine (hf) structure of CN in the
vibrational ground state to high precision.
At this point it is worthwhile mentioning that the rotational transition N= 1 → 0
at 113 GHz is also of cosmological interest as is shortly described now. In 1964
Penzias and Wilson [148] discovered during their work at the Bell Laboratories
the existence of the isotropic cosmic background radiation (CBR) which was soon
interpreted by Dicke et al. [44] as the relic of an early stage of our universe when
the electromagnetic field decoupled from matter. Interpretation of the intensity
ratios of the R(0) violet transition X 2 Σ+ → B 2 Σ+ at 3874.6 Å and the R(1)
transition by Thaddeus et al.[177] resulted in a rotational temperature [147] that
came close to the today excepted value for the CBR of 2.725 K [71] and led to the
conclusion that CN is thermally excited by the background microwave radiation;
an interpretation which is in sharp contrast to the one given in 1950 by Herzberg
[83] where it is said that ”the rotational temperature of 2.3◦ K [...] of course only
[has] a very restricted meaning”. This example shows nicely that the relevancy of
observations can change significantly with the progress of science.
Also vibrational excited states have been investigated. Important work was done
by Skatrud et al. [167], who determined the Dunham coefficients, the spindoubling, and the hf parameter for the v = 0,1,2,3 states. Johnson et al. [96]
have studied the v = 2 state and Ito et al.[93] gave an analysis of the excited
states up to v = 10. A good overview of this work for states from v = 0 to 7
and additional measurements up to the THz region is given in the PhD thesis of
E. Klisch [104].
Isotopic measurements of 13 CN have been done by Bogey et al. between 1984-86
and included ground state [16] and excited vibrational states ν ≤ 9 [17] as well as
a study of the isotopic dependence of the molecular constants.
12
C15 N was first measured in space with the KOSMA 3m telescope towards Orion
A by Saleck et al. [160] and little later spectroscopically characterized by Saleck
et al. [161] in 1994.
Thomson et al. [180] determined the dipole moment to be 1.45 Debye.
71
Figure 5.1: Top: Schematic diagram of electron configuration of CN π 4 σ 1 (X 2 Σ).
Bottom: CCN σ 2 π 1 (X 2 Π) electron configuration. On the right: CN changing from
π 4 σ 1 (Σ) into a π 2 σ 3 (Π) state after electron transfer. (see Engelke [52] and Rajendra
et al. [158]).
72
5 Linear Cn N, Cyanide Radicals
An important result of the isotopic measurements is that CN as many other
diatomic molecules like O2 , CO, and NO deviate significantly from the BornOppenheimer approximation.
C3 N The linear carbon chain radical C3 N (cyanoethynyl) was first detected in the gas
phase with a radio telescope by Guélin and Thaddeus [78, 79] in 1977 in the
molecular envelope of the carbon-rich star IRC+10◦ 216. The identification was
based on two emission line doublets at 89 and 99 GHz and the B, D and |γ|
molecular constants have been determined. The detection was later confirmed
by observations in many other interstellar sources (e.g. [56, 10]) and also the ρtype doubling and magnetic hyperfine constants were determined by astronomical
observations [76]. The laboratory detection of C3 N had to wait until 1983 when
Gottlieb at al. [66] made first measurements in the mm-range.
Mikami et al. [130] studied the ν5 vibrationally excited bending mode state of C3 N
by performing measurements at 208 to 278 GHz which resulted in the determination of several parameters including the l-type doubling parameter q.
Sadlej et al.[159] studied the A2 Π, B 2 Π, C 2 Σ and X 2 Σ ground state of C3 N by ab
initio calculations and obtained a dipole moment of 3.0 D.
First measurements on the isotopic species were done by McCarthy at al. [121]
in the mm-range (near 250 GHz). These efforts resulted in a detailed knowledge
of the geometry of C3 N and also a preliminary estimation of the hyperfine coupling constant bF (13 C) for the 13 CCCN and C13 CCN radicals. In the same work
Botschwina presented calculations of the vibration frequencies of C3 N. Magnetic
hyperfine structure (hfs) is a sensitive probe of the electronic structure of open
shell molecules and in this work a detailed measurement of the magnetic hyperfine
structure of 13 CCCN, C13 CCN, CC13 CN, and CCC15 N is presented with the aim of
getting information on the distribution of the unpaired electron spin density along
the carbon chain, (see Chapter 7). The electric quadrupole hyperfine structure of
the 13 C-isotopes was also determined.
During a line survey of the C-star envelope IRC+10◦ 216 carried out by Cernicharo
et al. [34] 10 lines of low intensity were assigned to 3 isotopic species of C3 N. Two
out of four lines assigned to 13 CCCN are not in agreement with the laboratory
work presented here, (see Chapter 8).
C5 N In 1991 Pauzat et al. [144] noted that for odd numbered Cn N chains with n>3 a
change from 2 Σ to 2 Π electronic ground state is expected and C5 N was predicted
to be in a 2 Π ground state. In detail this means, that if the energy of the molecular
orbital 7σ is higher than that of 3π, C5 N should be in a 2 Σ ground state. A 2 Π
state would apply if the energy of the 3π orbital is higher than that of the 7σ. High
level coupled cluster calculations by Botschwina [19] predicted the ground state
to have a 2 Σ symmetry. In 1997 Kasai et al. [99] published the first detection of
C5 N by Fourier transform microwave spectroscopy between 5 and 17 GHz and the
ground state was determined to have 2 Σ symmetry. Shortly after Guelin et al. [77]
73
detected C5 N in the dark cloud TMC-1, (see Chapter 8). Electronic transitions of
2
Π ← X 2 Σ of C5 N in a neon matrix have been measured in the visible by Grutter
et al. [72] between 427 and 471 nm.
C7 N The absorption bands of the 2 Π ← X 2 Σ electronic transition of C7 N have been
measured in the visible in a neon matrix by Grutter et al. [72]. They find a ” great
deal of similarity [...] in the vibrational pattern of the C5 N and C7 N” and conclude
that C7 N is probably also in a 2 Σ electronic ground state. An ab initio calculation
by Botschwina et al. [20] using restricted Hartree-Fock and partially restricted
open-shell coupled cluster theory yield an opposite result for which C7 N has not
2
Σ but instead a 2 Π electronic ground state. During this work a measurement
campaign was started for linear C7 N but ended without any result. Our conclusion
is that C7 N might be in a 2 Π ground state because if C7 N has a 2 Σ ground state
with a dipole moment of roughly -3.1 D to -4.2 D but is less abundant than C5 N
it still should have been detected during our search. The dipole moment of the
radical in a 2 Π state is calculated to be between -0.5 and 1.0 D [20] and could have
caused the emission of the radicals to fall under the detection limit of the FTMW
spectrometer, (see Chapter 7.3).
C9 N - C13 N Grutter et al.[72] published 6K neon matrices measurements of C5 N up
to C13 N radicals in the visible and near IR between 470 and 830 nm. For C9 N,
C11 N and C13 N the 2 Π ← X 2 Π states were studied with several vibrational bands
including the C≡C, C≡N, and C-C stretching modes.
The even numbered Cn N (n=2,4,6,8) members:
C2 N CCN was first observed in the laboratory by Merer and Travis [128] in 1965. The
experiment was done with a flash photolysis of diazoacetonitrile and they observed
an absorption spectrum of X̃ 2 Π → Ã2 ∆, X̃ 2 Π → B̃ 2 Σ− , and X̃ 2 Π → C̃ 2 Σ+ in
the region 4710-3480 Å. They deduced that CCN is linear in the ground as well as
in the excited states. Furthermore they found a Renner-Teller (R-T) interaction
for both X̃ 2 Π and Ã2 ∆ states. Kakimoto et al. [98] reinvestigated the (000)(000) band of the Ã2 ∆-X̃ 2 Π system through Doppler-limited dye laser excitation
spectroscopy and extended this study to the (010)-(010) and (020)-(020) sequence
band [100] in 1984. The experimental R-T splitting measured by Oliphant et al.
[143] is ∼ 144 cm−1 .
Theoretical work including high level ab initio calculations was performed by Mebel
and Kaiser [127], Pd and Chandra [145] and Martin et al. [116] which showed
that CCN(2 Π) does not seem to be the most stable isomer but CNC(2 Πg ) by 3.1
kJ/mol [116]; cyclic C2 N(2 A1 ) lies 50.7 kJ/mol above CNC, see Fig. 5.2; Merer
and Travis also observed CNC [129]. Measurement of laser-induced fluorescence
spectra yielding ground state vibrational frequencies at 1923 cm−1 (ν1 ), 325 cm−1
(ν2 ), and 1051 cm−1 (ν3 ) were done by Brazier et al. [23] and Oliphant et al.
74
5 Linear Cn N, Cyanide Radicals
Figure 5.2: Calculated geometries of C2 N. The bond distances are given in Ångstroms,
bond angles in degrees for the B3LYP/6-311G∗∗ and CCSD(T)/TZ2P (bold numbers)
calculations [116]. The point groups and electronic states are also given.
[143]. Measurements of vibration-rotation spectra were published by Suzuki et
al. [173] including hyperfine transitions in the electronic A state by a microwaveoptical double resonance technique. Feher et al.[55] measured the ν1 vibrationrotation transitions by infrared absorption spectroscopy using a tunable diode
laser. The first pure rotational spectrum of CCN in the 2 Π electronic ground
state was measured by Ohshima and Endo [142] in 1995 by Fourier transform
spectroscopy at 35 GHz. They determined the magnetic hyperfine constants a− ,
b, d, eQq0 and eQq2 and refined the known rotational, centrifugal distortion, and
fine structure constants to high precision. Pd et al. [145] and Ohshima et al. [142]
gave a nice overview of the field including comprehensive reference tables. The ν2
bending fundamental of the CCN radical in its X̃ 2 Πr state was studied by Allen
et al. [3] using infrared laser magnetic resonance spectroscopy.
C4 N Ding at al. [46] suggested that C4 N might be the first member among the Cn N radicals with even n having stable low-lying cyclic isomers with the three-membered
ring isomer NC-cCCC only 2.8 kcal/mol higher in energy than the linear CCCCN
but with a larger dipole moment of 0.62 D, (see Fig. 5.3). In this work the first
observation of the pure rotational spectrum of linear C4 N in the 2 Π electronic
ground state (as mentioned in [4]) is presented. Only the Ω = 21 spin sub levels
were examined. Transitions of C4 N with ∆ F = 0,-1 from J= 32 − 12 up to J= 92 − 72
were measured and yield precise hyperfine coupling constants due to the nitrogen
nucleus.
C6 N The C6 N radical is the largest member among the Cn N chains for which the pure
rotational spectrum was observed. In this work the molecule was found to have a
ground state with 2 Π symmetry as expected and the Ω = 21 spin sub levels were
− 19
were
examined. Here transitions with ∆ F = -1 from J= 92 − 72 to J= 21
2
2
75
Figure 5.3: Theoretical geometries of C4 N. The bond distances are given in Ångstroms
and the angles in degrees for the B3LYP/6-311G(d) and QCISD/6-311G(d) (in bold)
calculations, see [46]. The point groups are written under each structure.
measured.
C8 N The effort undertaken during this thesis to measure C8 N remained unrewarded. It
was expected to find a radical in a 2 Π ground state with a dipole moment larger
than 0.3 D. The rotational constant B was estimated to be ∼410 MHz.
In contrast to the odd-membered Cn N radicals (see Tab. 5.1) where already CN, C3 N,
and C5 N were detected in space none of the even-numbered molecules (see Tab. 5.2) were
observed so far beside the laboratory. There is no doubt that the detailed information
on the hyperfine structure of C4 N and C6 N is indispensable for their future astronomical
detection but the main obstacle is seen in their small ground state dipole moments of
0.14 - 0.33 D [144].
76
5 Linear Cn N, Cyanide Radicals
molecule
ground
state
CN
X2 Σ+
C3 N
X2 Σ
C5 N
X2 Σ
C7 N
probably
X2 Π
Table 5.1: Cn N, n odd.
dipole exp B value first
moment (predicted) detection
[Debye]
[MHz]
[astro-source]
-1.45
56693.47
astro,visible
astro,radio
lab,mm-µm
lab,THz
-2.2
4947.62
astro,mm
lab
-3.4
1403.08
lab
astro
0.8
(583±1)
not yet
detected
year
References
1941
1970
1977
1995
1977
1983
1997
1998
Adams [1]
Jefferts [95]
Dixon [47]
Klisch [103]
Guélin [78]
Gottlieb [66]
Endo [99]
Guélin [77]
Botschwina [20]
Dipole moments are taken from Pauzat et al. [144]
molecule
C2 N
C4 N
C6 N
C8 N
Table 5.2: Cn N, n even.
ground dipole exp B value first
state moment (predicted) detection
[Debye]
[MHz]
2
XΠ
0.40
11938.58
lab,UV-vis
lab,µm
X2 Π
0.14
2422.70
lab,µm
2
XΠ
0.31
873.11
lab,µm
X2 Π
(410±2)∗
not yet
detected
year
References
1965
Merer [128]
1995 Ohshima [142]
2000
this work
2001
this work
Dipole moments are taken from Pauzat et al. [144] and Pd & Chandra [145]
in the case of C2 N. * estimated by the author
6 Theoretical Considerations
“Die Überlegung ist lustig und bestechend; aber ob der Herrgott
nicht darüber lacht und mich an der Nase herumgeführt hat, das
kann ich nicht wissen...”
Albert Einstein, letter to C.Habicht, 1905
Although the history of spectroscopy dates back to the mid 19th century 1 the emission
and absorption of light by atoms and molecules can only be correctly understood in
a modern quantum mechanical treatment of the phenomenon. Today the basic theory
of the interaction of particles like atoms, molecules, and radicals with electro-magnetic
waves is on wide parts well understood but still not complete. Radicals for instance
are not only difficult to produce in the laboratory but show also special features in
their spectra which make the work with these molecules especially challenging. It is
not simply the rotational and vibrational motions which have to be considered but also
the electronic and magnetic behavior of these molecules which because of their open
shell structure can be very complicate. To demonstrate this a hypothetical energy level
diagram of an radical in a 2 Π ground state is given in Fig. 6.1 including an inlet showing a
spectra of several hyperfine components of one rotation transition. Transitions between
these energy levels are governed by selection rules and in many cases spin statistics
determine the intensity of the measurable lines. As has been seen in Chapter 4 the
used FTMW spectrometer has a very high frequency resolution and an extremely high
sensitivity so that in many cases even the faintest lines can be detected. For the analysis
of a measured spectra all of these lines have to be assigned and labeled by quantum
numbers corresponding to the energy levels. The focus of this chapter is to introduce
an appropriate Hamiltonian to describe the rotational spectra of linear radicals in a 2 Σ
or 2 Π electronic ground state; in particular for the Cn N radicals.
The basic references are the standard text books of Bernath, “Spectra of Atoms and
Molecules” [12]; Edmonds, “Angular Momentum in Quantum Mechanics” [51]; Gordy &
Cook, “Microwave Molecular Spectra” [63]; Herzberg, “Molecular Spectra and Molecular
1
In 1859 Kirchoff and Bunsen discovered that each element has its own characteristic spectrum.
78
6 Theoretical Considerations
spectrum
Π
Π
7B
3/2
J=5/2
N=3
f
e
intensity
2
5B
J=3/2
6B
f
e
S=+1/2
frequency
N=2
4B
2B
Aso
N=1
N=0
e
J=5/2
f
5B
S=−1/2
e
J=3/2
J=1/2
F=5/2
F=1/2
F=3/2
F=3/2
F=5/2
F=1/2
F=3/2
f
e
f
3B
Rotation
Π
F=1/2
F=3/2
F=1/2
1/2
Fine structure
Hund(b)
Λ −doubling
Hyperfine structure
Hund(a)
Figure 6.1: Hypothetical energy level diagram of a 2 Π radical including rotational,
fine structure, Λ-doubling and hyperfine structure effects. The inlet on the upper
right shows an exemplary spectrum of one rotation transition with several hyperfine
components.
Structure I & II” [83, 82], “The Spectra and Structure of Simple Free Radicals” [84];
Townes & Schawlow, “Microwave Spectroscopy” [181]. Important contributions came
also from papers and works of Brown & Schubert [27], Frosch & Foley [57], Kawaguchi
et al. [102], and Klisch [104].
The frequency ν of emission lines correspond to the difference of two energy levels
∆E = E 00 − E 0 = hν. If the energy levels are known all transitions can be computed
and frequency predictions can be made. Using the stationary Schrödinger equation the
energies are the eigenvalues of the Hamilton operator Ĥ
ĤΨ = EΨ
(6.1)
which reflects the properties of the molecule and also consists of all interactions that may
occur. Electrons are generally much faster than nuclei and their motion can very often
be treated separately. The generalization of this concept leads to the Born-Oppenheimer
6.1 Pure Rotation of Linear Molecules
79
approximation where the wavefunction Ψ of a molecule can be separated in a product
of sub-functions each representing a certain motion or property
Ψ ' Ψel Ψvib Ψrot Ψns
(6.2)
with Ψel the electron wavefunction, Ψvib and Ψrot the vibrational and rotational wavefunction respectively, and Ψns the nuclear spin wavefunction. Each of the sub-functions
is dependent on a certain set of quantum numbers but not necessarily on all, e.g. the
electron wave function Ψel (nLS) only depends on n the principal, L the orbital, and
S the electron spin quantum number but not on v the vibrational, J the rotational
and M the magnetic quantum number. Ψ forms a set of basis functions in which the
Hamiltonian can be written as a sum of sub-Hamiltonians, e.g.
Ĥ = Ĥel + Ĥvib + Ĥrot + Ĥns
(6.3)
If only pure rotational transitions are considered the expectation value hĤel + Ĥvib i = Eev
can be treated as a constant. In the case of radicals the electrons and nuclei have several
possibilities to interact with each other or with the overall motion of the molecule which
leads to extra terms in the Hamiltonian. But instead of refining the Hamiltonian 6.3 it
is more convenient to re-express the Hamiltonian in the form
Ĥ = Ĥrot + Ĥf + ĤΛ,l + Ĥhf s
(6.4)
that is to focus on the structure of the energy levels and to restrict oneself to the
relevant terms for the MW- and mm-wave measurements; here Ĥrot is the rotation term,
Ĥf the fine structure term caused by the electron spin and orbital angular momentum,
ĤΛ,l representing the Λ- and l-type doubling effect caused by rotation-electron orbit
interaction and effects of the bending vibration respectively, and Ĥhf s the hyperfine
structure term mainly caused by the nuclear spins and electric quadrupole interactions,
see Tab. 6.1. In the subsequent sections the effect of each term of the Hamiltonian 6.4
will be explained in more detail with special focus on the radicals relevant for this thesis.
6.1 Pure Rotation of Linear Molecules
As a first approach and if no vibration and electronic effects are considered a linear
molecule can be seen as a rigid rotor where the distances between the nuclei are fixed.
The energies resulting out of an end-over-end rotation can be obtained using
Ĥrot =
L̂2
h2
= 2 J(J + 1)
2I
8π I
(6.5)
with L̂ the angular momentum operator and J the eigenvalues of L̂ obeying L̂2 = ~J(J + 1).
2
The Hamiltonian can be simplified by introducing the rotational constant BSI = 8πh2 I
80
6 Theoretical Considerations
Table 6.1: Selection of important interactions and their constants
parameter interaction (IA)
Hamilton term
/ quantum numbers
/ energy term / relations
fine structure γ
ρ-type doubling
ĤN S = γ N̂ · Ŝ (1)
electr. spin - rotation IA
N, S
γD
distortion constant of γ
λ
electr. spin -electr. spin IA
ĤSS = 23 λ (3 ŝ2z − Ŝ 2 )
S
Aso
electr.spin - orbit IA
ĤSO = Aso (L̂ · Ŝ) (1)
S, L
Aef f
Aef f = ASo + γ
Λ and l-type p (= qΛ )
Λ-type doubling
e.g. EΛ = ±p 12 (J + 12 ) (2)
doubling
rotation - electr. orbit IA
for 2 Π1/2 in a pure Hund’s
R, L
case (a)
q
l-type doubling
El = ±qi 14 (vi + 1)J(J + 1)
bending vibration
for Π states (2) ,
vi , l
pef f
pef f = p + 2q
pDef f
distortion constant of pef f
magnetic hf
a, a+ , a− nuclear spin - orbit IA
ĤIL = a ΛIˆ · k̂ (1) ,
I, L
a+ = a + 12 (b + c)
a− = a − 12 (b + c)
b, bF
Fermi-contact
ĤF = b Iˆ · Ŝ, bF =b+ 3c (1)
I, S
c, t
elect.dipole- nucl.dipole IA
Ĥ = c (Iˆ · k̂)(Ŝ · k̂) (1)
I, S
t = 3c
d
hyperfine Λ-doubling
Ĥd = d 12 (exp(2iφ)I− S− +
(only for 2 π1/2 -states 6= 0)
exp(−2iφ)I+ S+ ) (3)
I, S
CI
nuclear spin - rotation IA
ĤCI = CI Iˆ · N̂
I, N
electr.
eQqo
1. and 2. order elec.quadr.IA
(3)
ĤeQqo = eQqo (3Iz2 − I 2 )×
(4I(2I − 1))−1
(3)
ĤeQq2 = eQq2 /(4I(2I − 1))
×(exp(2iφ)I−2 +
exp(−2iφ)I+2 )
1
from Townes & Schawlow [181]; 2 energy term calculated by perturbation theory, the
+ sign yields the upper Λ or l -doublet level and the - sign the lower level, see Gordy &
Cook [63], energy terms are expressed in MHz, i.e. normalized by 1/h · 10−6 (h Planck
constant); 3 Kawaguchi et al. [102]
quadrupole
eQq2
I
6.1 Pure Rotation of Linear Molecules
81
[Joule] to give Ĥrot = BSI J(J + 1). It is however customary to express B in MHz (or
cm−1 ) rather than in the SI-units
B=
h
× 10−6
8π 2 I
[MHz] .
(6.6)
For the rest of this thesis all molecular constants and energies are expressed in MHz (if
not otherwise indicated). The eigenvalues of Eq. 6.5 can thus be written as
hĤrot i = Erot = BJ(J + 1)
(6.7)
so that the energy is expressed in MHz. The molecular spectrum consists of transitions
between these energies, i.e.
