Ionization processes and
photofragmentation via multiphoton
excitation and state interactions
Kristján Matthíasson
Ionization processes and
photofragmentation via multiphoton
excitation and state interactions
Kristján Matthíasson
Dissertation submitted in partial fulfillment of a
Philosophiae Doctor degree in Physical Chemistry
Advisor
Ágúst Kvaran
PhD Committee
Oddur Ingólfsson
Ingvar Helgi Árnason
Gísli Hólmar Jóhannesson
Opponents
Christof Maul
Ragnar Jóhannsson
Faculty of Physical Sciences
School of Engineering and Natural Sciences
University of Iceland
Reykjavík, October 2011
Ionization processes and photofragmentation via multiphoton excitation
and state interactions
Dissertation submitted in partial fulfillment of a Philosophiae Doctor
degree in Physical Chemistry
Copyright © 2011 Kristján Matthíasson
All rights reserved
Faculty of Physical Sciences
School of Engineering and Natural Sciences
University of Iceland
Dunhagi 3
107, Reykjavik
Iceland
Telephone: 525 4000
Bibliographic information:
Kristján Matthíasson, 2011, Ionization processes and photofragmentation
via multiphoton excitation and state interactions, PhD dissertation,
Faculty of Physical Sciences, University of Iceland.
ISBN 978-9979-9935-9-9
Printing: Háskólaprent ehf.
Reykjavik, Iceland, October 2011
Abstract
My Ph.D. work was centered on observing the relative formation of
separate molecular and atomic fragments. This led to the development of
a new method for measuring and analysing data entailing the
simultaneous collection of mass and frequency data over a specific mass
area and frequency range, resulting in a detailed 2D map of the measured
area. From this map both a REMPI spectrum and a mass spectrum could
be extracted as needed.
Three separate molecules were studied, acetylene (C2H2), hydrogen
chloride (HCl) and methyl bromide (CH3Br). By observing the relative
formation of separate atoms and molecular fragments by photoexcitation
as function of laser power and frequency it was possible to determine the
dissociation mechanics for these molecules.
For HCl, the relative intensity of Cl+/HCl+ ions that formed via
photoexcitation proved to be a highly sensitive indicator of perturbation
between Rydberg and ion-pair states. A mathematical model was
developed to evaluate state interaction strengths from the relative
intensity of Cl+/HCl+ ions and the interaction strengths of several states
were calculated. The relative intensity of Cl+/HCl+ ions proved also to be
a highly useful tool in spectrum assignment.
iii
Útdráttur
Athugun á myndun sameinda- og atómbrota við ljósörvun var
þungamiðja doktorsverkefnis míns. Það leiddi til þróunar á nýjum
hugbúnaði og aðferðafræði við að safna og greina gögn með það‚ í huga
að safna samtímis massa og tíðni gögnum yfir tiltekið mælisvið. Þessi
aðferð myndar tvívíddar kort af mælisviðinu. Úr þessu korti má svo draga
fram bæði massaróf fyrir tiltekna tíðni jafnt og tíðniróf fyrir tiltekin
massa eftir þörfum.
Þrjár mismunandi sameindir voru rannsakaðar, asetýlen (C2H2), saltsýra
(HCl) og metýlbrómíð (CH3Br). Með því að bera saman hlutfallslega
massamyndun þeirra atóma eða sameindabrota sem myndast við
ljósörvun var hægt að ráða í niðurbrotsferla þessara sameinda.
Hlutfallslegur styrkur Cl+/HCl+ jóna sem mynduðust við ljósörvun á HCl
reyndist vera mjög nákvæmur vísir að víxlverkun milli Rydberg og
jónparaástanda fyrir bæði H35Cl og H37Cl samsæturnar. Stærðfræðilíkan
var þróað til að meta víxlverkunarstyrkinn út frá hlutföllum Cl +/HCl+ og
víxlverkunarstyrkur reiknaður fyrir nokkur ástönd. Þetta hlutfall reyndist
einnig vera nothæft tæki til að skilgreina litróf.
iv
Table of Contents
List of Figures ....................................................................................... vii
List of Tables ............................................................................................ x
List of abbreviations ...............................................................................xi
Acknowledgements .............................................................................. xiii
1 Introduction....................................................................................... 15
1.1 Acetylene (C2H2) ...................................................................... 16
1.2 Hydrogen Chloride (HCl) ......................................................... 17
1.3 Methyl bromide (CH3Br) .......................................................... 19
2 Experimental setup and analysis method ....................................... 21
2.1 Experimental apparatus ............................................................ 21
2.2 Analysis Method....................................................................... 23
2.2.1 Simulations ..................................................................... 25
2.2.2 Time of flight analysis ................................................... 26
3 Theoretical considerations ............................................................... 27
3.1 Electronic spectroscopy of diatomic molecules72-74 ................. 27
3.1.1 Electronic energy levels. ................................................ 27
3.1.2 Vibrational energy levels ............................................... 29
3.1.3 Rotational energy levels ................................................. 31
3.2 The intensity of electronic excitation spectroscopy
lines72-74..................................................................................... 34
3.2.1 Transition probabilities .................................................. 34
3.2.2 Boltzmann distribution ................................................... 35
3.2.3 Laser power dependence ................................................ 37
3.2.4 Multiphoton excitation intensities.................................. 38
3.3 Total angular momentum and Hund’s cases72 .......................... 39
3.3.1 Hund’s case a) ................................................................ 40
3.3.2 Hund’s case b) ................................................................ 42
3.3.3 Hund’s case c) ................................................................ 42
v
Symmetry properties72 ............................................................. 43
3.4.1 Parity of rotational levels .............................................. 44
3.4.2 Parity selection rules ..................................................... 44
3.5 Perturbations72 ......................................................................... 45
3.5.1 Rotational perturbations ................................................ 45
3.5.2 Perturbation selection rules ........................................... 46
3.6 Predissociation72 ...................................................................... 46
3.4
4 Published papers .............................................................................. 49
International Journals ......................................................................... 49
Icelandic Journals ............................................................................... 50
5
Ion formation through multiphoton processes for HCl35-39,77 .... 113
5.1 Formation of HCl+ ................................................................. 113
5.1.1 Ionization via Rydberg states ...................................... 113
5.1.2 Ionization via ion-pair state ......................................... 113
5.2 Formation of H+ ..................................................................... 115
5.2.1 Ionization via Rydberg states ...................................... 115
5.2.2 Ionization via ion-pair state ......................................... 115
5.3 Formation of Cl+ .................................................................... 116
5.3.1 Ionization via Rydberg states ...................................... 116
5.3.2 Ionization via ion-pair state ......................................... 117
6 The use of mass analysis to determine interaction constants .... 119
7 Ionization of acetylene and methyl bromide compared to
HCl................................................................................................... 123
8 Unpublished work .......................................................................... 125
8.1 C1 -State ............................................