νE 0 →E 00 = E 0 − E 00 = 2BJ 0
(6.8)
with E 0 the upper state energy and E 00 the lower state energy. However, a molecule is not
strictly a rigid rotor and centrifugal forces have to be considered so that the rotational
energy is of the form
Erot = BJ(J + 1) − D[J(J + 1)]2 + H[J(J + 1)]3 + ...
(6.9)
with D and H the first and second order centrifugal distortion coefficient respectively.
Only the centrifugal distortion constant D could be determined for the molecules discussed in this thesis because the FTMW spectrometer has a upper frequency limit of 40
GHz which in these cases correspond to low rotational excitations.
6.1.1 Selection Rules
Not every transition between rotational energy levels is allowed. For electronic dipole
transitions with dipole moment µ̂ the transition moment
Z
µ = Ψ0 (J 0 M 0 )∗ µ̂Ψ00 (J 00 M 00 )dτ
(6.10)
determines the intensity and if µ = 0 the transition is “forbidden” or if µ 6= 0 “allowed”
with I ∼ |µ2 | 2 . The transition moment µ depends on the wave functions and thus on
the quantum numbers which determine Ψ0 and Ψ00 in order that µ 6= 0 or not. Quantum
numbers that yield allowed transitions are determined by so called “selection rules”.
There are two types of selection rules: a) the rigorous electric dipole selection rule and
b) the approximate electric dipole selection rule. In a) the selection rules are independent
of the degree of approximation introduced in the wave function and in b) they are not.
Disregarding the effect of nuclear spin the resulting selection rule for linear molecules
are that only transitions with
∆J = J 0 − J 00 = ±1
2
(6.11)
Double primes (Ψ”) indicate the lower state and single prime (Ψ’) stands for the upper state .
82
6 Theoretical Considerations
are allowed 3 . This means that measurable transitions should have frequencies of the
form
νJ 0 ←J 00 = 2BJ 0 − DJ 03 .
(6.12)
6.2 Fine Structure
Any atom or molecule with unpaired electrons reveals some sort of sub-structure to the
rotational structure. These effects are mainly due to the electronic spin-orbital, spinspin, and the spin-rotational interaction which are called fine structure interactions. and
can be expressed in the Hamilton term Ĥf of Eq.6.4 as
Ĥf = ĤN S + ĤSS + ĤSO
.
(6.13)
The first term on the right hand side of Eq. 6.13 takes account of the electron spinmolecular rotation interaction
HˆN S = γ N̂ · Ŝ
(6.14)
which is always present for radicals with an electronic multiplicity of 2S + 1 ≥ 2. This
effect can be explained by the electrons participating in the rotation of the molecule
and thus inducing a weak magnetic field which then can interact with the electron spin
moment. In general this induced magnetic field is rather weak and the splitting of
the ĤN S energy levels small. On the other hand the spin-rotation interaction is the
only contribution to the fine structure for molecules in a 2 Σ state, e.g. C3 N and its
isotopomers.
If a molecule has more than one unpaired electron, e.g. O2 or C4 , the dominating term
of the fine structure is
2
(6.15)
HˆSS = λ(3ŝ2z − Ŝ 2 ).
3
This is somehow the corresponding quantum mechanical expression to the classic magnetostatical equations of two interacting dipoles.
If a molecule also has an electronic orbital angular momentum Λ 6= 0 an usually strong
interaction between the spin and the orbital angular momentum occurs:
HˆSO = ASO Ŝ · L̂
(6.16)
Since a molecular electron does not move in a spherically symmetric field (as it is possible
in an atom), torques are exerted on it by the field which in general causes the angular
momentum not to be constant. In a diatomic or linear molecule the fields are symmetric
about the molecular axis and no torque is exerted on a molecular electron about the
3
It is also ∆M = 0, ±1. Furthermore, there is a (+/-) parity rule found by Laport in 1924. Here
each energy level is labeled according to its inversion symmetry property with a plus or minus. The
transition rules are: + ↔ −, + = +, − = −. Irrespective of the presence or absence of nuclear
spin, this rule is strictly valid for dipole radiation.
6.2 Fine Structure
83
internuclear axis. The component Λ of the electronic angular momentum L is therefore
constant in this direction (other important angular momenta are listed in Tab. 6.2). In
a Hund’s case (a) the spin S is coupled to the molecular axis and Ω is a good quantum
number so that the spin-orbit term is separated by the amount ASO in fine structure
blocks with Ω = |Λ + S| and Ω = |Λ − S|. The labeling of these blocks are the Ω itself,
e.g. a 2 Π state has a Ω = 1/2 and a Ω = 3/2 block and a 2 ∆ state can be split into a
Ω = 3/2 and a Ω = 5/2 block. ASO is a constant of a pure electronic interaction and
usually much larger than the rotational constant B so that transitions with different Ω
usually do not occur in the microwave region due to the big energy gap between the Ωblocks. This was also the case in this work where only transitions of C4 N and C6 N were
measured with ∆Ω = 0. The typical energy ladder BN (N + 1) of rotational transitions
known from the Hund’s case (b) can not be found in a Hund’s case (a). Instead the
energy levels are widely separated in the two fine structure blocks which both reveal a
ladder structure due to the rotation.
Only if molecules are considered with Λ ≥ 1 and 2S + 1 ≥ 3 (e.g. in 3 Π states) all three
terms of Eq. 6.13 are simultaneously needed. For the C3 N isotopes in a 2 Σ state only
ĤN S had to be considered and also for the 2 Π molecules C4 N and C6 N only one fine
structure term (ĤSO ) is needed. The latter is due to a strong correlation between ASO
and γ in a strong Hund’s case (a) so that instead of using ASO and γ separately a new
constant Aef f = ASO + γ can be introduced to describe the structure of these radicals.
6.2.1 Hund’s Coupling Cases a) and b)
Radicals have one or more unpaired electrons and therefore a total spin S 6=0. In
addition the molecules can have a non vanishing electronic orbital angular momentum
and nuclear spins. The rotational energy expression (Eq. 6.9) is not strictly valid for
such molecules and a systematic way of including the extra angular momenta has to
be found. In 1926 Hund [91] introduced a method to deal with the coupling of angular
momenta which is basically a classification of ideal cases which are very often closely
approximated by real molecules. The Hund’s coupling cases are often correlated to the
electronic ground states of the radicals which follow the notation
2S+1
|Λ|
(6.17)
with S the total electron spin and 2S + 1 the electronic multiplicity, here Λ is the
electronic orbital momentum in units of ~, e.g. 0,1,2,3,..., which is represented by the
characters Σ, Π, ∆, Φ. The used angular momenta are summarized in table Tab. 6.2.
The Cn N (n odd) radicals have a 2 Σ electronic ground state, i.e. Λ = 0 and S = 1/2,
and the even membered radicals have a 2 Π ground state, i.e. Λ = 1 and S = 1/2.
Hund’s case (a): This case applies if Λ 6= 0 and the electronic spin-orbit (LS) coupling
is assumed to be strong, while the coupling of the rotation of the nuclei with the electronic
motion is very weak, i.e. the magnetic field generated by the rotation is small. Ω is then
a good quantum number even if R 6= 0, see Fig. 6.2. Ω and the rotational angular
84
R
L
Λ
S
Σ
N
J
Ω
I
F
6 Theoretical Considerations
Table 6.2: Angular momenta and their projections
angular momentum of the end-over-end rotation of the molecule
resultant electronic orbital angular momentum
component (projection) of L along the molecular axis Λ = |ML | = 0, 1, 2, ..., L
resultant electronic spin
projection of S along the molecular axis, Σ = S, S − 1, ..., −S
= R + L angular momentum without elect. spin
total angular momentum without nuclear spin
= |Λ + Σ| resultant angular momentum along molecular axis
nuclear spin
total angular momentum (with nuclear spin)
.
R
J
J
J
N
S
case a)
Λ
Σ
L
S
Ω
Λ
R
N
S
L
case b)
case b), molecule in
Σ state
.
Figure 6.2: Vector diagram of Hund’s coupling cases a) and b). On the left: Hund’s
case (a) with only the total angular momentum J fixed in space. The nutation of the
internuclear axis about J is indicated by the blue ellipse; the precession of L and S
about the figure axis are assumed to be much faster (green dash-dotted ellipses). In
the middle: Hund’s case(b) in the general case Λ 6= 0. Also here only the total angular
momentum J is fixed in space. The precision of N and S about J (green ellipse) is
much slower than the nutation of the internuclear axis about N (dash-dotted blue
line). On the right: Hund’s case(b) with Λ = 0.
6.2 Fine Structure
85
momentum R result in an angular momentum J. A criterium for a molecule to be in a
Hund’s case (a) is (Gordy & Cook [63])
2JB |ΛASO | .
(6.18)
Hund’s case (b): This case can be best explained in the most prominent case were
Λ = 0 but S 6= 0, i.e. Σ states almost always can be expressed in a Hund’s case (b).
Because there is no orbital field the spin moment can not couple to the internuclear
axis. The strongest influence to the spin moment comes from the weak magnetic field
generated by the end-over-end rotation of the molecule which causes S to couple with N
(which is the same as R because Λ=0). In some cases it can happen that light molecules,
e.g. OH, in a high rotational state J generate a large magnetic field by rotation that is
strong enough that the electronic spin S is rather resolved in direction of J than to the
internuclear axis even for Λ 6= 0. In general the Hund’s case (b) is defined as the ideal
case where S is coupled to N to form J as seen in Fig. 6.2.
Examples of the more complicate cases of the coupling of one or two additional nuclear
spins are discussed in Chapter 7.
Selection Rules
The distinction in a Hund’s case (a) or (b) involves the usage of different “good” quantum
numbers, i.e. J and Ω or N in which the selection rules can be expressed.
In the Hund’s case (a) the quantum number Σ is a good quantum number and the
selection rule
∆Σ = 0
(6.19)
is valid. This rule holds for combinations of the sets of rotational levels of various
multiplet components. The usage of Ω is more common and thus the selection rules for
linear molecules 4 are
∆J = ±1 and ∆Ω = 0, ±1
(6.20)
In the microwave region there are mainly transitions with ∆Ω = 0 to observe (because
of the higher energies involved in the other types of transitions) but this is not due to a
forbiddance of this transitions.
In the Hund’s case (b) the selection rule is
∆J = ±1 and ∆N = ±1 .
(6.21)
In the more complicate case where the molecule has atoms with nuclear spin, e.g. I1
and I2 , the total angular momentum is not J but
F = J + I1 + I2
4
and considering only cases of pure rotation
(6.22)
86
6 Theoretical Considerations
Now the analog of Eq. 6.11 holds rigorously for dipole radiation:
∆F = 0, ±1 with F = 0 = F = 0
(6.23)
Because the interaction with J and the nuclear spin is usually very weak the rule 6.11
for the quantum number J is still very strong even though not rigorous.
The selection rules 6.19 and 6.21 for N and S do not hold in intermediate coupling
cases between (a) and (b). A nicely summarized presentation of this topic including the
selection rules for magnetic dipole and electric quadrupole radiation is given in Herzberg
[84].
6.2.2 Λ-type Doubling, and l-type Doubling
Λ-type doubling. For radicals with an orbital angular momentum Λ 6= 0 the fine
structure energy terms split in doublet states labeled with e and f with reference to
the parity of the wave function Ψ. At this stage of development these doublet states
would be exactly degenerate but the influence of the molecular rotation on the electronic
orbital momentum lifts the degeneracy. This can be interpreted as a decoupling from
the electron orbital angular momentum from the internuclear axis 5 . The bigger the
Λ-type splitting the stronger the coupling of L towards R so that the molecule takes
an intermediate state between Hund’s case (a) and Hund’s case (d) which would be the
extreme case of a L-R vector coupling scheme. The Λ-doubling splitting is significantly
smaller than the fine structure splitting. Perturbation theoretical considerations are
leading to the following proportionalities (Landau-Lifschitz [109])
∆EΛ ∼ (me /M )2Λ
(6.24)
with me the mass of the electron and M of the molecule. The ratio of masses (me /M ) 1 and with Λ > 1 the chances of a measurable splitting of the Λ terms decrease rapidly so
that radicals with a ∆ or Φ electronic ground state are of nearly no interest concerning
this symmetry effect. On the other hand the Π states can have quite large splittings. In
Table 6.3 the approximate energy Λ-type splitting is given for 2 Π states in pure Hund’s
case (a) and (b).
In the case of C4 N and C6 N it was not the Λ-type doubling constant which was fitted
but an effective Λ-type doubling constant pef f , with pef f = p + 2q 6 which also includes
q the l-type doubling constant.
l-type doubling. Polyatomic linear molecules have vibrational bending modes νi which
can be excited. If a degenerate bending mode is excited an additional angular momentum
pz = l~ about the internuclear axis with l = vi , vi − 2, vi − 4, ..., −vi has to be taken into
account and the rotational energy can be written as
Erot = B[J(J + 1) − l2 ],
5
6
In a classical picture this would be interpreted as an effect of the Coriolis force.
p is used here as the Λ-doubling constant irrespective of the applied Hund’s case.
(6.25)
6.3 Hyperfine Structure
87
Table 6.3: Theoretical Λ-type doubling for 2 Π state, Gordy&Cook [63].
∆E
Hund’s
splitting of levels approx. theor
case
(approx.)
coupling constant
(a)
Ω=
1
2
b
2
1
)(J
4
pa =
3
)
2
4ASO B
νe
b
a
B
ASO
2
3
= νe8B
p (J −
+
p = 2p
ASO
(b)
pN (N + 1)
νe represents the transition frequency between the ground
level and the lowest Σ state; all constants are in frequency
units.
Ω=
3
2
pa (J + 12 )
with J the total angular momentum including l, so that J = |l|, |l| + 1, |l| + 2, ... . The
Coriolis coupling force which is proportional to v × ω between the vibrational motion v
and the angular rotation motion ω in it’s orthogonal plane, lifts the ±l degeneracy of
Eq. 6.25 and a doublet splitting of the rotational lines is produced. For |l| = 1, i.e. a
vibrational Π state, the l-type splitting is approximately
1
∆E|l|=1 = q (vi + 1)J(J + 1)
2
(6.26)
where vi is the vibrational quantum number of the ith degenerate bending mode and q
the vibration-rotational coupling constant. In the first excited state the energy splitting
simplifies to
∆E|l|=1 = qJ(J + 1)
(6.27)
In most cases q can be approximated to be (Gordy & Cook [63])
q ≈ 2.6
Be2
νbend
(6.28)
with Be the equilibrium rotational constant and νbend the degenerate bending frequency.
6.3 Hyperfine Structure
If a molecule has one or more nuclear spins the spectra will expose a further splitting
of the energy levels due to the interaction of the nuclear spins with the other angular
momenta of the molecule. This is most commonly called the hyperfine structure because
it is usually much smaller than the above discussed fine structure. However, in some
cases the substructure induced by the nuclear magnetic moment can be of the same
order or even larger than the electric fine structure interactions, e.g. the Fermi-contact
interaction in the case of 13 CCCN is larger than the electronic spin-rotation interaction.
88
6 Theoretical Considerations
For the hyperfine transitions different kinds of electromagnetic radiation can be involved.
A photon always carries an angular momentum of l~ with l=1,2,3,... which corresponds
to a classical radiation field of a 2l -pole. During an emission or an absorption process
not only the overall angular momentum but also the parity has to be conserved in the
photon-molecule system. The transformation properties (~r) → (−~r) of electric and
magnetic multi-pole radiation are not the same, i.e electric multi-pole radiation has a
(−1)l parity whereas magnetic multi-pole radiation has a (−1)l+1 parity. A transition
between two molecular states with the parity π1 and π2 can only occur if
π1 = (−1)l π2 ,
π1 = (−1)l+1 π2 ,
for El-radiation
for Ml-radiation
(6.29)
is fulfilled. For example: In the Hund’s case (a) the selection rule is ∆J = ±1 and with
a nuclear spin ∆F = 0, ±1 so that only magnetic dipole (l = 1) and electric quadrupole
(l = 2) are allowed and electric dipole and magnetic quadrupole transitions are forbidden
[104]. A molecule containing an atom with a quadrupole moment, e.g. 14 N in C4 N or 13 C
in CC13 CN, will always have a hyperfine structure in their spectrum. If the molecule
has an open shell structure with S 6= 0 the magnetic dipole (hfs) transitions usually
dominate upon the electric quadrupole transitions in terms of the line intensities. The
Hamilton term Ĥhf s of Eq. 6.4 can be written as
Ĥhf s = Ĥmag,hf s + ĤQ
(6.30)
with Ĥmag,hf s the magnetic interaction term and ĤQ the electric quadrupole term.
6.3.1 Magnetic Hyperfine Structure
The magnetic hyperfine structure Hamiltonian as it is used in this thesis can be written
as
Ĥmag,hf s = ĤIL + ĤF + ĤIS + Ĥd
(6.31)
with ĤIL the nuclear spin- electronic orbit interaction term, ĤF the Fermi contact term,
ĤIS the nuclear spin - electronic spin interaction (or short: dipole-dipole interaction),
and Ĥd the hyperfine Λ-doubling term. In general the Hamiltonian for an interaction
between a magnetic dipole and a magnetic field is of the form Ĥ = µ̂ · Ĥm where Ĥm
is the magnetic field and µ̂ the dipole, i.e. µI = gI µn I the magnetic spin moment with
gI the dimensionless gyromagnetic ratio (g-factor), µn the nuclear magneton, and I the
nuclear spin. The magnetic field Hm can be caused by the electronic orbital or spin
angular momentum and depending on the direction of the I,L, and S the Hamilton
equation can be written as
ĤIL = aΛIˆ · k̂
ĤF = bIˆ · Ŝ
ĤIS = c(Iˆ · k̂)(Ŝ · k̂)
(6.32)
(6.33)
(6.34)
6.3 Hyperfine Structure
89
with k̂ a unit vector along the molecular axis. The expressions Eq. 6.32 - 6.34 apply
accurately only when Λ is a “good” quantum number and holds for Hund’s case (a) and
(b). The introduced constants a, b, and c are
2µB µI 1
a =
(6.35)
I
r3 U
2µB µI 8π 2
3 cos2 θ − 1
b =
Ψ (0) −
(6.36)
I
3
2r3
U
3µB µI 3 cos2 θ − 1
c =
(6.37)
I
r3
U
with θ the angle between the molecular axis and r the radius from the nucleus to the
electron. Ψ(0) is the electron wavefunction at the interacting nucleus. (. . .)U denotes
that the mean value is taken over the unpaired electron. The Eq. 6.32 - 6.34 apply to
each electron in the molecule. It is evident that for electrons in the inner shells and for
those who are paired the terms nearly cancel out each other so that in most cases only
the unpaired electrons have to be considered.
Nuclear spin - electronic orbit interaction. The quantity a refers only to electrons
with an orbital angular momentum. According to the Biot-Savart law the unpaired
electrons with L 6= 0 generate a magnetic field at the nucleus which interacts with the
nucleus magnetic moment.
Fermi contact interaction. It is common to use the “Fermi contact” constant bF
instead of b which is defined as bF = b + c/3 with
2µB µI 8π 2
bF =
Ψ (0) .
(6.38)
I
3
U
(Ψ2 (0))U is the probability to find the unpaired electron at the nucleus which for an
electron in an p atomic orbit is negligibly small but for a s-type orbit can be quite large.
Hence, whenever there is a appreciable amount of s character to the wavefunction of
an unpaired electron the magnetic hyperfine interaction which is proportional to Ψ2 (0),
may be expected to dominate, i.e. bF > a.
Dipole-Dipole interaction.
Because of the (cos2 θ)U angular dependence this interaction cancels for a spherical
electron density distribution, e.g. s-type orbitals.
Hyperfine Λ-doubling.
The magnetic hyperfine interactions discussed so far are all identical for the two energy
levels of a Λ-doublet. For a Π state a certain type of electron spin-nuclear spin interaction
results in a different structure for the Λ doublet. Qualitatively this can be explained best
in a Hund’s case (b). The electron wave function has a eiφ ± e−iφ angular dependence
with φ the angle of rotation about the internuclear axis. The probability distribution
Ψ2 of the electrons is therfore proportional to sin2 φ and cos2 φ. For the lower Λ-doublet
state with a sin2 φ distribution, the field of the electron at the nucleus is parallel to I and
90
6 Theoretical Considerations
rotation
of
molecule
rotation
of
molecule
R
R
s
φ
s
I
s
I
molecular
axis
molecular
axis
lower Λ− doublet state
s
upper
Λ− doublet state
Figure 6.3: Unpaired electron distribution for a 2 Π state in Hund’s case (b) for the two
Λ-doublet states.
for the upper state it is directed oppositely to I, see Fig. 6.3. This causes the spin-spin
interaction energy to be different for the two Λ states, i.e. the hf Λ-doubling is parity
depending.
For a 2 Π state in a Hund’s case (a) the splitting due to the hyperfine Λ-doubling is
∆Ed = ±
d(J + 12 ) ˆ ˆ
I ·J
2J(J + 1)
(6.39)
for the 2 Π1/2 state and ∆E = 0 for the 2 Π3/2 state. The upper sign in Eq. 6.39 applies
to the upper Λ-doublet state. d is defined as
3µB µI
d=
I
sin2 θ
r3
(6.40)
U
In all molecules with a nuclear spin there is an interaction between the nuclear magnetic moment and the rotation of the molecule which can be calculated by Van Vlecktransformations of higher order terms and usually results in a small splitting which is
expressed in the constant CI . This type of interaction was not considered in this work
for the Cn N radicals.
Useful references for the definition of the magnetic interaction constants are Frosch &
Foley [57] and Steimle et al. [170].
6.3 Hyperfine Structure
91
6.3.2 The Electric Quadrupole Interaction
There can also be a hyperfine structure due to electric charge distribution in the nucleus.
If the nucleus is not assumed to be a point charge the charge distribution has to be
considered which may be in motion and produces magnetic fields which gives the nucleus
an angular momentum in quantities of I~ (I is an integer or half integer). If V is the
electrostatic potential produced at the nuclear center of mass by all electronic charges
in the atom the electrostatic energy of a nuclear charge ∆q = ρ(x, y, z)∆x∆y∆z, with ρ
the nuclear charge density, is ∆W (x, y, z) = ∆q(x, y, z)V (x, y, z). Quantum mechanical
considerations on the multi-pole expansion of the electrostatic potential V
V0 + x
∂V0
∂ 2 V0
∂V0
∂V0 1 2 ∂ 2 V0 1 2 ∂ 2 V0 1 2 ∂ 2 V0
+y
+z
+ x
+
y
+
z
+
xy
+ ... (6.41)
∂x
∂y
∂z
2 ∂x2
2 ∂y 2
2 ∂z 2
∂x∂y
reveal that the nucleus normally has no inherent dipole moment and that also all terms
involving odd powers of the coordinates will be zero ([181],p.132) thus leaving only a
term which is independed of the nuclear size or shape (i.e. ZeV , with Z= atomic number
, e=proton charge) and a term associated with the quadrupole moment of the nucleus.
The energy due to the electric quadrupole moment is than
1
WQ = − Q : ∇E
6
which is the inner product between the quadrupole moment dyadic
Z
Q = (3~r ⊗ ~r − r2 1) ρ d(3)~r
(6.42)
(6.43)
and the gradient of the electric field due to the electrons. Using a coordinate system
with z in the direction of the nuclear spin all non diagonal terms of Q vanish and the
entire quadrupole moment can be expressed in terms of one constant
Z
1
(3z 2 − r2 ) dx dy dz
(6.44)
Q=
e
called “the” nuclear quadrupole moment [181]. For nuclei with a spherical charge distribution Q is zero and the quadrupole moment can thus be seen as a measure of the
deviation from a spherical shape, i.e. if the nuclear charge distribution ρ is somewhat
elongated along z then Q is positive; if it is flattened along the nuclear axis, Q is negative. All isotopes with I=0 or 1/2 have a quadrupole moment equal zero because of
their spherical symmetry. From Eq. 6.42 it is clear that the energy also depends on the
gradient of the electric field at the nucleus. In a linear molecule the charge distribution is
symmetric around the molecular axis but varies along these axis so that the gradient of
the electric field depends on the position within the molecule. Nitrogen 14 N with I=1/2
has a Q of +0.02 · 1024 cm2 [181] but the electric quadrupole energy from C2 N is different
from that of CNC because of the different ∇E experienced by the nitrogen nucleus. In a
quantum mechanical treatment the Hamiltonian can be build out of Eq. 6.42 with Q and
92
6 Theoretical Considerations
e − I 2 1 has the same angular
d Because 3 (II + II)
∇E replaced by operators Q̂ and ∇E.
2
dependence with respect to nuclear orientation as 3~r ⊗ ~r − r2 1, Q̂ can be expressed as
3
eQ
2
e −I 1
Q̂ =
(II + II)
(6.45)
I(2I − 1) 2
d can be shown to be
and ∇E
7
d=
∇E
q
3
2
f
(JJ + JJ) − J 1
J(2J − 1) 2
(6.46)
2
with q = (JJ| ∂∂zV2 |JJ) depending on J. The energies of the Hamiltonian ĤQ = − 16 Q̂ :
d are therefore of the form
∇E
E = −eQq f (J, Ω, I, F )
(6.47)
where eQq is called the quadrupole coupling constant and f (J, Ω, I, F ) a function 8 which
involves the coupling of the angular momenta. In the tensor notation the quadrupole
interaction can be written as
HQ =
X
eQq2
61/2 eQq0 2 ˆ ˆ
2 ˆ ˆ
T0 (I, I) −
e2iqΦ T2q
(I, I)
4I(2I − 1)
4I(2I − 1) q=±1
(6.48)
ˆ I)
ˆ a standard
with eQq0 and eQq2 the two electric quadrupole parameters and T 2 (I,
2nd-rank spherical tensor with components expressed in the molecule-fixed axis system,
see [27]. It is
2 sin θ
2
(6.49)
eQq2 = −3e Q
r3
T
with the index T indicating that the mean value is taken over the total (i.e. the paired
and unpaired) electrons, see Ohshima et al. [141]. This equation (6.49) together with
Eq. 6.37 enables an estimation of the non-axial distribution of the wavefunctions. The
matrix elements of HˆQ in a Hund’s case (a) are discussed in 6.4.1 in more detail.
7
8
Eq. 6.46 is only valid if J is a “good” quantum number.
Under certain assumptions f is the Casimir function but in general Eq. 6.48 has to be applied.
6.4 Matrix Representation of the Hamiltonian
93
6.4 Matrix Representation of the Hamiltonian
For non-singlet states even the rotational Hamiltonian Ĥrot = BR2 can be significantly
more complicate than in the singlet case because only with the usage of “good” quantum
numbers is the calculation of the energy expression meaningful. If an electronic orbital
angular momentum and an spin is present the Hamiltonian can be written as
Ĥrot = B(Jˆ − L̂ − Ŝ)2
.
(6.50)
On way to proceed is to re-express Eq. 6.50 as
Ĥrot = B(Jˆ − Jˆz2 )2 + B(Ŝ − Ŝz2 )2 + B(L̂ − L̂2z )2
−B(Jˆ+ L̂− + Jˆ− L̂+ )2 − B(Jˆ+ Ŝ − + Jˆ− Ŝ + )2 + B(L̂+ Ŝ − + L̂− Ŝ + )2 (6.51)
using Jˆ+ , Jˆ− as lowering (+) and raising (-) operators respectively and L̂+ , L̂− , Ŝ + ,
Ŝ − as raising (+) and lowering (-) operators in the common sense of definition. With
Eq. 6.51 it is already evident that in some cases, e.g. 2 Π states, a mixing of the states
is necessary to build the correct Hamiltonian. As an example the basis set of a 2 Π state
is given here as
|2 Π3/2 i, |2 Π1/2 i, |2 Π−1/2 i, |2 Π−3/2 i,
(6.52)
which can be written as e/f parity basis functions:
|2 Π3/2 i ± |2 Π−3/2 i
√
,
| Π3/2 e/f i =
2
|2 Π1/2 i ± |2 Π−1/2 i
√
| Π1/2 e/f i =
2
2
2
(6.53)
with (+) referring to the e parity and (-) referring to the f parity. The rotational
Hamiltonian can now be expressed as
|2 Π3/2 e/f i

|2 Π1/2 e/f i
B[(J + 1/2)2 − 1]
−B[(J + 1/2)2 − 1]1/2
Ĥ = 


2
1/2
−B[(J + 1/2) − 1]
(6.54)
2
B[(J + 1/2) + 1]
Every Hamiltonian term in Eq. 6.4 can be written in such a matrix form. For 2 Σ states
the off-diagonal terms in the matrix are very often zero and a matrix representation is
not necessary in such a case but for 2 Π states the situation is completely different.
6.4.1 The Matrix Representation of the 2 Π-Radicals
The fit of the 2 Π radicals C4 N and C6 N proved to be not as easy as expected and it is
therefore useful to examine the 2 Π matrix elements in more detail. The matrix elements
of the rotation, spin-orbit, Λ-doubling and magnetic hyperfine interaction of 2 Π states
in the Hund’s case (a) are calculated in Brown et al. [26]. The most influential term of
94
6 Theoretical Considerations
Table 6.4: Matrix with Spin-Orbit, Rotation and Λ-doubling
h2 Π±
3/2 JIF |......
h2 Π±
1/2 JIF |......
|2 Π±
3/2 JIF i
|2 Π±
1/2 JIF i
1
1 2
2 {A + AD [(J + 2 ) − 1]}
− 21 γD Z
+B[(J + 21 )2 − 1] − DZ(Z +
∓ 12 qD (J − 12 )(J + 12 )(J + 32 )
−{B − 12 γ − 12 γD (Z + 2) − 2D(J + 12 )2
∓ 12 q(J + 12 ) ∓ 14 (pD + 2qD )(J + 12 )
∓ 12 qD (J + 12 )3 }Z 1/2
1)
− 12 {A + AD (Z + 2)}
−γ − γD 12 (3Z + 4)
+B[(J + 12 )2 + 1] − D(Z 2 + 5Z + 4)
∓ 12 (p + 2q)(J + 12 )
∓ 12 (pD + 2qD )(J + 12 )(Z + 2)
∓ + 12 qD (J + 12 )Z
(Hermitian)
with Z(J)= (J- 12 )(J+ 32 ) = (J+ 12 )2 -1
Upper and lower sign choice refer to e and f levels respectively.
the Hamiltonian is one containing the rotational, spin-orbit, and Λ-doubling interaction
and the matrix representation is given in Tab. 6.4.
As an example and because of the importance in the fit of the C4 N radical the matrix
elements of the electric quadrupole interaction is given here.
HQ of Eq. 6.48 in the Hund’s case (a) can be expressed using 3j- and 6j-Symbols 9 :
0
0
−1
F J I
(−)
2 I J0
0
J 2 J
0
1/2
J 0 −Ω
×[(2J + 1)(2J + 1)]
δΛ0 Λ δΩ0 Ω eQq0 (−)
−Ω 0 Ω
0
X
0
0
J
2 J
+
δΛ0 ,Λ∓2 (6)1/2 eQq2 (−)J −Ω
(6.55)
0
−Ω −q Ω
1
hηΛ SΣJ Ω IF |HQ |ηΛSΣJΩIF i =
4
0
I 2 I
−I 0 I
J+I+F
q=±2
This formula was directly used in the fit program to analyze the C4 N and C6 N spectra.
A disadvantage of this representation is that it is not very intuitive and it is therefore
2 ±
desirable to express HQ in a matrix of the form h2 Π±
Ω0 JIF |HQ | ΠΩ JIF i as it can be
seen in Tab. 6.5. The derivation is given in the Appendix B. In short: 2 Π states have Ω
or Ω0 values of 3/2 or 1/2 so that Ω’=Ω ± 1. For the energy the ∆J = 0 elements were
9
see Brown & Schubert [27], Eq. 2
6.4 Matrix Representation of the Hamiltonian
95
Table 6.5: Matrix with electr. hf interaction
|2 Π±
3/2 JIF i
h2 Π±
3/2 JIF |......
h2 Π±
1/2 JIF |......
with
K(F ) =
eQq0
27
2 K(F )[ 4
| 2 Π±
1/2 JIF i
− J(J + 1)]
1
1
3 1/2
2
2
± eQq
4 K(F )[(J − 4 )(J + 2 )(J + 2 )]
eQq0
3
2 K(F )[ 4
(Hermitian)
− J(J + 1)]
3R(F )[R(F )+1]−4J(J+1)I(I+1)
I(2I−1)(2J+3)(2J+2)(2J)(2J−1)
R(F ) = F (F + 1) − J(J + 1) − I(I + 1)
Matrix elements in non-parity conserving basis derived by Tom C. Killian and Guido Fuchs
from Brown & Schubert, [27].
calculated using the basis functions
|2 Π±
|Ω| , Ji =
10
|Λ, Σ, J, Ωi ± | − Λ, −Σ, J, −Ωi
√
2
(6.56)
with ± referring to the e/f parity respectively and following the convention of Brown et
al. [25]. It was necessary to include the off-diagonal term eQq2 in the analysis of the
C4 N spectrum to achieve a good fit, see Chapter 7.1.
Another problem appeared when fitting the C6 N spectrum. In this case a correlation
between the magnetic hfs constant a− and eQq0 seemed to jeopardize the analysis. The
matrix for the magnetic hfs is given in Tab. 6.6 in terms of the constants a, bF and c
as it appeared in Brown et al. [26]. If only transitions between one of the Π3/2 or Π1/2
states are measured it is advantageous to use a transformation (a,bF ,c) → (a+ ,a− ,b)
which separates the magnetic hf constants for the Ω=3/2 and Ω=1/2 states:



 

 
a
a+
a + 12 (b + c)
a + 12 bF + 31 c
 bF  →  a−  =  a − 1 (b + c)  =  a − 1 bF − 1 c 
2
2
3
c
b
b
bF − 3c
The new matrix is given in Tab. 6.7 and it can be seen that a+ is the interaction constant
for Π3/2 states only and a− and d for Π1/2 states only. b can be determined using Π3/2 or
Π1/2 transitions either. The analysis of the C6 N spectrum was based on this Hamiltonian
and includes only the a− constant, see Chapter 7.2.
Some other than the here mentioned approach from Brown & Schubert [27, 26, 24] to
the theoretical study of the 2 Π Hamiltonian are made by Frosch & Foley [57], Kawaguchi
et al. [102], Davies et al. [42].
10
The matrix elements are in a non parity conserving basis.
96
6 Theoretical Considerations
Table 6.6: Matrix with magnetic hyperfine interaction
|2 Π±
3/2 JIF i
h2 Π±
3/2 JIF |......
h2 Π±
1/2 JIF |......
R(F )
[3a
2J(J+1) 2
+ 34 bF + 12 c]
(Hermitian)
|2 Π±
1/2 JIF i
R(F )
[(J− 12 )(J+ 32 )]1/2 1
[ 2 bF
2J(J+1)
R(F )
[1a
2J(J+1) 2
− 14 bF − 16 c ∓ 12 d(J + 12 )]
with R(F ) = F (F + 1) − J(J + 1) − I(I + 1)
Table 6.7: Transformed matrix with magnetic hyperfine interaction
|2 Π±
3/2 JIF i
h2 Π±
3/2 JIF |......
R(F ) 3
a
2J(J+1) 2 +
h2 Π±
1/2 JIF |......
(Hermitian)
| 2 Π±
1/2 JIF i
R(F )
− 16 c]
[(J− 12 )(J+ 32 )]1/2 1
b
2J(J+1)
2
R(F ) 1
[a
2J(J+1) 2 −
∓ d(J + 12 )]
with R(F ) = F (F + 1) − J(J + 1) − I(I + 1)
7 Measurements and Analysis
“ The great tragedy of Science - the slaying of a beautiful hypothesis
by an ugly fact. ”
Thomas H. Huxley (1825 - 1895)
The production of the C3 N isotopomers and the C4 N, C6 N production has been already
described in Chapter 4.1. In short: For speed and convenience, all of the C3 N isotopic
measurements were made with enriched samples; with the 13 C-HCCH sample. Line
intensities were typically 2-3 times stronger than those of the same lines observed in
natural abundance. When the 13 C-methylcyanide sample was employed instead, lines
of CC13 CN were three times more intense than those observed with 13 C-acetylene 1 . In
this chapter the results of the measurements are presented and an interpretation of the
data is given.
CCC15 N is discussed first because of its relative simple spectrum which is in fairly good
agreement with the theoretical predictions, i.e. the b(15 N) and c(15 N) values, derived
from the CCC14 N measurements done by Gottlieb et al. [66] but which had not been
resolved in the CCC15 N measurements of McCarthy et al. [121] so that only the constants
B, D and γ were known.
CCC15 N as well as the 13 C mono-substituted C3 N isotopomers have a 2 Σ ground state
but in the case of the 13 C isotopic species of C3 N two nuclear spins have to be considered
which causes an extra splitting of the energy levels compared to that of the CCC15 N
species.
Only the B, D, γ and bF (13 C) values were known for the 13 CCCN, C13 CCN, and CC13 CN
species from millimeter-wave measurements done by McCarthy et al. [121]. In the same
work the c(13 C) values were not determinable and set to zero. Also the bF (14 N ) and
1
Short summary: 9 GHz antenna set at room temperature, A/D delay around 16 or 20 µs, discharge
voltage of 1100 - 1250 V, general valve opening time 300 - 480 µs, gas entrance pressure of 2.5 atm,
total flow rate of 30 - 32 sccm with 9 sccm Ne, 1.25 sccm 0.18 % HC3 N in Ne and 0.5 sccm 1.5
% H13 CCH (statistical mixture), for CCC15 N it was 0.5 sccm 5% CH3 C15 N, 200 - 5000 shots were
integrated for one spectrum. A “short-nozzle” with a “normal” tip was used.
98
7 Measurements and Analysis
Figure 7.1: Measured CCC15 N transition with Zeeman splitting
c(14 N ) constants were not fitted but assumed to be close to the values for the CCCN
radical which were bF (14 N )=-1.20(3)MHz and c(14 N )=2.84(9)MHz. In this work all
relevant magnetic hyperfine constants could be fitted plus the electrical quadrupole
constant due to the 14 N nucleus.
C4 N and C6 N do not have a 2 Σ but a 2 Π electronic ground state and had therefore to be
treated separately with a computer program written by John Brown, see Chapter 6.4.1.
Both radicals are detected in the laboratory for the first time and no spectroscopic data
were available for this molecules sofar.
7.1 The C3N Mono-Substituted Isotopomers
7.1.1 CCC15 N
CCC15 N was measured in the 9.5 - 38.4 GHz region corresponding to rotational transitions from J = 1 → 0 up to J = 4 → 3 respectively, see Table 7.1. The analysis
7.1 The C3 N Mono-Substituted Isotopomers
99
Table 7.1: Measured Rotational Transitions of CCC15 N in the X 2 Σ+ State
Frequencya O − C b
Transition
J’
F’
N
J
F
(MHz)
(kHz) N’
1
3/2
2
0
1/2
1
9593.486
−4
2
5/2
3
1
3/2
2
19195.842
0
2
5/2
2
1
3/2
1
19195.863
1
2
3/2
2
1
1/2
1
19213.911
4
2
3/2
1
1
3/2
1
19243.521
0
3
7/2
4
2
5/2
3
28798.215
1
3
7/2
3
2
5/2
2
28798.215
−1
3
5/2
2
2
3/2
1
28816.243
−2
3
5/2
3
2
3/2
2
28816.350
−3
4
9/2
5
3
7/2
4
38400.553
2
4
9/2
4
3
7/2
3
38400.553
4
a
Estimated experimental uncertainties (1σ) are 2 kHz.
b
Calculated frequencies derived from the best fit constants in Tab. 7.2
was done with a standard Hamiltonian for a linear molecule in a 2 Σ electronic ground
state similar to Eq. 7.8 and 7.9 for the 13 C isotopic species but with one nuclear spin.
The angular momenta coupling scheme was J = N + S and F = J + I(15 N ). 11 lines
were sufficient to fit 6 molecular constants but for the final fit also the mm-data from
McCarthy et al. [121] were included, see Table 7.2. Radicals are paramagnetic and react
on outer magnetic fields like the Earth’s magnetic field as can be seen in the spectrum
of CCC15 N Fig. 7.1 where the J 3/2→ 1/2, F 2→1 transition is split due to the Zeeman
effect. CCC15 N is the only one of the isotopic species of C3 N which shows a notable
Zeeman splitting of 20-30 kHz in its spectrum. Helmholtz coils were mounted around
the FTMW cavity to cancel outer magnetic fields but was not used during the measurements for this work. Unlike the cases of CCCN or the 13 C isotopic C3 N species there
has to be no electrical quadrupole to be considered for CCC15 N.
The bF (14 N) and c(14 N) values from the mm-measurements [121] could be used to estimate the values for the 15 N isotope (see Townes & Schawlow, p.196 [181]):
µI
bF (14 N )
bF ∼
⇒
=
I
bF (15 N )
µI (14 N )
I(14 N )
µI (15 N )
I(15 N )
=
µI (14 N ) I(15 N )
= −0.7131
µI (15 N ) I(14 N )
(7.1)
so that bF (15 N)est. ≈ 1.68 MHz and c(15 N)est. ≈ -3.98 MHz using µI (14 N)= 0.4036,
µI (15 N)= -0.2830, I(14 N)=1, and I(15 N)=1/2. This prediction was good enough to find
the actual transition lines within 1-2 MHz.
CCC15 N obeys Hund’s case (bβJ ) which can be seen using the formulas in Townes &
Schawlow (p.199) were an estimation of the magnitude for the hyperfine splitting for
the Hund case (bβJ ) is given. In the case of a molecule in a 2 Σ ground state the formula
100
7 Measurements and Analysis
Table 7.2: Molecular Constants of CCC15 N (in MHz).
Data reduction was done by using the Pickett-program [153].
a
Constant
this workb
mm-data onlyc
recommendedd
values
B
4801.2277(5)
4801.2264(4)
4801.2267(1)
−3
D ×10
0.76(2)
0.7062(3)
0.7064(1)
γ
−18.218(3)
−18.17(4)
−18.208(1)
γD ×10−3
0.6(2)
−0.02(2)
...
15
bF ( N)
1.87(1)
3(17)
1.883(9)
c(15 N)
−4.26(3)
12.(73)
−4.30(3)
w-rmse
0.43
0.42
0.97
a
Uncertainties (in parentheses) are (1σ) in the last significant digit.
b
11 lines were used, see Tab. 7.1.
The uncertainties of the lines is estimated to be 2 kHz.
c
28 lines from [121] were used.
The uncertainties of the lines are estimated to be between 22-86 kHz.
d
Total fit with all measured 39 lines.
e
w-rms weighted rms, i.e. rms normalized with uncertainties of measured lines.
(8-10)2 can be reduced to (J=N-1/2):
ξ
WJ=N −1/2
z
= −
}|
{
b
c
+
I ·J
2N + 1 (2N − 1)(2N + 1)
(7.2)
with I · J = 12 (F (F + 1) − J(J + 1) − I(I + 1)). ∆F=1 with J=J’ and N=N’ determines
the hyperfine splitting ∆Whf s :
∆Whf s
1 0 0
1
= ξ (F (F + 1) − ...) − (F (F + 1) − ...)
2
2
1
=
ξ [(F + 1)(F + 2) − F (F + 1)]
2
= ξ(F + 1)
(7.3)
With I(15 N)=1/2 and F=(N-1/2)-1/2 we obtain
∆WJ=N −1/2 = ξN
= −
2
Townes & Schawlow, p.199
N
N
·b+
· c,
2N + 1
(2N − 1)(2N + 1)
N 6= 0(!)
(7.4)
7.1 The C3 N Mono-Substituted Isotopomers
101
In the case of CCC15 N b=bF -c/3=3.3154 MHz so that
1
(c − b) = −2.54MHz
3
2 1
∆WJ=N −1/2 (N = 2, F = 1 → 2) =
( c − b) = −1.90MHz
5 3
and ...
b
N → ∞ : ∆WJ=N −1/2 = − = −1.66MHz
2
∆WJ=N −1/2 (N = 1, F = 0 → 1) =
(7.5)
The corresponding formulae for Eq. 7.4 for J=N+1/2 is
c
b
+
(F + 1), with F=J-1/2
∆WJ=N +1/2,hf s =
2N + 1 (2N + 1)(2N + 3)
N +1
N +1
=
·b+
·c
(7.6)
2N + 1
(2N + 1)(2N + 3)
and thus
1
∆WJ=N +1/2 (N = 0, F = 0 → 1) = b + c = bF = 1.883MHz
3
2
1
∆WJ=N +1/2 (N = 1, F = 1 → 2) =
(b + c) = 1.637MHz
3
5
and ...
b
N → ∞ : ∆WJ=N +1/2 =
= 1.66MHz
2
(7.7)
These estimations are in fairly good agreement with the measurements, i.e. the energy
output-file of the fit program, and indicates that we have a nearly pure Hund case (bβJ ).
The energy level of CCC15 N is given in Fig. 7.2.
102
7 Measurements and Analysis
.
CCC 15 N (X 2 Σ )
E
GHz
splitting x 183
splitting x 13.7
F=1
1.888 MHz
F=2
J=3/2
60
N=3
50
γ (N+1/2)
F=3
1.619 MHz
J=5/2
F=2
.
30
F=0
N=2
.
2.518 MHz
F=1
J=1/2
20
27.3 MHz
1.649 MHz
J=3/2
F=2
F=1
10
N=1
0
F=0
N=0
Rotation
1.883 MHz
J=1/2
b
F
F=1
Hyperfine−Structure
Fine−Structure
γ =−18.2 MHz
b =1.88 MHz
F
c=−4.30 MHz
.
Figure 7.2: Energy level diagram of CCC15 N. The rotational transition N 1 → 0 corresponds to an energy difference of ∼ 9.6 GHz. The fine structure splitting which is due
to the spin-rotation interaction is approximately γ(N+1/2). For the N=0, F 0 → 1
transition the hyperfine structure is solely determined by the Fermi contact interaction
and the splitting is therefore a direct measure for the bF . The dotted vertical lines
represent measured transitions and are sorted in increasing frequency. Only ∆J=∆N
transitions which are the strongest are displayed here, i.e. not all measured lines are
shown here.
7.1 The C3 N Mono-Substituted Isotopomers
Figure 7.3: Measured
7.1.2
13
13
103
CCCN transitions.
CCCN, C13 CCN and CC13 CN
The hyperfine structures of 13 CCCN, C13 CCN and CC13 CN were analyzed with a standard Hamiltonian for a linear molecule in a 2 Σ electronic state including the 13 C and
14
N nuclear spins [57]:
H = Hrot + Hf + Hhf s
(7.8)
with
Hrot = BN2 − DN4
Hf = γN · S + γD (N · S)N2
1
Hhf s = bF I(13 C) · S + c[I(13 C)z Sz − I(13 C) · S]
3
1
+bF I(14 N ) · S + c[I(14 N )z Sz − I(14 N ) · S]
3
(2)
14
+eQq/4To (I( N ))
(7.9)
where N is the rotational angular momentum of the molecule, S is the electron spin
angular momentum, and I(13 C) = 1/2 and I(14 N ) = 1 are the nuclear spins of the
respective nuclei. The z axis is taken to lie along the linear carbon chain. Hrot is the
104
7 Measurements and Analysis
I(14 C)
Hund case (b β s )
2 nuclear spins
13
I( C)
F1
F
F2
S
I( 14 C)
Hund case (b βJ )
2 nuclear spins
I(13C)
F
F1
N
N
Λ
L
S
J
R
quantization
axis
Λ
R
quantization
axis
L
Figure 7.4: Hund case bβs and bβJ with 2 nuclear spins. Hund case bβs (left): The
subscript β indicates that the nuclear spin is not coupled to the molecular axis but to
some other vector. In this case the nuclear spin I(13 C) is coupled with the electron
spin S to form F2 . J = N + S does not appear, see Townes & Schawlow p.197 [181],
instead a new quantum number F1 is used here. Hund case bβJ (right): In this case,
which is expected to be more common, the electron spin couples to the rotation N to
give J. Then J and I couple to give F1 . This coupling scheme was exploited in the fit.
rotation and centrifugal distortion Hamiltonian and Hf is the fine structure Hamiltonian,
i.e. the magnetic interaction between the electronic spin and the molecular rotation.
Hhf s is the hyperfine structure Hamiltonian which includes the interaction between the
electron spin and the 13 C nucleus as well as the interaction between the electron spin
and the 14 N nucleus in terms of the Fermi contact and the electron-nuclear dipole(2)
dipole constants. The last term is the electrical quadrupole interaction with To (I)
the molecule fixed component of the quadrupole moment tensor. Herb Pickett’s [153]
program was used to analyze the data and the coupling scheme
J = N + S, F1 = J + I(13 C), F = F1 + I(14 N ),
(7.10)
was applied to examine the hyperfine structure of the two here measured 13 C isotopic
species of C3 N. For 13 CCCN, a more natural choice for the coupling scheme would be
F1 = N + I(13 C), F2 = F1 + S, F = F2 + I(N) because the 13 C hyperfine interaction
is larger than that of spin-rotation [181] , see Fig. 7.4. However the fitting program can
readily handle large off-diagonal terms in the Hamiltonian matrix which occur when the
coupling scheme in Eq. 7.10 is used, so, for uniformity, it was adopted for 13 CCCN as
well. Some of the observed rotational transitions of 13 CCCN are indicated in the energy
level diagram in Fig. 7.5. The data were fitted in two steps.
In initial fits to the carbon-13 Fourier transform centimeter-wave data (see Table 7.6,
7.7 and 7.8), the rotational constant B and the centrifugal distortion constant D were
constrained to the values previously determined from the millimeter-wave data, and the
three nitrogen hyperfine constants (bF , c, and eQq) were constrained to the values for
normal CCCN [66]. The three remaining constants, the spin-rotation constant γ, bF
(13 C), and c(13 C), were varied to fit the lowest-J transitions, yielding a rms of typically
7.1 The C3 N Mono-Substituted Isotopomers
13
105
2
CCC N (X Σ )
E
GHz
splitting x 56
arbitrary scaling (less than x 0.1)
28 MHz
50
J=3/2
45.1 MHz
J=5/2
40
F=1,3 F=2
F=0 F=2
F=1
F 1 =2
F 1 =1
F 1 =3
F=2
F=1 F=3
F 1 =2
61 MHz
N=2
J=1/2
20
966 MHz
27.0 MHz
10
F=2
F=1 F=2
F=0
F=1 F=2
F=3
30
J=3/2
F=3,4
956 MHz
F 1 =1
F 1 =2
F 1 =0
F=1
F 1 =1
F=1 F=2
F 1 =1
F=2 F=1
F=0
N=1
0
N=0
Rotation
J=1/2
Fine−Structure
γ =−18.0 MHz
F=0
1.2 MHz
980 MHz
F=1
F 1 =0
magnetic Fine−Structure, I( 13 C)
b =973.5 MHz
c=139.5 MHz
F
Hypefine Structure
Figure 7.5: 13 CCCN energy level scheme. The splitting of the order 900-1000 MHz due
to the magnetic interaction of the 13 C is much stronger than those of the 14 N (or
15
N). For the low lying rotation transitions the 13 C Fermi contact and dipole-dipole
interaction dominates the energy splitting and is even larger than the spin-rotation
interaction (for N<50). The magnetic interaction of the 14 N nuclear spin provides the
hyperfine structure in the order of 1 MHz. The dotted vertical lines (on the right)
represent measured transitions and are sorted in increasing frequency. Only ∆J=∆N
transitions which are the strongest are displayed here.
≤20 kHz; subsequently, B and the three nitrogen constants were varied as well, giving
an rms comparable to the 2-5 kHz measurement uncertainty. After the centimeterwave transitions were assigned, global fits including the millimeterwave data [121] were
done. The centimeter-wave lines were assigned a frequency uncertainty of 2 kHz, and
the millimeter-wave lines uncertainties between 15 kHz and 150 kHz, with 25 kHz for
most. Each hyperfine line was thus given a weight of about 100 relative to each of the 5-7
millimeter-wave lines in the range of N=11 to 29. The final hyperfine parameters derived
from the global fits are nearly identical to those calculated from the initial fits, and the
global rms are comparable to those obtained from the millimeter-wave data alone. As
an example Tab. 7.3 shows the molecular constants of 13 CCCN during each of these
steps; the analogous tables for C13 CCN and CC13 CN are in Appendix C. In Tab. 7.4
the final fits for 13 CCCN, C13 CCN and CC13 CN are summarized. For comparison, the
spectroscopic constants of normal CCCN from [66] are also given.
With the 13 C hyperfine constants given in Table 7.4, it is possible to make systematic
comparisons between the electronic structure and chemical bonding of C3 N, isoelectronic
C4 H, and isovalent CCH. Such comparisons are appropriate because all three chains
106
7 Measurements and Analysis
Table 7.3: Molecular Constants of
Constanta
this workb
13
CCCN (in MHz).
mm-data onlyc
recommendedd
values
B
4771.218(1)
4771.2193(1)
4771.2195(2)
D ×10−3
0.62(5)
0.6991(1)
0.6993(2)
γ
−17.96(2)
−17.93(2)
−17.963(5)
γD ×10−3
0.2(7)
−0.020(9)
...
13
bF ( C)
980.(4)
973.(3)
973.(2)
c(13 C)
140.(5)
108.(1)
139.5(3)
14
bF ( N)
−1.17(7)
−30.(20)
−1.26(6)
14
c( N)
3.1(2)
0.(10)
3.4(1)
eQq0
−4.45(4)
−6.(52)
−4.48(4)
w-rmse
0.61
2.720
1.177
a
Uncertainties (in parentheses) are (1σ) in the last significant digit.
b
11 lines were used, see Tab.7.6. The uncertainties of the lines is
estimated to be 2 kHz. c 20 lines from [121] were used.
The
uncertainties of the lines are estimated to be between 22-86 kHz.
d
Total fit with all measured 31 lines. e w-rms is the weighted rms,
i.e. the rms normalized with uncertainties of measured lines.
Table 7.4: Spectroscopic constants of the 13 C isotopic CCCN species. The fit included
the MWFT data and the mm-data from McCarthy et al. [121]
13
Constanta
CCCNb
CCCN
C13 CCN
CC13 CN
B
4947.6207(11) 4771.2195(2) 4920.7095(2) 4929.0640(2)
D×103
0.7535(16)
0.6993(2)
0.7453(4)
0.7497(3)
γ
-18.744(6)
-17.963(5)
-18.574(5)
-18.648(3)
γD ×103
-0.006(11)
...
...
...
bF (13 C)
...
973(2)
188.6(2)
23.55(2)
13
c( C)
...
139.5(3)
52.9(1)
2.17(3)
bF (14 N )
-1.20(3)
-1.26(6)
-1.234(6)
-1.182(8)
14
c( N )
2.84(9)
3.4(1)
2.82(3)
2.88(2)
eQq
-4.32(10)
-4.48(4)
-4.331(9)
-4.323(8)
w-rmsc
...
1.19
1.16
0.77
number of
...
11+(20)
13+(28)
32+(12)
transitions used
MWFT+(mm)
a
Units are MHz. The 1σ uncertainties (in parantheses) are in the units of
the last significant digits. The spectroscopic constants were derived from the
hyperfine-split centimeter-wave transitions in Tables 7.6, 7.7, 7.8 and the mmwave transitions in [121]. b Ref.[66] c Normalized standard deviation of the fit.
7.1 The C3 N Mono-Substituted Isotopomers
107
.
1
2
C C C N
C C C N
.
.
C C C N
4
C C C N
.
3
Figure 7.6: Resonance structure of CCCN
are σ-bonded radicals with 2 Σ ground states, and because the hyperfine constants are
proportional to important expectation values of the valence electron, providing highly
specific probes of the molecular wave function. Carbon-13 is particularly useful because
it probes the wave function at all the substituted positions along the carbon chain. There
are only two non-zero hyperfine parameters for a 2 Σ state: the Fermi-contact term bF
and the dipole-dipole term c.
The Fermi-contact constant bF is a useful measure to localize the unpaired electron, or
more accurate to determine the spin density along the carbon chain in σ bonded radicals
like Cn N with odd n (e.g. CN and C3 N) and Cn H with even n (e.g. C2 H and C4 H).
This is because only s electrons have non-zero amplitude at (r=0) 3 and in this case the
unpaired electron is expected to have significant s character, see Fig. 5.1. The magnetic
dipole coupling constant c also provides useful information on the orbital occupation of
the unpaired electron, because it is a function of both an angular average and the radial
expectation value of 1/r3 .
C3 N is isoelectronic to C2 H and C4 H and shows similar behavior in the hyperfine structure. Before comparing these radicals it is worthwhile thinking of a qualitative model for
the Fermi contact interaction along the carbon chain which is basically similar for these
molecules (e.g. N is replaced by CH in the case of Cn H, n=2,4). A description of the
bonding in CCCN requires a superposition of several different electronic structures as it
is shown in Fig. 7.6. Structure 1, with the unpaired electron localized on the terminal
carbon has the highest stability of all the resonance structures because of it’s four π
bonds: two between C(1) and C(2) , two between C(3) and N. Resonance structure 2, with
the unpaired electron on C(2) , and structure 4, with the electron on N, are less stable
because they only have three π bonds. Structure 3, with the unpaired electron on C(3) ,
has only two π bonds and is the least stable structure. It is therefore expected that
the spin density should be greatest at C(1) , less at C(2) and N, and least at C(3) . Assuming that the electron configuration is identical in all three here relevant isotopomers
13
CCCN, C13 CCN, and CC13 CN, then bF (13 C) for each isotopomer is a measure of the
3
With (r, θ) the spherical coordinates of the electron.
108
7 Measurements and Analysis
Table 7.5: bF (13 C) and c(13 C) values
13 C
position →
CCH
CCCN
CCCCH
bF (13 C)-values / MHz
1
2
3
900.7(6) 161.63(10)
—
973.46(2) 188.513(1) 23.555(23)
396.8(6)
57.49(5)
-9.54
c(13 C)-values / MHz
1
2
3
142.87(3) 64.07(5)
—
139.5(3)
53.0(1) 2.17(3)
89.12(1) -1.91(3) 9.84(8)
spin density at carbon C(i) . In Tab. 7.4 the bF -values are listed with 973, 189 and 24
MHz for C(1) through C(3) , which qualitatively is the predicted decrement.
Figure 7.7 shows the magnitude of the two hyperfine constants at different positions
along the carbon chain for the three radicals. Although bF (13 C) and c(13 C) are nearly
the same for 13 CCH and 13 CCCN and for C13 CH and C13 CCN, the same two constants
are each smaller by about a factor of two or more at the same substituted positions of
CCCCH. The reason for these difference may be the large zero-order mixing between the
low-lying 2 Π state and the X 2 Σ+ ground state of C4 H: the 2 Π - X 2 Σ energy separation is
calculated to be 3600 cm−1 for CCH [150, 151], 2400±50 cm−1 for C3 N, but only 100±50
cm−1 for C4 H [121] 4 . Owing to strong vibronic coupling between these states, the 2 Σ
ground state of C4 H probably possesses significant 2 Π character, unlike the ground states
of CCH or C3 N, which are nearly pure 2 Σ.
With simple atomic orbitals [170] it is possible to estimate crudely the fractional 2s and
2p character in the 2σ molecular orbital of C3 N, on the assumption the unpaired electron
is localized on either of the two carbon atoms furthest from the nitrogen. Within a few
percent, this calculation yields the same unpaired electron spin density on the terminal
carbon atom (74%) and adjacent carbon atom (26%) for C3 N as that previously derived
for CCH [120], and little contribution from the pπ electronic configuration. In contrast,
the relative amount of pπ character is estimated by the same calculation [121] to be
about 28% for C4 H, a result in good agreement with that of Hoshina et al. [90], who
concluded on the basis of LIF measurements that the admixture is about 40%.
4
The bF (13 C) of CC13 CCH is -9.54 MHz (see Tab. 7.4) which can be explained by a spin polarization
effect which arises when the paired electrons in the σ orbital are slightly polarized by the electrons
2
in the nearby p orbitals [30] : bF = 2µBI µI h 8π
3 Ψ (0)iU + spin polarization.
7.1 The C3 N Mono-Substituted Isotopomers
109
CCH
1000
CCCCH
800
CCCN
F
Fermi contact (b , in MHz)
1200
600
400
200
0
0
1
2
3
4
5
0
1
2
3
4
5
Dipole-dipole (c, in MHz)
200
150
100
50
0
carbon atom
Figure 7.7: (Top:) bF -values of different isoelectronic carbon chains. Each number n
stands for the position of a 13 C-atom within the molecule as seen from the terminal
C-atom, i.e. n=2 for the CCCN isotope is C13 CCN. In a pure 2 Σ ground state the
unpaired electron would be completely localized at the terminal carbon atom. For a
small 2 Π admixture in the 2 Σ ground state the spin density is highest at the terminal
C-atom and decreases with increasing n which is reflected by the decreasing bF -values.
CCCCH has more 2 Π character in the ground state and hence a smaller |hΨ(0)i|2 which
results in smaller bF compared with the more pure X2 Σ species CCH and CCCN.
(Bottom:) c-values of isoelectronic carbon chains.
110
7 Measurements and Analysis
Table 7.6: Measured Rotational Transitions of 13 CCCN in the X 2 Σ+ State.
Frequencya O − C b
Transition
J’
F’1
F’
N
J
F1
F
(MHz)
(kHz) N’
1
3/2 2
3
0
1/2 1
2
9528.817
1
1
3/2 1
2
0
1/2 0
1
9542.475
−3
2
5/2 3
3
1
3/2 2
2
19073.604
−2
2
5/2 3
4
1
3/2 2
3
19073.886
−1
2
5/2 2
2
1
3/2 1
1
19084.532
−3
2
5/2 2
3
1
3/2 1
2
19084.612
3
2
3/2 2
3
1
1/2 1
2
19085.382
0
3
7/2 4
5
2
5/2 3
4
28617.158
2
3
7/2 3
3
2
5/2 2
3
28626.762
1
3
7/2 3
4
2
5/2 2
3
28626.796
4
3
5/2 3
4
2
3/2 2
3
28627.817
−3
a
Estimated experimental uncertainties (1σ) are 2 kHz.
b
Calculated frequencies derived from the best fit constants in Tab. 7.3
Table 7.7: Measured Rotational Transitions of C13 CCN in the X 2 Σ+ State.
Frequencya O − C b
Transition
J’
F’1
F’
N
J
F1
F
(MHz)
(kHz) N’
1
3/2 2
2
0
1/2 1
1
9829.369
−1
1
3/2 2
3
0
1/2 1
2
9830.396
1
1
3/2 1
1
0
1/2 0
1
9839.603
−1
1
3/2 1
2
0
1/2 0
1
9840.701
−2
2
5/2 3
3
1
3/2 2
2
19672.508
6
2
5/2 3
4
1
3/2 2
3
19672.780
−5
2
5/2 2
3
1
3/2 1
2
19681.164
−7
2
5/2 2
2
1
3/2 1
1
19681.175
3
2
3/2
2
1
1
1/2
1
1
19684.220
1
2
3/2 2
3
1
1/2 1
2
19684.755
2
3
7/2 3
4
2
5/2 2
3
29521.725
3
3
7/2 3
3
2
5/2 2
2
29521.758
1
3
5/2 3
4
2
3/2 2
3
29626.764
−4
a
Estimated experimental uncertainties (1σ) are 2 kHz.
b
Calculated frequencies derived from the best fit constants in Tab. 7.3
7.1 The C3 N Mono-Substituted Isotopomers
Table 7.8: Measured Rotational Transitions of CC13 CN in the X 2 Σ+ State.
Frequencya O − C b
Transition
J’
F’1
F’
N
J
F1
F
(MHz)
(kHz) N’
1
3/2 2
2
0
1/2 1
1
9847.713
−3
1
3/2 2
3
0
1/2 1
2
9848.755
2
1
3/2 1
1
0
1/2 0
1
9853.055
5
1
3/2 1
2
0
1/2 0
1
9853.282
8
1
1/2 1
2
0
1/2 1
2
9873.604
2
2
5/2 3
3
1
3/2 2
2
19706.620
3
2
5/2 3
4
1
3/2 2
3
19706.889
2
2
5/2 3
2
1
3/2 2
1
19706.914
3
2
5/2 2
2
1
3/2 1
1
19709.044
−7
2
5/2 2
3
1
3/2 1
2
19709.080
5
2
3/2 2
3
1
1/2 1
2
19723.673
3
2
3/2 1
2
1
1/2 0
1
19726.516
−3
3
7/2 4
4
2
5/2 3
3
29564.843
0
3
7/2 4
3
2
5/2 3
2
29564.907
−3
3
7/2 4
5
2
5/2 3
4
29564.970
2
3
7/2 3
3
2
5/2 2
2
29566.119
−3
3
7/2 3
4
2
5/2 2
3
29566.174
5
3
7/2 3
2
2
5/2 2
2
29568.747
−6
3
5/2 3
3
2
3/2 2
3
29580.140
−2
3
5/2 2
2
2
3/2 1
2
29581.389
−3
3
5/2 3
3
2
3/2 2
2
29582.300
−8
3
5/2 3
2
2
3/2 2
1
29582.480
3
3
5/2 3
4
2
3/2 2
3
29582.569
1
3
5/2 2
2
2
3/2 1
1
29583.673
0
3
5/2 2
3
2
3/2 1
2
29583.913
5
3
5/2 2
1
2
3/2 1
1
29584.491
1
4
9/2 5
5
3
7/2 4
4
39422.912
−5
4
9/2 5
6
3
7/2 4
5
39422.990
1
4
7/2 4
4
3
5/2 3
3
39440.879
−1
4
7/2 4
5
3
5/2 3
4
39440.986
0
4
7/2 3
3
3
5/2 2
2
39441.702
−2
4
7/2 3
4
3
5/2 2
3
39441.785
6
a
Estimated experimental uncertainties (1σ) are 5 kHz.
b
Calculated frequencies derived from the best fit constants in Tab. 7.3
111
7 Measurements and Analysis
Theoretical Intensity
112
21,74
21,76
Frequency [GHz]
21,78
21,8
Theoretical Intensity
21,72
0
20
40
60
Frequency [GHz]
Figure 7.8: C4 N stick spectrum calculated for Trot =3K.
7.2 C4N and C6N
For the first time the linear cyano radicals C4 N and C6 N could be measured in the
laboratory. The spectra were observed between 7.2 and 21.7 GHz for C4 N and 7.8 and
18.3 GHz for C6 N, i.e. at least four rotational transitions of each radical fall within
the frequency range of the used spectrometer. The measured laboratory frequencies for
these molecules are given in Table 7.11 and 7.12, and typical lines are shown in Fig. 7.9
and 7.10. Searches for the rotational spectra of C4 N and C6 N were guided by ab initio
calculations of Pauzat et al. [144]. The rotational constants for both molecules were
estimated by scaling these ab initio rotational constants by the ratio of the experimental
7.2 C4 N and C6 N
113
B value to that calculated at the same level of theory for C2 N, C3 N, and C5 N. Rotational
transitions predicted in this way turned out to be quite accurate - to within 0.25% for
C4 N and C6 N.
The present identifications are extremely secure: (i) the two new molecules are almost certainly radicals because their rotational transitions are separated in frequency by
halfinteger quantum numbers, and their lines exhibit the expected Zeeman effect (i.e., a
fairly modest broadening owing to the small magnetic g factor of a 2 Π1/2 state) when a
permanent magnet is brought near the molecular beam; (ii) the carriers of the observed
lines are nitrogen-bearing molecules because the lines disappear when cyanoacetylene
is replaced with diacetylene, and because characteristic hyperfine structure from the
nitrogen nucleus was observed in all of the assigned spectra; (iii) impurities from contaminants in the gas samples and van der Waals complexes with the buffer gas can
also be ruled out, because the lines were produced with acetylene plus cyanogen as the
precursor gas, and when Ar replaced Ne as the buffer gas; and (iv) the identifications
of C4 N and C6 N are also supported on spectroscopic grounds by the close agreement of
B and D with those estimated by scaling from the ab initio geometries and the Cn H
chains of similar size. In addition, the Λ-doubling constant p + 2q in the 2 Π1/2 ladder
of C4 N and C6 N can be predicted to within a factor of two by scaling from CCN [142]
on the assumption of free precession. The nitrogen hyperfine constants a − (b + c)/2, b,
and d also smoothly decrease in magnitude from CCN to C6 N, as one might expect if
the unpaired electron is delocalized along the chain; a similar decrease in the hydrogen
hyperfine constant a−(b+c)/2 has been observed in the odd-numbered acetylenic chains
up to C13 H [64]. Under optimized experimental conditions, the strongest rotational lines
of C4 N were approximately 15 times less intense than those of C3 N, but were still observed with a signal to noise of approximately 25 after one minute of integration; the
decrement in peak signal strength from C4 N to C6 N was only about a factor of three.
An effective Hamiltonian for molecules in a 2 Π electronic state used in the present
analysis is expressed as
H = Hrot + HSO + HΛ + Hhf s
were the terms on the right side of the equation are the rotational energy, the spin-orbit
interaction, the Λ-type doubling interaction, and the hyperfine interaction, respectively,
see Chapter 6.3.1. The hyperfine structure term includes the magnetic and the electricquadrupole interaction due to the 14 N nucleus. Unlike in the case of C2 N the spinrotation interaction was not needed to result in a good fit. Instead of the pure ASO spin
orbit constant Aef f = ASO + γ was used for the fit, see Chapter 6.2.
The lowest rotational transitions of both C4 N and C6 N in the ground 2 Π1/2 fine structure
ladder are split into six components by Λ-doubling on the scale of 2-5 MHz and then
by hyperfine structure from the nitrogen nucleus which is generally smaller by about
an order of magnitude (i.e. on the scale of 0.2-0.5 MHz). Rotational transitions from
the higher-lying X 2 Π3/2 ladder were not observed, because this level lies at least several
tens of Kelvin above the X 2 Π1/2 level and is apparently not appreciably populated in
the generally rotationally cold molecular beam (Trot = 0.2 - 3 K). The fits were done
114
7 Measurements and Analysis
Figure 7.9: Measured C4 N transition. Shown are the ∆F=∆J transitions at 12094.384
MHz and 12094.480 MHz with F 5/2 → 3/2 and F 3/2 → 1/2 respectively.
Figure 7.10: Measured transition of C6 N. Shown are the transitions F 17/2→15/2 and
F 15/2→13/2 at 13086.043 MHz and F 13/2→11/2 at 13086.146 MHz.
7.2 C4 N and C6 N
115
14
I( N)
Hund case a
1 nuclear spin
F
J
R
Λ
L
Σ
quantization
axis
S
Figure 7.11: Hund’s case a with one nuclear spin. In the case of C4 N is L=1, S=1/2,
R=0,1,2,... , and I(14 N)=1/2.
with the HUNDA program written by J. Brown [27] which is based on the effective
Hamiltonian of Brown et al. [26, 24] in the strong Hund’s case (a) with 2JB |ΛASO |,
see Fig. 7.11. The spin-orbit constant Aef f = ASO +γ was constrained at 40 cm−1 (∼ 1.2
THz) because no information of the Π3/2 states was available and it was assumed that
ASO + γ from C4 N and C6 N is of the same order of magnitude than that from C2 N [142].
At most nine spectroscopic constants: the rotational constant B, centrifugal distortion
D, two Λ-doubling constants p + 2q and (p + 2q)D , and five hyperfine constants, the
diagonal term a− = a − (b + c)/2, the off-diagonal term b, the parity-dependent term
d, the electric quadrupole term eQq0 , and the nonaxially symmetric quadrupole term
eQq2 were required to reproduce the 29 measured lines of C4 N and the 42 of C6 N to
better than 2 kHz. If eQq2 was constrained to zero in the C4 N fit, the rms increases by
more than a factor of five. In Fig. 7.14 the energy level diagram of C4 N is shown. With
the spectroscopic constants for C4 N and C6 N as listed in Table 7.9, precise frequencies
for the astronomically interesting transitions can be calculated to very high precision.
Fig. 7.8 shows a stick spectrum with a calculated intensity distribution corresponding
to a rotational temperature of 3 K. For both radicals the strongest lines are found for
∆F = ∆J transitions (mainly with F’=J’+1). In the case of C4 N transitions with
∆F = 0 and ∆F = −1 could be observed but ∆F = 0 transitions of C6 N are very weak
and only ∆F = −1 transitions could be measured. That resulted in a strong correlation
between the a− and the eQq0 of ∼1 in the fit for the C6 N radical. The eQq0 is nearly
constant for all known Cn N chains, with n<6, and was fixed to -4.38 MHz to avoid that
correlation.
The Cn N, n=2,4,6, are isoelectronic to Cn H, with n=3,5,7 and with the exception of
C7 H there are already some data at hand concerning their magnetic and electronic
quadrupole hyperfine structure. The Frosch & Foley hyperfine parameters a, bF , c, and
d give information about the unpaired and total electron distribution h1/r3 i, hsin2 θ/r3 i,
h3 cos2 θ − 1/r3 i, and hψ 2 (0)i. Unfortunately, it is impossible to obtain a complete set
116
7 Measurements and Analysis
Table 7.9: Spectroscopic Constants of C4 N and C6 N in the X 2 Π State.
Constanta
C4 N
Aef f
1200000b
(40 cm−1 )
B
2422.6963(1)
−6
D [× 10 ]
90(3)
P ef f
4.5525(8)
PDe f f [× 10−3 ] 5.23(2)
a−
15.005(1)
b(14 N )
16.2(1)
d
22.4254(9)
eQq0
-4.389(1)
eQq2
5.6(3)
transitions
∆ F = 0,-1
no. of lines
29
exp. uncert.
2 kHz
rms
1 kHz
w-rms
0.614
C6 N
1200000b
(40 cm−1 )
873.11224(6)
11.5(7)
1.939(5)
0.066(2)
8.7(5)
7.4(10)
13.23(1)
-4.38b
...
∆ F = -1
33
2 kHz
3.6 kHz
1.803
a
Units are in MHz. The 1σ uncertainties (in
parentheses) are in the units of the last significant
digits. b fixed value
of these parameters, owing to lack of data for the a+ = a + (b + c)/2 constant for which
Ω3/2 transitions are needed. Ohshima et al. [142] showed how it is possible to use some
simple assumptions concerning the missing constants and to estimate the molecular
parameters. It is mainly the fact that the ratios a/d and −c/d should be in the ranges
of 0.70-0.75 and 0.52-0.54 respectively for these kinds of radicals. For the C4 N and C6 N
the molecular parameters could be calculated by scaling the C2 N value appropriate to
the notation of [181, 142], i.e. using Eq. (6.35), (6.37), (6.38), and (6.40). The results for
the Cn N chains are listed in Tab. 7.10 together with the values for the isoelectronic CH,
C3 H, C5 H radicals; some of them are plotted in Fig 7.2. The d and the eQq2 constants
are associated with the non-axial symmetry hsin2 θ/r3 i of the electron distribution in the
radical. The difference between both constants is that d refers to the unpaired electrons
(U) and eQq2 to the total electrons (T). In the case of C2 N hsin2 θ/r3 iU ≈ hsin2 θ/r3 iT
which means that the non-axial distribution is mainly caused by the unpaired electron.
For C4 N the situation is different because hsin2 θ/r3 iT − hsin2 θ/r3 iU = 6 · 1024 cm−3 and
it is therefor not the unpaired electron that dominates the non-axial term. A comparison
with other hsin2 θ/r3 iT -values from higher members of the Cn N (n even) chains would
be desirable but for C6 N no eQq2 was determined and higher members are not detected
so far.
log (relative abundance)
7.2 C4 N and C6 N
117
C N radicals
n
n=3
0
4
-1
6
5
-2
2
3
4
5
6
7
number of carbon atoms
Figure 7.12: Relative abundances of the Cn N radicals per gas pulse in the supersonic
molecular beam as a function of chain length.
Lines of C4 N and C6 N are readily observed in the supersonic molecular beam, even
though both radicals are calculated ab initio to possess rather small dipole moments
- 0.14 D for C4 N and 0.31 D for C6 N [144]. In FTM spectroscopy, line strengths are
proportional to the first power of the dipole moment µ, not µ2 , as in classical absorption
spectroscopy; rotational lines of small µ molecules are therefore relatively much more
intense in FT spectroscopy than in conventional spectroscopy. Bauder and co-workers,
for example, have detected a number of deuterated hydrocarbons [157] using the present
technique; many with dipole moments in the range of 10−1 - 10−3 D.
Relative abundances (see Fig. 7.2) of the nitrogen-bearing carbon chain radicals here
to one another and to C3 N and C5 N were determined from intensity measurements on
lines as close in frequency as possible to minimize variations in instrumental gain. These
were converted to absolute abundances by comparing line intensities with those of the
118
7 Measurements and Analysis
CnN, n=2,4,6 (positive)
-3
0,4
4
3
0,2
0,1
2
0
4
n
6
6
2
3
4
n
5
6
CnN, n=2,4,6
-3
cm
6
24
0,3
2
24
Cn+1H, n=2,4 (scale x40)
(x40)
0
Cn+1H, n=2,4 (scale x25)
5
4
3
3
〈 sin ϑ /r 〉U / 10
CnN, n=2,4,6
8
Cn+1H, n=2,4 (negative)
〈1/r 〉 / 10 cm
24
|〈 Ψ(0) 〉 | /10 cm
-3
0,5
2
2
(x25)
1
0
2
4
n
6
Figure 7.13: Molecular constants h1/r3 i, hsin2 θ/r3 i, and hψ 2 (0)i of Cn N, n=2,4,6 and
Cn+1 H, n=2,4 as estimated in Tab. 7.10
rare isotopic species of OCS in a supersonic beam of 1% OCS in Ar in the absence of a
discharge, taking into account differences in the rotational partition functions and dipole
moments. As Fig. 7.2 shows, the two new chains here are more than a factor of two
more abundant than C5 N.
The formation of carbon chain radicals in our molecular beam is apparently different
for chains with odd and even numbers of carbon atoms. Although the abundance data
for Cn N is much less complete than for Cn H, it is worth noting that the plot in Fig. 7.2
is similar to that previously derived for the acetylenic radicals (see Fig. 2 of Ref.[64]),
implying similar, if not common, formation mechanisms in the discharge. Most of the
C2n+1 H and C2n N chains are more abundant than the corresponding C2n H and C2n+1 N
chains. If nonpolar carbon chains C2n+1 are more abundant than even-numbered chains
C2n , for example, subsequent reactions involving the radicals C2 H or CN (produced
directly via cleavage of the central C-C bond of either HC4 H or HC3 N) may produce the
odd-even alternation that is observed. Evidence to support this formation mechanism is
the mass distribution of a diacetylene discharge which exhibits an even-odd alternation
in abundance for chains beyond C9 , with the odd chains being more abundant [156].
7.2 C4 N and C6 N
2
Π
119
∆ W =q D (J 2−1/4) (J+3/2)
Π
7B
3/2
J=5/2
N=3
f
e
5B
f
e
J=3/2
6B
S=+1/2
2B
e transitions with ∆ F = 0
f transitions with ∆ F = −1
f transitions with ∆ F = 0
N=2
Aso = 40 cm −1
4B
e transitions with ∆ F = −1
∆ W = p eff (J+1/2)
N=1
N=0
F=5/2
F=1/2
e
J=5/2
F=3/2
f
e
f
3B
Rotation
Π
Fine structure
F=1/2
F=3/2
f
F=1/2
e
p eff = 4.5 MHz
1/2
Hund(b)
F=1/2
e
J=3/2
J=1/2
F=5/2
f
5B
S=−1/2
F=3/2
F=3/2
14 MHz
Λ −doubling
Hyperfine structure
(a +d)=37 MHz
−
(a −−d)=7 MHz
Hund(a)
Figure 7.14: Schematic C4 N energy level. The dominating splitting in the energy level
diagram is due to the spin-orbital interaction which separates the Π3/2 and Π1/2 states.
Transitions involving a Π3/2 state have not been measured and the energy separation
is assumed to be 1.19 THz according to other similar species like C2 N, see [142]. In
contrast to a Hund’s case (b) as it is plotted on the left with (2N)B spacings the fit was
done in Hund’s case (a) and the rotational energy levels are now (2N+1)B separated.
The Λ-doubling components are labeled by the e/f parity. The hyperfine structure is
due to the nitrogen magnetic and quadrupole moment.
7 Measurements and Analysis
120
d
Radical
C2 N
C4 N
C6 N
C3 H
C5 H
Table 7.10: Hyperfine and Molecular Constants of Carbon Chain Radicals
bF
-25b
-12b
-7b
c
16.2
10.9 h
46.8
22.4
13.2
d
-
-9.2
5.6
-
eQq2
0.1558
0.11
5.9
2.8
1.7
h1/r3 iU
0.2389
0.16
-2.9
-1.4
-0.8
h(3 cos2 θ − 1)/r3 iU
0.1368
0.09
5.5
2.6
1.5
hsin2 θ/r3 iU
-
5.6
-3.4 c
-
hsin2 θ/r3 iT
-0.0208
-0.03
0.24
0.25
0.04
hΨ2 (0)iU
Molecular Constants (1024 cm−3 )
a
11.4
12.2
1.7
28.3
19.1 g
Hyperfine Parameters (MHz)
34a
16.3a
9.6a
-13.8
-21.8 f
14
12.3
8.3 e
14
0 µI ( N )
I (H)
The calculations were done using Eq. (6.35), (6.37), (6.38), and (6.40) with 2µI(
= 5.7208 and ( µI(H)
)/( µI(I (14 NN)) ) ≈ 13.84.
14 N )
a
calculated as in [142] with a/d = 0.70 − 0.75; b calculated as in [142] with −c/d = 0.52 − 0.54; c same -3e2 Q as in [142]; d
constants taken from [67]; e estimation from a(H) with a/d = 0.76 like in the case of C3 H. f the b value is derived from the
H
C5 D b-value [88] with b(H)est = 2µ
b(D) and b(C5 D) = −4.32M Hz. bF is than estimated with bF = b + c/3; g estimation
µD
from c(H) with c/d = 1.75 like in the case of C3 H. h constant taken from [35];
7.2 C4 N and C6 N
Table 7.11: Measured Rotational Transitions C4 N in the X 2 Π1/2 State.
Transition
Frequency a
e/f b
O−C c
0
0
J →J
F →F
(MHz)
Λ Comp. (kHz)
1.5 → 0.5 1.5 → 1.5
7234.345
f
1
2.5 → 1.5
7247.840
e
-1
1.5 → 0.5
7249.186
e
0
2.5 → 1.5
7255.402
f
-1
1.5 → 1.5
7256.628
e
-1
0.5 → 0.5
7257.124
e
0
0.5 → 0.5
7261.707
f
0
1.5 → 0.5
7271.774
f
-1
2.5 → 1.5 2.5 → 2.5 12073.322
f
-1
1.5 → 1.5 12084.411
f
-1
3.5 → 2.5 12085.235
e
1
1.5 → 0.5 12086.839
e
0
3.5 → 2.5 12091.162
f
2
2.5 → 2.5 12094.262
e
2
2.5 → 1.5 12094.384
f
1
1.5 → 0.5 12094.480
f
0
1.5 → 1.5 12094.777
e
0
3.5 → 2.5 4.5 → 3.5 16921.368
e
-1
3.5 → 2.5 16921.448
e
-1
2.5 → 1.5 16922.195
e
0
4.5 → 3.5 16926.823
f
1
3.5 → 2.5 16928.186
f
-1
2.5 → 1.5 16928.220
f
0
4.5 → 3.5 5.5 → 4.5 21757.146
e
2
4.5 → 3.5 21757.171
e
-1
3.5 → 2.5 21757.636
e
0
5.5 → 4.5 21762.464
f
-1
4.5 → 3.5 21763.210
f
-1
3.5 → 2.5 21763.220
f
2
a
Estimated experimental uncertainties (1σ) are 2 kHz.
Designation of e and f levels is based on the assumption that the hyperfine constant d is positive.
c
Calculated frequencies derived from the best fit constants in Table 7.9.
b
121
122
7 Measurements and Analysis
Table 7.12: Measured Rotational Transitions C6 N, HUNDA-fit
Transition
Frequency a
e/f b
O−C c
0
0
J →J
F →F
(MHz)
Λ Comp. (kHz)
4.5 → 3.5
5.5 → 4.5
7851.036
e
-1
4.5 → 3.5
7851.047
e
0
3.5 → 2.5
7851.318
e
0
5.5 → 4.5
7853.245
f
-3
4.5 → 3.5
7853.677
f
0
3.5 → 2.5
7853.677
f
-4
5.5 → 4.5
6.5 → 5.5
9596.072
e
2
5.5 → 4.5
9596.072
e
-2
4.5 → 3.5
9596.260
e
0
6.5 → 5.5
9598.199
f
-1
5.5 → 4.5
9598.474
f
3
4.5 → 3.5
9598.474
f
2
6.5 → 5.5
7.5 → 6.5
11341.066
e
-1
6.5 → 5.5
11341.066
e
-2
5.5 → 4.5
11341.203
e
0
7.5 → 6.5
11343.149
f
-1
6.5 → 5.5
11343.336
f
0
5.5 → 4.5
11343.336
f
0
7.5 → 6.5
8.5 → 7.5
13086.043
e
-1
7.5 → 6.5
13086.043
e
0
6.5 → 5.5
13086.146
e
0
8.5 → 7.5
13088.099
f
1
7.5 → 6.5
13088.233
f
0
6.5 → 5.5
13088.233
f
2
8.5 → 7.5
9.5 → 8.5
14831.011
e
2
8.5 → 7.5
14831.011
e
4
7.5 → 6.5
14831.085
e
-1
9.5 → 8.5
14833.047
f
3
8.5 → 7.5
14833.145
f
-1
7.5 → 6.5
14833.145
f
2
9.5 → 8.5 10.5 → 9.5
16575.958
e
-1
9.5 → 8.5
16575.968
e
1
8.5 → 7.5
16576.024
e
-1
10.5 → 9.5
16577.985
f
-2
9.5 → 8.5
16578.057
f
0
8.5 → 7.5
16578.068
f
3
10.5 → 9.5 11.5 → 10.5 18320.906
e
-4
10.5 → 9.5
18320.916
e
3
9.5 → 8.5
18320.973
e
...
11.5 → 10.5 18322.929
f
1
10.5 → 9.5
18322.986
f
-2
9.5 → 8.5
18322.990
f
-2
a
Estimated experimental uncertainties (1σ) are 2 kHz.
b
Designation of e and f levels is based on the assumption that the hyperfine constant d is positive.
c
Calculated frequencies derived from the best fit constants in Table 7.9.
7.3 The Search for C7 N
123
7.3 The Search for C7N
Laboratory searches were also undertaken for C7 N using experimental conditions and gas
mixtures that optimize the production of either C5 N or C6 N, or both molecules simultaneously. Searches were based on a high-level coupled cluster calculation by Botschwina
[20], and covered frequency ranges that correspond to ±1% of the predicted rotational
constants. Two searches, one assuming a 2 Σ ground state with rotational lines separated
in frequency by integer quantum numbers, and one assuming a 2 Π ground state with rotational lines separated in frequency by half-integer quantum numbers, were performed,
but no lines which could be attributed to C7 N were found in either survey. The absence
of lines requires the C7 N line intensities to be at least 60 times less than those of C5 N,
which is readily observed in the molecular beam with a signal to noise of better than 25
in one minute of integration. The failure to detect C7 N may indicate a 2 Π ground state
for this molecule. Botschwina concluded on the basis of RCCSD(T)/cc-pVTZ calculations [20] that the ground state of C7 N is 2 Π (µ = 0.96 D), but that a 2 Σ+ state (µ =
3.86 D) is very close in energy, lying only 250 cm−1 above ground at the highest level of
theory. If we assume the same abundance decrement from C5 N to C7 N as from C3 N to
C5 N (a factor of 17) and a 2 Π ground state, the C7 N lines would be 180 times less intense
than those of C5 N, i.e. three times below our present upper limit. If the ground state
is 2 Σ+ instead, the expected decrease in line intensity is only a factor of 45. In either
case, significant rovibronic interaction may occur between these two low-lying electronic
states, a factor which could hinder spectral analysis and assignment regardless of the
symmetry of the ground state. Detection of C7 N may still be possible: with further
improvements in instrumentation and production efficiency a factor of five or more in
sensitivity may be within reach.
7.4 Conclusions and Prospects
Without a further improvement of the sensitivity of the FTMW spectrometer the detection of higher members of the Cn N chains, like C7 N or C8 N seems exceedingly difficult.
For the same reason measurements on C5 N, C4 N, and C6 N isotopomers, i.e. to determine the exact bonding length or the spin density distribution in these radicals, appear
less feasible. However, additional isotopic spectroscopy using 13 C-enriched samples of
cyanogen, cyanoacetylene, methylcyanide, etc. may allow the distribution of carbon in
the discharge source to be determined, providing clues to the chemical processes at work.
This could turn out to be an important tool for a molecule production improvement.
It is known that also non linear structures are build in a discharge jet [123]. Lowlying isomers of C4 N and C6 N may be amenable to laboratory detection with present
techniques. Ding et al. [46] recently calculated the potential energy surface of C4 N,
and concluded that 13 isomers, some with unusual ring, branched, and caged structures,
probably exist. The isomer of the most immediate laboratory interest is the ring-chain
analog to c-C5 H, with the CCH group replaced by a nitrile group. This isomer is
124
7 Measurements and Analysis
predicted to have considerable kinetic stability towards isomerization and dissociation,
and is calculated to lie only 2.8 kcal/mol above the linear chain. Because it is also
predicted to possess a substantial dipole moment (µ = 0.63 D), and because c-C5 H has
already been detected with the same discharge source [4], detection of c-C4 N may succeed
with dedicated searches. Other lowlying polar isomers of C4 N such as CCCNC (23.4
kcal/mol; 1.38 D) may also be within reach. The electronic spectra of C4 N and C6 N
are completely unknown. Both radicals probably possess strong 2 Π - X 2 Π electronic
transitions at visible or near infrared wavelengths, like the shorter chain CCN [142] and
most of the acetylenic chains Cn H up to C10 H. Many of these have now been studied
by sensitive laser techniques (see e.g., Ref. [110]), including LIF, cavity ring-down laser
absorption spectroscopy (CRLAS), and most recently, resonant two-color, two-photon
ionization spectroscopy (R2C2PI) combined with time-of-flight mass detection. All of
the species up to C6 N have abundances near the throat of the discharge nozzle of > 109
molecules per pulse - an adequate number density for all three techniques - but the
best choice would appear to be R2C2PI because the optical spectrum of linear C3 H is
significantly broadened owing to rapid internal conversion [45], and because REMPI is
more sensitive than CRLAS and is mass selective as well.
Up to now there is also a lack of ro-vibrational data even if one considers only linear Cn N
radicals. In the case of C2 N - the first member of the linear Cn N chains - the Â2 ∆-X̂ 2 Π
electronic transition of the CCN free radical has been observed by Oliphant et al. [143]
in emission with a high-resolution Fourier transform spectrometer. Spectroscopic constants were derived including the ground-state vibrational frequencies, ν3 =1050.7636(6),
2ν3 =2094.8157(18), and ν1 =1923.2547(69) cm1 . But for the C3 N radical the vibrational
frequencies have only been investigated by ab initio theory. Botschwina [121] using coupled cluster calculations RCCSD(T) determined the asymmetric stretching vibrations to
be at ν3 = 2311.8 cm−1 and ν2 = 2116.6 cm−1 . There is no verification of these numbers
by gas phase experiments so far, whether in the IR nor in the visible spectral range.
For the C4 N radical the vibration frequencies are calculated to be at ν2 =1995 cm−1 and
ν1 =2186 cm−1 by Ding et al.[46]. C3 N and C4 N are therefore good candidates for a IR
gas phase detection, e.g. using the Cologne IR experiment.
Part III
Linear CnN Chains in Space
8 CnN Chains in Space
Remember, too,
That the whole sky is revolving
With its constellations, its planets.
I have to force my course against thatNot to be swept backwards as all else is. [...]
Even if you were able to stick to the route
You have to pass
The horns of the Great Bull, the nasty arrows
Of the Haemonian Archer, the gaping jaw
Of the infuriated Lion,...
Ted Hughes, ”Tales from Ovid”, Phaethon
Presently there are more than 125 gas phase molecules found in space. The species
range in size from 2-13 atoms. They are typically found in dense interstellar clouds
with tremendous sizes of 1-100 light years, average gas densities of 102 -103 cm−3 , and
temperatures in the range 10-60 K 1 . On the other hand many of the organic molecules
are detected in extended circumstellar envelopes of cool, old stars that are carbon rich
like CW Leo/IRC+10216 or in the somewhat ’special cases’ of molecular clouds TMC-1
and TMC-2.
The large abundance of highly unsaturated carbon chains and radicals, most of which
are linear, is a characteristic feature of IRC+10216 2 and except TMC-1 3 no other
source in the sky shows such a wealth of long linear chains [34].
1
Both, higher temperatures and higher gas densities are found in localized regions where star formation
is occurring.
2
IRC+10216 belongs to the stars with initial masses in the range from about 1 to 8 M . When these
stars “evolve off the main sequence, they go through several stages of evolution in which mass loss
plays a crucial role [. . . ]. For such stars the mass loss usually occurs as a cool, low-velocity wind.
During the asymptotic giant branch (AGB) evolutionary phase, mass loss rates may reach 1 × 10−4
M yr−1 . The resulting high density of such winds near the star and the low temperature of the
stellar photosphere assure that most of the ejected material is in molecular form.“ [15].
3
TMC-1 (Taurus Molecular Cloud 1) is a star forming region with low temperatures (T= 6 - 10 K).
128
8 Cn N Chains in Space
Figure 8.1: The molecular clouds in the plane of the Milky Way, as seen in the 1-0
rotational transition of CO. So far, most of the over 120 astronomical molecules have
been detected in a small number of locations, sometimes only one or two. IRC+10216
is one of the reaches molecular sources in space and CN, C3 N and C5 N have been
found in this object. [179]
So far, detection of Cn N radicals succeeded for the odd members C3 N and C5 N whereas
non of the even membered cyano chains, e.g. C2 N, could be observed in the interstellar
space.
C3 N was first found in the circumstellar envelope of IRC+10216 by Gúelin & Thaddeus
[78]. Since then it has been found in many other sources like IRAS 15194-5115, the proto
planetary nebulae (PPN) CRL 618 and CRL 2688, and the molecular clouds (MC) TMC1, TMC-2 and HCL-2. A list of astronomically measured lines is given in the appendix
(Tab. D.2). C3 N can best be seen in IRC+10216 were it has a rotational temperature
of Trot ≈ 20 K.
So far, only one survey has been undertaken in which isotopes of C3 N were detected
(Cernicharo et al. [34], see appendix Tab. D.1). Unfortunately not all astronomically
observed transitions match the predictions obtained from the newly presented laboratory
data. The astronomical survey reveals that C3 N isotopomers have very weak intensities
and are hardly to be recognized. The discrepancy in the line assignment could therefore
be due to a misinterpretation of astronomical data. In Fig. 8.2 a detail of the line
survey is shown. On the left side of the picture are three lines indicated by arrows.
The left (L1) and middle (L2) line are assigned to 13 CCCN and the right one (L3) to
the U152681 unidentified line. The problem is that non of the laboratory measured
transitions corresponds to the left line (L1). If the lines L2 and L3 are assigned to
13
CCCN instead of L1 and L2 all disagreements between laboratory and astronomical
data are solved. However, an other misassignment at 143104.0 MHz (which can not be
seen in Fig. 8.2) remains4 .
The next larger member of the odd Cn N chains C5 N was first detected in TMC-1 and
IRC+10216 by Gúelin et al. [77]. C5 N appears to be two orders of magnitude less
4
Other unidentified lines in the survey at 142831.1 ± 10 MHz and 143575.8 ± 15 MHz do not match
to laboratory transitions at 143129.47 MHz and 143136.22 MHz.
129
Figure 8.2:
13
CCCN detection in IRC+10216 by Cernicharo et al.[34]
abundant than the related molecule HC5 N, i.e. N (HC5 N/C5 N)' 200. In comparison
the HC3 N to C3 N abundance ratio is of the order of 20, i.e. N (HC3 N/C3 N)= 19. It
is assumed that the rotational temperature of C5 N is the same as from HC5 N, i.e.
Trot ≈ 29K.
In 1991 Pauzat et al. [144] analyzed the feasibility of linear Cn N detection in space
and concluded that due to the small dipole moments all even Cn N members in their 2 Π
electronic ground state would be poor candidates for interstellar detection. Recently,
in a theoretical work Mebel & Kaiser [127] examined the formation of interstellar C2 N
isomers via neutral-neutral reactions in the interstellar medium like
C(3 Pj ) + HCN → C2 N + H(2 S1/2 ) .
(8.1)
The formation of the C2 N isomers is calculated to proceed without any barrier, but
reactions forming CCN, CNC, and c-C2 N are found to be strongly endothermic by 52.7,
59.0, and 99.6 kJ mol−1 , respectively. Considering this result it seems to be highly unlikely that C2 N can be synthesized in cold molecular clouds where average translation
Fig.
2. continued
temperatures
of the reactants are only 10-15 K. The physical conditions in circumstellar
envelopes of late type stars like IRC+10216, are different. Close to the photosphere of
the central star temperatures can reach 4000 K and the elevated velocity of the reactants in the long tail of the Maxwell-Boltzmann distribution can overcome the reaction
endothermicity to form CCN. These type of environments represent ideal targets for
hitherto undetected C2 N in the infrared as well as in the microwave region.
Unfortunately, a simple reaction (see Eq. 8.1) is not a realistic scenario for complex
environments like the IRC+10216 envelope, PPN, molecular clouds or other interstellar
molecule sources. In this situation, astrochemical models specified for the environment
in question can be helpful for estimations of molecule abundances. Nowadays these
models are of great complexity and it is often not easy to determine the most important
synthesis of a species. Especially, if one considers the fact that reaction rates depend
on the density, temperature, and radiation which in turn are functions of the position
in the circumstellar envelope or cloud it is clear that the synthesis of a specific species
is also a function of time and position. Because of the importance of IRC+10216 as a
130
8 Cn N Chains in Space
C 2H 2
CN
HC3 N
C H
2
H 2
C 2
C 4H 2
CN
HC N
C3 N
HCN
5
C H
2
H 2
C 2
C 6H 2
HCN
CN
HC7 N
C5 N
HCN
C 2H
N
C 3H
C 4H
N
C 5H
C 6H
C H
2
HC9 N
Figure 8.3: Major pathways to cyanopolyyne formation in IRC+10216. Although C3 N is
probably build by photo-destruction of HC3 N it seems to play an important role in the
formation process of HC5 N and consequently for all higher cyanopolyynes. [131],[38]
major molecule source with great diversity a short description of the Millar & Herbst
[131, 132] astrochemical model of its circumstellar envelope is given here.
The gas around IRC+10216 is assumed to expand in a spherically symmetric outflow
5
with a velocity of 14 kms−1 and a mass-loss rate of 3 × 10−5 M yr−1 . The model
follows the chemistry from an inner radius ri = 1 × 1016 cm to an outer radius of 1018
cm. At ri parent species (H2 ,He,CO,C2 H2 ,CH4 ,HCN,NH3 ,N2 , and H2 S) are injected into
the outward flow. The choise of an inner radius is governed by the onset of the photochemistry [132]. As the parent molecules flow outwards they are dissociated into reactive
daughter products by the incident interstellar ultraviolet radiation field6 . For molecules,
the average time to travel from the inner to the outer radius takes approximately 10 000
years. The number density of the gas follows an r−2 distribution, while the temperature
profile T(r) in K is assumed to be T (r) = 100(r/ri )0.79 but never to be less than 10 K.
In this way, the temperature never decreases below 10 K. The rates of photodissociation and photoionization as well as the strength of the un-extinguished radiation field
is included in the model. The model network contains 407 species connected by 3851
reactions 7 . In this circumstellar model, as opposed to the interstellar models, neutralneutral reactions and photo-destruction are very important especially for the formation
of larger hydrocarbons.
In the distance of 3·1016 cm where much of the chemistry takes place the major formation
5
This smooth outflow is a oversimplification since observations [117] have revealed that the envelope
consist of discrete, concentric shells.
6
that is by UV radiation coming from far outside IRC+10216
7
Hydrocarbons with more than 23 atoms are not included in the network.
131
mechanism for C3 N (cyanoacetylene) seems to be the photo-destruction of HC3 N. The
latter is formed mainly via the two reactions
CN + C2 H2 −→ HC3 N + H
HCN + CCH −→ HC3 N + H
(8.2)
(8.3)
On the other side the major depletion mechanism for C3 N is photo-destruction to form
C2 and CN. C3 N is also an important constituent in the major pathways to cyanopolyyne
formation in IRC+10216, as can be seen in Fig. 8.3. Similar to C3 N the next member of
the Cn N (n odd) chains C5 N seems to be formed by photo-destruction of HC5 N which is
produced similar to Eq. 8.2 and 8.3, i.e. by CN+C4 H2 → HC5 N + H and HCN + C4 H
→ HC5 N + H.
The main question for Cn N (n even) astrochemistry is how likely the detection of C2 N
is. Following this model a list of theoretical and observed column densities including
the precursor molecules HCn N and Cn H is given in Tab. 8.1 and plotted in Fig. 8.4.
C2 N has probably a two magnitudes smaller column density than C3 N so that it can
hardly be seen in normal line surveys. The column density ratios 8 NL (HC3 N/C3 N)
and NL (HC5 N/C5 N) are of the order of 10. If this is also valid for NL (HC2 N/C2 N) an
astronomical search seems to be reasonable. The parent molecule HC2 N has already
been observed towards IRC+10216 and the column density of C2 N is expected to be less
than 3.6 · 1012 cm−2 which should hence be detectable as well. For comparison: When
HC11 N was unambiguously detected in TMC-1 in 1997 by Bell et al. [8] 9 the signal
corresponded to a column density of 2.8 · 1011 cm−2 at Trot =10 K. Assuming a rotational
temperature similar to C3 N (Trot = 20 K) the best frequency range to search for C2 N is
between 150 and 180 GHz with the transitions J 6.5→5.5 and 7.5→6.5.
8
9
Not to be confused with the abundance ratios mentioned earlier in this chapter.
The 1982 detection in IRC+10216 by Bell et al. [9] was probably incorrect
132
8 Cn N Chains in Space
molecule
HCN
HC2 N
HC3 N
HC5 N
HC7 N
HC9 N
C2 H
C3 H
C4 H
C5 H
C6 H
C7 H
C8 H
CN
C2 N
C3 N
C4 N
C5 N
C7 N
Trot
[K]
20
35
25
35
35
52
20
35
theor.
observed
Tex
Col.Dens.
Col.Dens. Frac. abund.
[K]
[cm−2 ]
[cm−2 ] N(X)/N(H2 )
1.7 1016
2.8 1016
12
1.2-1.8 1013
26
1.8 1015 0.8-1.7 1015
25-35
7.1 1014 1.3-3.7 1014
26
2.2 1014
1.3 1014
12-23
5.8 1013 2.7-4.0 1013
16
5.7 1015 4.6-5.0 1015
7.1 10−6
8.5
1.4 1014
5.6 1013
15
1.0 1015 2.4-3.0 1015
4.3 10−6
13
14
27(Π1/2 ) / 39(Π3/2 )
8.7 10
0.4-2.9 10
6.3 10−8
35(Π3/2 ) / 46(Π1/2 )
5.8 1014 0.6-1.7 1014
7.8 10−8
13
12
4.5 10
2.2 10
3.1 10−9
1.1 1014
1.0 1013
1.4 10−8
8.7
1.0 1015
6.2 1014
12
3.6 10
15
3.2 1014 2.5-4.1 1014
3.5 10−7
8.2 1009
1.4 1014
6.3 1012
9.0 10−9
7.8 1012
Table 8.1: Molecular column densities in IRC+10216, observed values are taken from
Cernicharo et al. [34] and Kawaguchi et al. [101]. Theoretical values are from Millar
& Herbst [132].
column density [cm ]
-2
column density [cm ]
-2
1e+09
1e+10
2
4
2
n
HC2N
6
8
HCnN
observed
theor.
4
10
column density [cm ]
-2
n
1e+12
1e+13
1e+14
1e+15
1e+16
0
6
2
4
n
8
8
observed
(n odd) theor.
(n even) theor.
6
CnN
observed
(n odd) theor.
(n even) theor.
CnH
Figure 8.4: Column densities of Cn N, Cn H, and HCn N in IRC+10216, see Tab. 8.1.
0
0
1e+11
1e+12
1e+13
1e+14
1e+15
1e+16
1e+13
1e+14
1e+15
1e+16
1e+17
10
10
133
134
8 Cn N Chains in Space
.
TA* (K)
Figure 8.5: Possible C2 N transition towards IRC+10216 at 248 GHz. The left line
appears at the C2 N 248 GHz transition frequency with µ2 S=1.2 - 1.9 D2 . The dotted
line results from a line shape fit for molecules in a circumstellar envelope. The line at
the right hand side could not be identified. The total integration time was 170 min.
8.1 The Search for Interstellar C2N
In the previous section it has been shown that the detection of C2 N may be in reach with
the present day radio telescope techniques. The astronomical search for this molecule
was guided by the use of laboratory data. In 1995 Ohshima and Endo [142] did measurements on C2 N using a Fourier transform spectrometer in the Microwave region. Their
molecular spectroscopic constants were used as reference as well as the constants derived
by Kakimoto and Kasuya [98] to calculate the millimeter rotational spectrum of C2 N
(see Tab. 8.3).
8.1.1 Observation
In September 2002 a search was performed for the C2 N radical towards IRC+10216
employing the IRAM 30m telescope at Pico Veleta, Spain (see Fig. 8.8). The observations
were done at position (Eq 1950) RA 09:45:14.8 Dec 13:30:40.0 and focused on four 500
MHz broad frequency bands with centers at 83 GHz, 154 GHz, 224 GHz and 248 GHz
corresponding to the J=7/2 → 5/2, 13/2 → 11/2, 19/2 → 17/2 and 21/2 → 19/2
rotational transitions of C2 N, respectively. The integration time was 4 - 4 1/4 hours
8.1 The Search for Interstellar C2 N
135
.
TA* (K)
.
TA* (K)
Figure 8.6: Possible C2 N transitions towards IRC+10216. The C2 N transitions appear
at 224.5 GHz (with µ2 S = 1.9 - 2.3 Debye2 and a total integration time of 265 min.)
and 153.6 GHz (with µ2 S = 4.2 - 5.8 Debye2 and a total integration time of 250 min.).
The dotted lines result from line shape fits for molecules in a circumstellar envelope.
The right line in the top picture at 224.7 GHz is C17 O (v=0, J 2 → 1). The C2 N line
at 224.5 GHz can also be due to a possible upper sideband image of SiC2 at 232534
MHz.
136
8 Cn N Chains in Space
Table 8.2: Observational parameters, IRC+10216
molecule
transition
obs.freq.
a
Tsys
J
(MHz)
(K)
C2 N
21/2 → 19/2(e/f)
[ 19/2 → 17/2(e)
[ 19/2 → 17/2(f)
13/2 → 11/2(f)
248189.9(3)
224545.2(12)
224551.2(12)
153644.7(5)
800
650
650
400
U1d
C17 O
C2 S
NaCN
U2d
HC5 N
(v=0) 2 → 1
11,12 → 11,11
100,10 → 90,9
248291.22(8)
224714.18(15)
153449.21(5)
153557.04(7)
153842.29(9)
82538.835(3)
800
650
400
400
400
105
31 → 30
ρ
vexp
R
T∗A dν
[km m−1 ]
(K.km s−1 )
0.49
0.53
0.53
0.67
14.6
14.7
14.7
14.7
0.78(7)
0.12(9) ]c
0.12(9) ]c
0.04(1)
0.49
0.53
0.67
0.67
0.67
0.80
14.0
14.7
13.9
12.7
16.1
14.0
2.69(7)
1.78(3)
0.81(5)
0.84(5)
0.60(6)
0.73(3)
Rest frequencies (assuming a source LSR velocity of -27 km s−1 ) in IRC+10216;
The numbers in parenthesis are the estimated uncertainties (1σ);
c poss. upper sideband image of SiC at 232534 MHz;
2
d unidentified line
a
b
and for most of these bands the r.m.s. noise is 9 - 13 mK 10 , low enough to reveal lines
as weak as 0.01 - 0.04 K. Optically thin lines from the outer shells of the IRC+10216
envelope have a U-shaped profile (see Fig. 8.5 and 8.6) where the two horns 11 arise
from the blue-shifted (front), and red-shifted (rear) polar caps. The emission at the
center originates from the meridian ring perpendicular to the line of sight. The horn-tocenter intensity ratio of emissions coming from spherical shells of constant thickness and
constant radial velocity12 depend primarily on the shell diameter relative to the telescope
beam [73], i.e. for a given frequency we have: the larger the shell, the larger the ratio.
The lines at 224 and 248 GHz reveal the typical U-shape which suggests that the carrier
of these lines is essentially present in the outer envelope. The measured intensities
are given in TA∗ , the effective antenna temperature corrected for spillover losses and
atmosphere attenuation. TA∗ is related to TM B the main beam-averaged source brightness
temperature by Ta∗ = ρTM B , where ρ = ρ(ν) is the 30m telescope beam efficiency, see
Table 8.2.
scale is in TA∗ , the effective antenna temperature corrected for spillover losses and atmosphere attenuation.
11
This notion is taken from [73].
12
see vexp in Tab. 8.2.
10
8.1 The Search for Interstellar C2 N
137
8.1.2 Data Analysis
The Grenoble molecular line reduction software CLASS was used to fit the observed lines
to an U-shaped line profile. Two lines are observed13 at frequencies of C2 N transitions
with integrated line intensities of at least 0.78 and 0.24 K km s−1 , and one weaker line
is found at 154 GHz with an intensity of 0.04 K km s−1 , see Table 8.2. The frequency
scale is computed for a LSR source velocity of -27 kms−1 .
The total molecular column density NT as well as the rotational temperature T are
important for the unambiguous assignment of the observed transitions to a certain
molecule. There
to calculate this values. The integrated
R are some formulas needed
2
line intensity Tl dν is proportional to µ S, with S the line strength of the transition.
The dipole moment of C2 N has been calculated by Pd et al. [145] to be µ=0.425 Debye.
The line strength can be calculated from the intensity I of a transition or vice versa
with the following formula [154]
10Ip Q(T )
µS=
l
4.16231 · 10−5 · ν exp −E
− exp
kT
2
−Eu
kT
(8.4)
with Ip the logarithm of the intensity 14 ,ν in MHz, µ the relevant component of the
dipole moment of the molecule in Debye, Q the partition function [152], El the lower
state energy and Eu the upper state energy of the transition. For reasons of conformity
the theoretical intensities of the C2 N transitions were calculated with the dpfit and dpcat
program written by Herb Pickett. Here T is set to 300 K 15 .
In case of small optical depth 16 the column density Nu in its upper level can be calculated
by 17
R
Nu
17 TM B dv
= 1.669813 · 10
(8.5)
gu
νµ2 S
R
with gu the statistical weight of the level [196], TM B dv the line integral 18 in (K km s−1 ),
ν in MHz and µ2 S from Eq.8.4.
The line width in IRC+10216 of the newly measured transitions are of the order 30 km s−1
corresponding to 20-25 MHz for 248 GHz, see Fig. 8.5.
If C2 N is the carrier of the absorption lines many hyperfine transitions remain unresolved,
i.e. three lines at 153 GHz, six lines at 224GHz and also six at 248 GHz, see Fig. 8.5
13
The line at 224.5 GHz is a possible upper sideband image of the SiC2 line at 232.534 GHz.
The Pickett program uses the logarithm Ip of the intensity I instead of the intensity itself in its
catalog files, i.e. I = 10Ip
15
This is a necessary standard procedure because the Pickett program sums over a finite amount of
transitions to calculate the partition function and not over all. Thus differences can occur if an other
temperature is chosen. Q is given in the Pickett filename.out file. For C2 N Q(300K) = 5737.4682
16
and for TexR hν/k and Tex Tbg , see [196]
Tl dv
3k
17 Nu
gu = 8π 3 νµ2 S
18
Some
times the line integral Ris given in K·MHz instead of K·km·s−1 . The conversion equation is
R
Tl dv [K km s−1 ]= 10−3 νc Tl dν [K MHz] with c the speed of light in [m/s] and ν the transition
frequency in [MHz].
14
138
8 Cn N Chains in Space
Table 8.3: Line parameters, IRC+10216
molecule
C2 N
U1
C17 O
C2 S
NaCN
U2
HC5 N
transition
obs.freq.a
calc.freq.
o-c
Eupper
J
(MHz)
(MHz)
(MHz)
(K)
21/2 → 19/2(e/f)
[ 19/2 → 17/2(e)
[ 19/2 → 17/2(f)
13/2 → 11/2(e)
13/2 → 11/2(f)
[ 7/2 → 5/2(e)
[ 7/2 → 5/2(f)
248189.9(3)
224545.2(12)c
224551.2(12)c
153644.70(8)c
-
248189.1(1)
224545.2(1)
224551.2(1)
153617.9(1)
153644.70(8)
82701.63(1)
82743.70(1)
0.8
27.8
-
68.6
56.7
56.7
27.8
9.1
9.1
11.2d ]
11.2d ]
(v=0) 2 → 1
11,12 → 11,11
100,10 → 90,9
31 → 30
248291.22(8)
224714.18(15)
153449.21(5)
153557.04(7)
153842.29(9)
82538.835(3)
224714.389(3)
153449.774(11)
153557.651e
82539.040
-0.21
-0.56
-0.61
-0.21
16.2
53.8
63.4
13.5
10.2
9.3
log(Nu )
(with Nu
in cm−2 )
11.0
10.6 ]
10.6 ]
-
Rest frequencies (assuming a source LSR velocity of -27 km s−1 ) and intensities in IRC+10216;
The numbers in parenthesis are the estimated uncertainties (1σ).
c In a free fit the rest frequencies have been 224549.64(188) MHz for the 19/2 → 17/2(e/f)
transitions and 153642.61(10) for the 13/2 → 11/2(f) transition. Because of the close lying
doublet components both transitions have been fitted with fixed rest frequencies.
d integrated noise, 0.003K · 30 km s−1
e see [34] on-line data
a
b
and 8.6. In this case a mean line strength S̄ of the unresolved transitions is computed
and multiplied by the number n of these lines to give S̄s the summed line strength that
replaces S in Eq. 8.5.
If several resolvable transitions, e.g. rotational transitions, of a molecule are observed a
rotational temperature can be assigned by using
Nu
NT
Eu
=
exp −
(8.6)
gu
Q(Trot )
kTrot
where NT is the total molecular column density, Q the partition function, and Eu the
energy of the upper level. Eq. 8.6 can be rewritten in the form
Nu
NT
1
log10
= log10
−
log10 (e) Eu [in K]
(8.7)
gu
Q(Trot )
Trot
where Trot and NT
19
19
can be determined by a least-square fit [114]. The result can be
The partition function for a temperature T has been calculated by Q(T ) = α · T β , where α and β
are determined by the Q(Ti ) values given by the Pickett program. In the case of linear closed shell
molecules β is always one but for the C2 N radical α=6.7 and β = 1.2 .
8.1 The Search for Interstellar C2 N
139
11,5
11,0
log10(Nu/gu)
log10(Nu/gu)
11,0
10,5
10,5
10,0
10,0
9,5
0
20
40
Eu[K]
60
0
20
40
Eu[K]
60
Figure 8.7: Boltzmann plot for C2 N. The left plot is calculated for a non-diluted beam
and the right plot is calculated for a diluted beam. (Left) A rotational temperture
of 78±60 K and a column density of 1014 cm−2 could be estimated in the case of a
diluted beam.
plotted in a Boltzmann plot.
The spacial extend of a molecular gas can influence the value of the integrated line
intensities. This is because the beam size diameter θB of the telescope varies with
frequency, i.e.
θB ∼ 1/ν
(8.8)
The IRAM 30m telescope beam width is roughly 2400”/ν[GHz], i.e. 28” for 83 GHz, 15”
for 154 GHz, 10” for 224 GHz, and 9” for 248 GHz. The range of possible line intensities
can be estimated by considering two cases of telescope beam and source diameter ratios.
In one case the area of emitting molecules is larger than the beam size so that the beam
is completely ’filled’ independent of frequency. On the other hand, when the source is
small the telescope beam can easily be larger than the diameter θs of the emitting area
, i.e. the beam is diluted. Assuming that the intrinsic intensity distributions Ts of a
source is Gaussian a beam filling factor can be introduced to calculate the measured
intensity TL , i.e.
θS2
TL = TS ·
(8.9)
2
θS2 + θB
2
If θs θB this equation reduces to TL = TS · ( θθ2 ) and applying Eq. 8.8 gives
B
TL (ν) ∼ TS ·
ν
νnorm
2
.
(8.10)
with νnorm > ν. A factor (ν/νlowest )2 added on the right side of Eq. 8.5 modifies the
column densities and thus also the rotational temperature Trot into T̃rot in the Boltzmann
plot, see Fig. boltz, i.e. T̃rot represent the cases of a diluted beam. The distribution
of the C2 N radicals around IRC+10216 is not known. However, if it is similar to the
140
8 Cn N Chains in Space
C3 N intensity distribution (see [15]) which is shell like with some larger irregularities
then the determination of the filling factor for each frequency can only be obtained by
mapping the star envelope. This has not been done here. The result of the Boltzmann
fit for a diluted beam is the temperatures T̃rot = 78±60 K and the total C2 N column
density NT = 1014 cm−2 . The uncertainties of the temperature fit are very large and
partly due to the fact that the integrated line intensity at 224 GHz is lower than the
one at 248 GHz, i.e. it does not exactly follow a boltzmann distribution 20 . Calculations
with a non-diluted beam result in a negative temperature. If the three lines at 154, 224
and 248 GHz belong to C2 N, it has to be shown that the non-detection of the 83 GHz
transition is consistent with this assignment. To proof this the noise at the 83 GHz line
positions were integrated according to the beam filling factor 1 or (83/154), see Tab. 8.3.
The integrated noise intensities are above the fitted line (dotted) in Fig. 8.7 (left) which
marks the level of consistent signal intensities. The expected C2 N signal at 83 GHz is
smaller than the noise intensity and should therefore not be detectable. Hence, the non
detection of the 83 GHz is consistent with a C2 N assignment of the other three lines.
8.1.3 Discussion
If C2 N is produced via photo-destruction of HC2 N the physical conditions and the region
in which they are detected should be similar or at least correlated to each other. In 1991
Guélin & Cernicharo [74] detected HCCN towards IRC+10216 using the IRAM 30m
telescope. They found a source diameter ≤ 25” (i.e. little or no beam dilution). Comparison of the line profile of HC2 N with HC3 N and HC5 N indicate that this molecule
is essentially present in the outer envelope. The rotational temperature of HCCN is
Trot = 12 ± 4 K and C3 N has a rotational temperature of 20 K [34]. Guélin & Cernicharo detected a faint signal which coincides with the 13/2 → 11/2 of C2 N but no
feature stronger than 0.02 K at the frequency of the 11/2 → 9/2 transition. Both the
non-detection at 130 GHz by Guélin & Cernicharo as well as the discrepancy of the rotational temperatures in the case of a non-diluted beam between HC2 N and C2 N make
it difficult to assign the newly observed transitions to the C2 N molecule. Guélin & Cernicharo who assumed a dipole moment of 1.3 Debye for C2 N estimated an upper limit
of NT (1.3 D) = 5 · 1013 cm−2 for the column density of C2 N towards IRC+10216. The
observation presented in this thesis together with the assumption that C2 N has a dipole
moment of 0.425 Debye (Pd & Chandra [145], 2001) suggest that the column density of
C2 N is NT (0.425 D)= 1014 cm−2 whereas astrophysical models by Millar & Herbst [132]
predict a column density21 of 3.6 · 1012 cm−2 , see Table 8.1.
20
In this situation the uncertainties of the individual line intensities become particular important for
the result of the fit.
21
Note: It should be NT (0.425 D) ≈ 10 · NT (1.3 D).
8.1 The Search for Interstellar C2 N
141
Figure 8.8: The IRAM 30m telescope at Pico Veleta, Granada
8.1.4 Conclusions and Prospects
During the measurements at the IRAM 30m telescope (see Fig. 8.8) three lines at frequency positions of C2 N transitions could be detected and have been assigned to C2 N as
a possible carrier. This assignment can only be tentative and more data is needed. However, an upper limit of the column densities of C2 N towards the envelope of IRC+10216
can be given. They are of the same order than those obtained from previous measurements by Guélin & Cernicharo [74] and are a factor of ten larger then predicted values
by Millar & Herbst [132]. An unambiguous detection of C2 N may still be possible with
dedicated searches using long integration times. In a free line fit procedure the observed
line positions reveal deviations > 1σ with reference to the calculated frequencies. Up to
now the predicted line positions in the mm range are mainly based on laboratory measurements at 35 GHz by Ohshima et al. [142]. Therefore new laboratory measurements
of C2 N are necessary in the frequency region between 100 and 300 GHz.
The measurements reported in Chapter 7 should serve as a guide for future astronomical
observations of C4 N, C6 N, and the isotopic species of C3 N. The provided spectroscopic
constants allow the astronomically most interesting radio lines of these to be predicted
to an uncertainty of 0.30 km sec−1 or better up to 50 GHz. Astronomical detection of
the carbon-13 species of C3 N in the cold molecular cloud TMC-1 is also likely, because
they have already been detected by Cernicharo et al. [34] in the circumstellar shell of
the evolved carbon star IRC+10216.
142
8 Cn N Chains in Space
Part IV
Appendix
A Linear CnH
Linear Cn H radicals are iso-electronic to Cn N and therefore of interest for this thesis.
The following table is the analogue to Tab. 5.1 and 5.2 for Cn N radicals.
Table A.1: Linear Cn H (n=1-8) radicals
molecule
ground
state
dipole
moment
[Debye]
exp. B
B value
[MHz]
first
detection
lab, vis (1920-25)
astro, vis (1937)
astro, radio (1973)
lab, MW (1983)
lab (1985)
astron (1985)
lab (1986)
astron (1986)
lab (1996)
astron (1997)
lab (1997)
lab (1997)
lab (1998)
orig. contribution
(see for reference)
Cn H, n odd
CH
X2 Π
1.46
425472.8
C3 H
X2 Π
3.29
11186.335
C5 H
X2 Π
4.44
2395.131
C7 H
X2 Π
5.29
875.484
C9 H
C11 H
C13 H
X2 Π
X2 Π
X2 Π
413.258
226.900
137.710
(Herzberg [83])
Dunham, Swings [125, 174, 49, 83]
Turner [185]
Brazier, Brown [22]
Gottlieb, Vrtilek [68]
Thaddeus, Hjalmarson [178]
Gottlieb, Thaddeus [65]
Cernicharo, Kahane [36]
Travers, McCarthy [182]
Guelin et al. [75]
McCarthy [122]
McCarthy [122]
Gottlieb [64]
Cn H, n even
C2 H
X2 Σ
0.769
43674.53
C4 H
X2 Σ
4.09
4758.657
C6 H
X2 Π
5.05
1391.186
C8 H
X2 Π
6.94
587.264
C10 H
C12 H
C14 H
X2 Π
X2 Π
X2 Π
301.410
174.784
110.242
astron (1974)
lab (1981)
astron (1978)
lab (1983)
lab (1988)
astron (1986)
lab (1996)
astron (1996)
lab (1998)
lab (1998)
lab (1998)
Tucker, Kutner, Thaddeus [183]
Sastry, Helminger [163]
Guelin, Green [79]
Gottlieb [66]
Pearson, Gottlieb [146]
Suzuki, Ohishi [172]
McCarthy [119]
Cernicharo [32]
Gottlieb [64]
Gottlieb [64]
Gottlieb [64]
A general overview is given in Takahashi [176] and Pauzat [144]. Isotopomers of CCH were examined
by McCarthy et al. [120] and Saleck et al. [162]. Isotopic CCCCH was measured by Chen et al. [37].
146
A Linear Cn H
B The HQ Matrix Elements
The matrix elements of the electric quadrupole interaction HQ (Eq.6.48) can be written
in the Hund’s case (a) using 3j- and 6j-Symbols 1
−1
1
F J I
I 2 I
0
0 0
J+I+F
hηΛ SΣJ Ω IF |HQ |ηΛSΣJΩIF i =
(−)
2 I J0
4 −I 0 I
0
J 2 J
0
1/2
J 0 −Ω
×[(2J + 1)(2J + 1)]
δΛ0 Λ δΩ0 Ω eQq0 (−)
−Ω 0 Ω
X
0
0
J0 2 J
+
δΛ0 ,Λ∓2 (6)1/2 eQq2 (−)J −Ω
(B.1)
−Ω0 −q Ω
q=±2
This equation can be split in two matrices, M (eQq0 ) and M (eQq2 )
−1
1
I 2 I
F J I
J+I+F
(−)
M (eQq0 ) =
2 I J0
4 −I 0 I
0
J 2 J
0
1/2
J 0 −Ω
×[(2J + 1)(2J + 1)]
δΛ0 Λ δΩ0 Ω eQq0 (−)
(B.2)
−Ω 0 Ω
−1
1
I 2 I
F J I
J+I+F
M (eQq2 ) =
(−)
[(2J 0 + 1)(2J + 1)]1/2
2 I J0
4 −I 0 I
X
0
J
2 J
1/2
J 0 −Ω0
×
δΛ0 ,Λ∓2 (6) eQq2 (−)
(B.3)
−Ω0 −q Ω
q=±2
Π states have Ω or Ω0 values of 3/2 or 1/2 so that Ω’=Ω ± 1. For the energy the ∆J = 0
elements are calculated using the basis functions 2
2
|2 Π±
|Ω| , Ji =
|Λ, Σ, J, Ωi ± | − Λ, −Σ, J, −Ωi
√
2
(B.4)
with ± referring to the e/f parity respectively. To calculate the 3j- and 6j-symbols the
following equalities are useful:
4J ≡ [(2J + 3)(2J + 2)(2J + 1)(2J)(2J − 1)]1/2
I ≡ [(2I + 3)(2I + 2)(2I + 1)(2I)(2I − 1)]1/2
1
2
see Brown & Schubert [27], Eq. 2
The matrix elements are in a non parity conserving basis.
148
B The HQ Matrix Elements
X = −R(F ) ≡ J(J + 1) + I(I + 1) − F (F + 1)
K(F ) ≡
3R(F )[R(F )+1]−4J(J+1)I(I+1)
I(2I−1)(2J+3)(2J+2)(2J)(2J−1)
s ≡ F +J +I
The following formula are taken or derived from Edmonds [51].
2[3I 2 − I(I
I 2 I
=
−I 0 I
I
2
2[3Ω − J(J
J 2 J
= (−1)J−Ω
−Ω 0 Ω
4J
2[3X (X − 1) − 4J(J + 1)I(I
F J I
= (−1)s
2 I J
4J I
J
2
J
J
J
2J+2
= (−1)
Ω −2 Ω − 1
Ω Ω−1
s
(J + Ω − 1)(J − Ω + 2) J
J
J
2
J
= 3
Ω Ω − 1 −2
Ω Ω−2
(2J + 3)(2J − 1)
s
(J + Ω − 2)(J − Ω + 3) J
J
J
1
J
=−
Ω Ω − 2 −1
Ω
Ω
−
3
(2J)(2J + 1)
For Eq. B.9
3
+ 1)]
+ 1)]
+ 1)]
2
−2
1
−1
0
0
(B.5)
(B.6)
(B.7)
(B.8)
(B.9)
(B.10)
and Eq. B.10 ([51], Eq. 3.7.13) was used.
The diagonal matrix elements M (eQq0 ) can be calculated directly using Eq. B.5 - B.7
with J = J 0 and Ω = 1/2 for the lower left matrix element of Tab. B.1 and Ω = 3/2 for
the upper right matrix element.
In Eq. B.3 the index q of the sum separates the upper right and lower left matrix element
of M (eQq2 ). HQ is hermitian and it is thus sufficient to calculate only one addend.
0
J
2
J
≡ Ai
(B.11)
−Ω0 −q Ω
is non zero if (−Ω0 + (−q) + Ω) = 0, but because |q| = 2 and Ω0 , Ω{±1/2, ±3/2} this
is only possible for (Ω0 = −3/2, q = +2, Ω = 1/2)1 or (Ω0 = 3/2, q = −2, Ω = −1/2)2 .
Because of the δΛ0 ,Λ∓2 only A1 applies and M (eQq2 ) can be derived by setting Ω0 = −3/2
and Ω = 1/2 using Eq. B.8 with (−Ω0 (= −3/2)=Ω
b = 3/2 and Ω(= 3/2)=Ω
b − 1 = 1/2).
Eq. B.8 can be solved by Eq. B.9 and B.10. In the case Ω = 3/2 it is
J
J 0 (Ω=3/2)! J
J 0
=
= (−1)J−Ω (2J + 1)−1/2
(B.12)
Ω Ω−3 0
Ω −Ω 0
The result is summarized in Tab. B.1.
3
With j1 = j2 ≡ J, j3 = 2, m1 = Ω, m2 = Ω − 1, m3 = −2 to terms vanish because j3 + m3 = 0
149
Table B.1: Matrix with electr. hf interaction
|2 Π±
3/2 JIF i
h2 Π±
3/2 JIF |......
h2 Π±
1/2 JIF |......
with
K(F ) =
eQq0
27
2 K(F )[ 4
− J(J + 1)]
(Hermitian)
|2 Π±
1/2 JIF i
1
1
3 1/2
2
2
± eQq
4 K(F )[(J − 4 )(J + 2 )(J + 2 )]
eQq0
3
2 K(F )[ 4
− J(J + 1)]
3R(F )[R(F )+1]−4J(J+1)I(I+1)
I(2I−1)(2J+3)(2J+2)(2J)(2J−1)
R(F ) = F (F + 1) − J(J + 1) − I(I + 1)
Matrix elements in non-parity conserving basis derived by Tom C. Killian and Guido Fuchs
from Brown & Schubert, [27]
150
B The HQ Matrix Elements
C Molecular Constants of C13CCN and
CC13CN
In Chapter 7.1.2 the measurements and analysis of the 13 C-C3 N isotopomers have been
described. Tab. 7.4 shows the results of the global fits including the mm-data from
McCarthy et al. [121] and the newly measured MW-data. The fit of the data has been
done in 3 steps. First the mm-data were fitted with Herb Pickett’s spfit/spcat program.
With the B and D constants contraint to the values of the mm-data fit a new fit with
only MW-data was done. A final fit including all available mm- and MW data was done
to derive the ’recommended values’ of the C3 N isotopomers. Tab. 7.3 shows the result
of the intermediat steps of the fit for 13 CCCN. The tables for the intermediate results
for C13 CCN and CC13 CN are given here.
Table C.1: Molecular Constants of C13 CCN (in MHz).
Data reduction was done with the Pickett-program.
a
Constant
this workb
mm-data onlyc
recommendedd
values
B
4920.7107(8)
4920.712(2)
4920.7095(2)
D ×10−3
0.78(4)
0.749(2)
0.7453(4)
γ
−18.62(2)
−18.9(2)
−18.574(5)
γD ×10−3
2.4(8)
0.2(2)
...
13
bF ( C)
188.6(2)
210.(30)
188.6(2)
c(13 C)
52.4(2)
−40.(200)
52.9(1)
14
bF ( N)
−1.244(7)
−8.(200)
−1.234(6)
14
c( N)
2.86(4)
−40.(100)
2.82(3)
eQq0
−4.(1)
−30.(200)
−4.331(9)
w-rmse
1.35
0.54
1.16
a
Uncertainties (in parentheses) are (1σ) in the last significant digit.
b
13 lines were used, see Tab.7.7.
The uncertainties of the lines is estimated to be 2 kHz.
c
28 lines from [121] were used.
The uncertainties of the lines are estimated to be between 22-86 kHz.
d
Total fit with all measured 41 lines.
e
w-rms is normalized with uncertainties of measured lines.
152
C Molecular Constants of C13 CCN and CC13 CN
Table C.2: Molecular Constants of CC13 CN (in MHz).
Data reduction was done with the Pickett-program.
a
Constant
this workb
mm-data onlyc
recommendedd
values
B
4929.0640(5)
4929.0639(2)
4929.0640(2)
−3
D ×10
−0.76(2)
0.7496(2)
−0.7497(3)
γ
−18.643(7)
−18.60(2)
−18.648(3)
γD ×10−3
−0.2(2)
−0.02(1)
...
13
bF ( C)
23.54(3)
21.(6)
23.55(2)
c(13 C)
2.19(4)
40.(100)
2.17(3)
14
e
bF ( N)
−1.184(8)
−1.193
−1.182(8)
c(14 N)
2.87(2)
2.837e
2.88(2)
e
eQq0
−4.32(1)
−4.321
−4.323(8)
f
w-rms
0.79
1.00
0.77
a
Uncertainties (in parentheses) are (1σ) in the last significant digit.
b
32 lines were used, see Tab.7.8.
The uncertainties of the lines is estimated to be 5 kHz.
c
12 lines from [121] were used.
The uncertainties of the lines are estimated to be between 22-86 kHz.
d
Total fit with all measured 44 lines.
e
fixed value.
f
w-rms is normalized with uncertainties of measured lines.
D Tables: Interstellar C3N ,C5N, and
C3N Isotopomers
C3 N was first detected in gas phase with a radio telescope by Guélin and Thaddeus
[78, 79] in 1977 towards IRC+10216. Further C3 N sources are IRAS 15194-5115, IRC
+10216, TMC-1, TMC-2, HCL 2, CRL 618, CRL 2688, and it has also been observed
in direction of Cas A. Table D.2 summerizes the astronomical measured transitions of
C3 N.
During a line survey towards IRC+10216 Cernicharo et al. [34] detected three 13 C
mono-substituted C3 N isotopomers. In the case of 13 CCCN the assignement of two of
the astronomical observed lines is not in agreement with the data derived in this thesis,
see Table D.1.
In 1998 Guelin et al. [77] detected C5 N in the dark cloud TMC-1. Up to now TMC-1
and IRC+10216 are the only sources in which C5 N has been detected, see Table D.3.
Table D.1: Transitions of isotopic C3 N in IRC+10216, Cernicharo et al. [34]. The
transitions with a question mark do not agree with the laboratory data of this work
and a correct assignment is not possible.
R
isotope
transition
frequency
Tmb dν
(N,J,F1 ,F)”→(N,J,F1 ,F)’
[MHz]
[K km/s]
13
CCCN
(15,,,)→(14,,,)a ?
(143 104.0) ?
0.71
(15,31/2,15,)→(14,31/2,14,)
143 124.0
0.92
(16,,,)→(15,,,)a ?
(152 640.0) ?
0.62
(16,33/2,17,)→(15,31/2,17,)
152 659.7
1.26
C 13 CCN
(14,29/2,14,)→(13,27/2,14,)
137 763.2
1.17
(14,27/2,[13],)→(13,25/2,[12],)
137 778.3
0.55
(15,31/2,[16],)→(14,31/2,[15],)
147 602.2
0.45
(15,29/2,14,)→(14,27/2,14,)
147 617.6
0.38
13
CC CN
(14,29/2,15,)→(13,27/2,14,)
137 996.2
1.30
(14,27/2,[14],)→(13,25/2,[13],)
138 014.7
1.17
154
D Tables: Interstellar C3 N ,C5 N, and C3 N Isotopomers
Table D.2: Astronomical detections of C3 N
source
CSE1
IRAS 15194-5115
IRC +10216
frequency
(N,J,F)”→(N,J,F)’
[MHz]
(11,23/2,)→(10,21/2,)
(17,33/2,)→(16,31/2,)
(17,35/2,)→(16,33/2,)
(16,31/2,)→(15,29/2,)
(16,33/2,)→(15,31/2,)
(15,29/2,)→(14,27/2,)
(15,31/2,)→(14,29/2,)
(14,27/2,)→(13,25/2,)
(14,29/2,)→(13,27/2,)
(11,21/2,)→(10,19/2,)
(11,23/2,)→(10,21/2,)
(10,19/2,)→( 9,17/2,)
(10,21/2,)→( 9,19/2,)
(9,17/2,)→(8,15/2,)
(9,19/2,)→(8,17/2,)
(5,9/2,)→(4,7/2,)
(5,11/2,)→(4,9/2,)
(4,7/2,)→(3,5/2,)
(4,9/2,)→(3,7/2,)
(3,5/2,)→(2,3/2,)
(3,7/2,)→(2,5/2,)
108 834.27
168 213.1
168 194.4
158 321.1
158 302.3
148 427.8
148 409.1
138 534.6
138 515.7
108 853.0
108 834.3
98 939.9
98 958.6
89 045.7
89 064.4
49 485.2
49 466.5
39 590.2
39 571.3
29 695.1
29 676.1
2.14
2.14
0.18
0.13
0.13
0.14
0.226
0.270
0.172
0.205
0.043
0.058
29 695.13
29 695.13
29 694.99
29 676.28
29 676.14
29 676.14
19 800.121
19 799.951
19 781.094
19 780.826
19 780.800
9 885.89
0.15
0.15
0.04
0.12
0.11
0.11
0.055
0.022
0.094
0.05
0.058
0.02
MC2
TMC-1
(3,5/2,7/2
(3,5/2,5/2
(3,5/2,3/2
(3,7/2,9/2
(3,7/2,7/2
(3,7/2,5/2
(2,3/2,5/2
(2,3/2,3/2
(2,5/2,7/2
(2,5/2,3/2
(2,5/2,5/2
(1,3/2,5/2
(continued on next page)
1
2
T∗A
(Tmb )
[K]
transition
circumstellar envelopes
molecular cloud
)→(2,3/2,5/2)
)→(2,3/2,3/2)
)→(2,3/2,1/2)
)→(2,5/2,7/2)
)→(2,5/2,5/2)
)→(2,5/2,3/2)
)→(1,1/2,3/2)
)→(1,1/2,1/2)
)→(1,3/2,5/2)
)→(1,3/2,1/2)
)→(1,3/2,3/2)
)→(0,1/2,3/2)
R
RTA dν
( Tmb dν)
[K km s−1 ]
(0.4)
(10.90)
(10.08)
(24.00)
(22.47)
(27.97)
(26.37)
(27.89)
(26.27)
5.58
6.82
4.01
5.04
1.13
1.69
reference
[140]
[34]
[34]
[34]
[34]
[34]
[34]
[34]
[34]
[79], [15]
[79], [15]
[78]
[78]
[78]
[78]
[101]
[101]
[101]
[101]
[101]
[101]
[56], [76]
[56], [76]
[56]?, [76]
[56], [76]
[56], [76]
[56], [76]
[76]
[76]
[76]
[76]
[76]
[76]
155
(continued from previous page)
source
transition
[MHz]
29 676.14
29 676.28
19 781.094
T∗A
(Tmb )
[K]
0.06
0.07
-
(,21/2,)→(,19/2,)
(,19/2,)→(,17/2,)
(9,17/2,)→(8,15/2,)
(9,19/2,)→(8,17/2,)
89 045.7
89 064.4
(0.1)
(0.13)
0.2
0.2
[28]
[28]
[139]
[139]
(1,3/2,)→(0,1/2,)
9 885 ?
0.01
[10]
(N,J,F)”→(N,J,F)’
(3,7/2,7/2 )→(2,5/2,5/2)
(3,7/2,9/2 )→(2,5/2,7/2)
(2,5/2,7/2 )→(1,3/2,5/2)
TMC-2
HCL 2
PPN3
CRL 618
CRL 2688
other
molecules in
direction Cas A
frequency
R
RTA dν
( Tmb dν)
[K km s−1 ]
Table D.3: Transitions of C5 N in IRC+10216 and TMC-1, see [77]
R
source
transition
frequency
Tmb dν
(N,J)”→(N,J)’
[MHz]
[mK km/s]
TMC-1
(9,19/2)→(8,17/2) 25 249.938
7.3
(9,17/2)→(8,15/2) 25 260.649
6.4
IRC+10216 (32,65/2)→(31,63/2) 89 785.6
95
(32,63/2)→(31,61/2) 89 797.0
105
3
proto planetary nebulae
reference
[56]
[56]
[33]
156
D Tables: Interstellar C3 N ,C5 N, and C3 N Isotopomers
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Bibliography
List of Figures
2.1
2.14
Spectra of C2 at 516 nm obtained by using two different types of molecular
sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C60 mass spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-temperature diagram of graphite . . . . . . . . . . . . . . . . .
The Cologne Laser Ablation Source . . . . . . . . . . . . . . . . . . . . .
Jet produced by excimer laser ablation technique. . . . . . . . . . . . . .
QMS experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass spectrum of Nd:YAG laser ablated graphite rod . . . . . . . . . . .
Excimer laser ablation on different kinds of material. . . . . . . . . . . .
The effect of an Nd:YAG laser beam on different kinds of material. . . .
Discharge slit nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jets produced by a discharge slit nozzle. . . . . . . . . . . . . . . . . . .
Experimental setup for mass spectrometry on a molecular beam . . . . .
Energy distribution of a He+ produced in the ion source of the plasma
monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass spectra of a molecular beam . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
The Cologne carbon cluster experiment . . .
Sensitivity of IR detectors . . . . . . . . . .
Frequency calibration . . . . . . . . . . . . .
Rovibrational transition of C3 at 2067 cm−1
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
Block diagram of the FTMW low band system, 5 - 25 GHz . . . . . . . .
The Production of Cn N radicals . . . . . . . . . . . . . . . . . . . . . . .
Nozzle for the production of molecules and radicals . . . . . . . . . . . .
Test nozzle to optimize the geometry of the discharge nozzle . . . . . . .
The radical nozzle during a discharge . . . . . . . . . . . . . . . . . . . .
The supersonic jet expansion . . . . . . . . . . . . . . . . . . . . . . . . .
The long nozzles during a discharge . . . . . . . . . . . . . . . . . . . . .
Continuum free-jet expansion . . . . . . . . . . . . . . . . . . . . . . . .
Mach number and Temperature along the centerline axis of a free expansion
Model of flow development . . . . . . . . . . . . . . . . . . . . . . . . .
Theoretical intensities of the C4 N rotational transitions . . . . . . . . . .
Cavity mode Lorentzian line shape . . . . . . . . . . . . . . . . . . . . .
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
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10
11
13
14
15
17
20
23
24
25
26
27
28
29
34
35
36
38
43
46
47
48
50
50
51
53
56
57
62
65
174
List of Figures
4.13 Measured Qef f and calculated Qth for the Fabry-Perot cavity . . . . . . .
4.14 Time and Frequency Domains . . . . . . . . . . . . . . . . . . . . . . . .
66
68
5.1
5.2
5.3
Schematic diagram of electron configuration of CN and CCN . . . . . . .
Calculated geometries of C2 N . . . . . . . . . . . . . . . . . . . . . . . .
Theoretical geometries of C4 N . . . . . . . . . . . . . . . . . . . . . . . .
71
74
75
6.1 Hypothetical energy level diagram of a 2 Π radical . . . . . . . . . . . . .
6.2 Vector diagram of Hund’s coupling cases a) and b) . . . . . . . . . . . .
6.3 Unpaired electron distribution for a 2 Π state in Hund’s case (b). . . . . .
78
84
90
Measured CCC15 N transition with Zeeman splitting . . .
Energy level diagram of CCC15 N . . . . . . . . . . . . .
Measured 13 CCCN transitions. . . . . . . . . . . . . . . .
Hund case bβs and bβJ with 2 nuclear spins . . . . . . .
13
CCCN energy level scheme . . . . . . . . . . . . . . . .
Resonance structure of CCCN . . . . . . . . . . . . . . .
bF and c-values of different isoelectronic carbon chains .
C4 N stick spectrum . . . . . . . . . . . . . . . . . . . . .
Measured C4 N transition . . . . . . . . . . . . . . . . . .
Measured transition of C6 N . . . . . . . . . . . . . . . .
Hund’s case a with one nuclear spin . . . . . . . . . . . .
Relative abundances of the Cn N radicals per gas pulse in
molecular beam as a function of chain length. . . . . . .
7.13 Molecular constants h1/r3 i, hsin2 θ/r3 i, and hψ 2 (0)i . . .
7.14 Schematic C4 N energy level. . . . . . . . . . . . . . . . .
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
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the supersonic
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The molecular clouds in the plane of the Milky Way . . . . . . . .
13
CCCN detection in IRC+10216 . . . . . . . . . . . . . . . . . .
Major pathways to cyanopolyyne formation in IRC+10216 . . . .
Column densities of Cn N, Cn H, and HCn N in IRC+10216 . . . . .
Possible C2 N transition towards IRC+10216 at 248 GHz . . . . .
Possible C2 N transitions towards IRC+10216 at 154 and 224 GHz
Boltzmann plot for C2 N . . . . . . . . . . . . . . . . . . . . . . .
The IRAM 30m telescope at Pico Veleta, Granada . . . . . . . . .
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98
102
103
104
105
107
109
112
114
114
115
117
118
119
128
129
130
133
134
135
139
141
List of Tables
1.1
Known Interstellar and Circumstellar Molecules (Dec 2002) . . . . . . . .
5
2.1
2.2
2.3
Particle numbers of C3 , C9 and C13 using excimer laser ablation . . . . .
Technical data of applied ablation lasers . . . . . . . . . . . . . . . . . .
Relative C-cluster concentration of different production techniques . . . .
16
19
21
4.1
Free jet flow properties for Ne . . . . . . . . . . . . . . . . . . . . . . . .
59
5.1
5.2
Cn N, n odd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cn N, n even . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
76
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Selection of important interactions and their constants .
Angular momenta and their projections . . . . . . . . . .
Theoretical Λ-type doubling for 2 Π state . . . . . . . . .
Matrix with Spin-Orbit, Rotation and Λ-doubling . . . .
Matrix with electr. hf interaction . . . . . . . . . . . . .
Matrix with magnetic hyperfine interaction . . . . . . . .
Transformed matrix with magnetic hyperfine interaction
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94
95
96
96
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
Measured Rotational Transitions of CCC15 N in the X 2 Σ+ State
Molecular Constants of CCC15 N . . . . . . . . . . . . . . . . . .
Molecular Constants of 13 CCCN . . . . . . . . . . . . . . . . . .
Spectroscopic constants of the 13 C isotopic CCCN species. . . .
bF (13 C) and c(13 C) values . . . . . . . . . . . . . . . . . . . . .
Measured Rotational Transitions of 13 CCCN in the X 2 Σ+ State.
Measured Rotational Transitions of C13 CCN in the X 2 Σ+ State.
Measured Rotational Transitions of CC13 CN in the X 2 Σ+ State.
Spectroscopic Constants of C4 N and C6 N in the X 2 Π State. . .
Hyperfine and Molecular Constants of Carbon Chain Radicals .
Measured Rotational Transitions C4 N in the X 2 Π1/2 State. . . .
Measured Rotational Transitions C6 N, HUNDA-fit . . . . . . . .
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99
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106
106
108
110
110
111
116
120
121
122
8.1
8.2
8.3
Molecular column densities in IRC+10216 . . . . . . . . . . . . . . . . . 132
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
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176
List of Tables
A.1 Linear Cn H (n=1-8) radicals . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.1 Matrix with electr. hf interaction . . . . . . . . . . . . . . . . . . . . . . 149
C.1 Molecular Constants of C13 CCN . . . . . . . . . . . . . . . . . . . . . . . 151
C.2 Molecular Constants of CC13 CN . . . . . . . . . . . . . . . . . . . . . . . 152
D.1 Transitions of isotopic C3 N in IRC+10216 . . . . . . . . . . . . . . . . . 153
D.2 Astronomical detections of C3 N . . . . . . . . . . . . . . . . . . . . . . . 154
D.3 Transitions of C5 N in IRC+10216 and TMC-1 . . . . . . . . . . . . . . . 155
Acknowledgments
There are many people who have made my graduate career at the Universität zu Köln
and the Harvard-Smithsonian Institution a successful and rewarding time for me.
Surely the first to mention here is Prof. Gisbert Winnewisser. It has been a pleasure to
have him as a thesis advisor. He was always interested in the progress of my work and he
cared about my questions and problems. His connection to Prof. Patrick Thaddeus gave
me the possibility for an important and memorable time as a researcher at the Harvard
Smithsonian Institution. And back at home I felt that his door was always open for me.
Thanks for that!
Prof. Patrick Thaddeus gave me the opportunity to work in his research group, and I
learned a lot from him since he is a brilliant scientist. As my research advisor at the
Harvard Smithsonian Institution, he really took excellent care of me which I appreciated
so much and for which I want to thank him a lot. Especially his charismatic TuesdayWednesday meetings were always very motivating and inspiring for me.
I thank Dr. Thomas Giesen for being my lab advisor. Even before the beginning of
my Diplom thesis he provided me with the day to day help, advised me and got me on
the road towards molecular spectroscopy. I felt really at home in his work group and
never felt any lack of support. His patience in answering clever and sometimes not at
all clever questions is remarkable. I wish him all the best for his future career as a first
grade scientist.
Dr. Michael C. McCarthy did a really great job as my lab advisor in Harvard. Not
only is he an excellent scientist but he also is capable of making the work in his group
very pleasant. I just loved following the daily lunch conversations with Carl which were
always interesting, informative, and delightful. Also his first day crash course in the
lovely FTMW spectrometer will always keep in my mind.
Carl Gottlieb was one of my big oracles - whenever I had a question he had an answer. It
was very nice to work together with him and I still see him in front of me writing formulas
on the white board and make me think that we were working on really important things.
Complementary to that his wife Elaine Gottlieb gave me support in Fortran to get some
numbers out of Carl’s theories. Both of them gave me a warm welcome and good travel
advises, Acadia is great!
I also profited a lot by the experience of Sam Palmer whose knowledge about the experiments and especially the radio techniques is just incredible and who is a person who
always seemed to be in a relaxed mood. His interest in teaching and the rest of the
outside world brought up a lot of interesting discussions.
178
Acknowledgments
I also want to thank the rest of the Thaddeus group for creating such a good atmosphere
in which to work. First of all I want to mention Maria E. Sanz who is an excellent
merengue dancer and who’s Spanish is just to lovely to listen to. She helped me a lot in
getting started with the experiment.
Need a good tip for a restaurant or pub in Cambridge or Boston? Call John Dudeck.
But don’t make the mistake and bet a beer for who wins the next Tour de France! He
supported me with his self-made HC3 N precursors and consequently was indispensable
for the success of this project.
Jane Kucera is one of the most diligent first year students I know and it was a pleasure
to work with her. I hope that her future career will continue in that successful manner.
Tom Dame was helpful in many ways, e.g. working on data to optimize the discharge
nozzle dimensions and supporting me with figures and maps of the Milky Way.
Dr. Rolf Berger provided the quadrupole mass spectrometer and was invaluable in
getting it started. Thanks to Dr. Ute Berndt, Petra Neubauer-Guenther, and Michael
Caris which were great lab-mates. Especially Petra helped me whenever she could in
terms of getting the lab supply organized or by advising ’our’ molecular physics students.
I hope that for both of the doctores-to-be, Michael and Petra, the work in Lab 320 will
be interesting and that they will have a rich scientific harvest.
I also want to thank Frank Schlöder, Dr. Frank Schmülling, and Michael Olbrich for
their computer support. Especially Frank Schlöder was very helpful with his patience
concerning my Linux, LATEX and dada problems.
Friedrich Wyrowski helped me when ever I struggled with astrophysical problems. Thanks!
Sandra Brünken, Patrick Pütz, Jörg Stodolka, Guido Sonnabend, and Daniel Wirtz are
great comrades and I think we had a lot of fun working together in the I. Institut.
The machine shop did a great job and never ran out of solutions. Thanks!
No doubt, Thomas Giesen and Katja Roth did a great job in correcting this thesis.
Thanks!
My family has always given me their total support. I would like to thank my parents,
Agnes and Werner Fuchs, my brother Tobias and sister Sabine, as well as Christel and
Josef Feldt who have always provided me with every opportunity. My aunt Elisabeth
and uncle Wilhelm guided me through all steps of my education - thanks.
Special thanks go to my wife Uli. Both of us studied at the same time, same place and
nearly on the same topic: The pitfalls of physics and molecules. There is no other person
to whom I owe such high esteem than her who during many years of scientific battle
never stopped hoping that it all will have an happy end.
This work was supported by the Deutsche Forschungsgemeinschaft and the Smithsonian
Institution.
Ich versichere, daß ich die von mir vorgelegte Dissertation selbstständig angefertigt, die
benutzten Quellen und Hilfsmittel vollständig angegeben und die Stellen der Arbeit - einschließlich Tabellen, Karten und Abbildungen -, die anderen Werken im Wortlaut oder
dem Sinn nach entnommen sind, in jedem Einzelfall als Entlehnung kenntlich gemacht
habe; daß dieser Dissertation noch keiner anderen Fakultät oder Universiät zur Prüfung
vorgelegen hat; daß sie abgesehen von unten angegebenen Teilpublikationen noch nicht
veröffentlicht worden ist, sowie daß ich eine solche Veröffentlichung vor Abschluß des
Promotionsverfahrens nicht vornehmen werde.
Die Bestimmung der Promotionsordnung sind mir bekannt. Die von mir vorgelegte Dissertation ist von Herrn Prof. Dr. G. Winnewisser betreut worden.
(Guido W. Fuchs)
Parts of this thesis are published in:
1. M.C. McCarthy, G.W. Fuchs, J. Kucera, G. Winnewisser, and P. Thaddeus, Rotational Spectra of C4 N, C6 N, and the Isotopic Species of C3 N, Journal
of Chemical Physics, 118, 3549 - 3557 (2003)
Publication List:
1. T.F. Giesen, U. Berndt, K.M.T. Yamada, G. Fuchs, R. Schieder, G. Winnewisser,
R.A. Provencal, F.N. Keutsch, A. Van Orden, and R.J. Saykally, Detection of the
Linear Carbon Cluster C10 : Rotationally Resolved Diode-Laser Spectroscopy, ChemPhysChem 2, 242-247 (2001)
2. P. Neubauer-Guenther, T. F. Giesen, U. Berndt, G. Fuchs, and G. Winnewisser
The Cologne Carbon Cluster Experiment: Ro-Vibrational spectroscopy
on C8 and other small carbon clusters Spectro.Chem.Acta Part A, 59/3,
431 - 441 (2003)
Curriculum Vitae
Personal
representation:
Name:
Date of birth:
Marital status:
Fuchs, Guido Wilhelm
14th December, 1971, Polch
Germany
married
Education:
1978 - 1982
1982 - 1988
1988 - 1991
Grundschule Kehrig
Realschule Mayen
Kurfürst-Balduin-Gymnasium
Münstermaifeld
Community
service:
03/1992 - 04/1993
Arbeiter-Samariter-Bund (ASB)
LV Köln
Studies:
10/91 - now
Universität zu Köln:
Subject: Physics
Vordiplom
Diplom:
”Charakterisierung einer
Kohlenstoff-Cluster-Quelle”
10/94
01/1999
Studies in
foreign countries:
02/1996 - 11/1996
03/2001 - 9/2001
Activities:
03/1995 - 04/1995
03/1996 - 11/1996
05/1998 - 02/1999
02/1999 - 02/2001
12/1999 - 06/2000
9/2001 - now
Köln, 15th May 2003
University of Cape Town
theor. physics
Termination: B.Sc. (Honours)
Harvard-Smithsonian Institution,
Center for Astrophysics
(FTMW research on reactive
molecules)
”Miniforschung” at the
Universität zu Köln (I.PI) section
for receiver technology
tutor for ”first year students”
at the University of Cape Town
student assistant at the I.PI
scientific assistant at the I.IP
lecturer at the IFBM Cologne
(Institut für Biologie und Medizin)
scientific co-worker at the I. IP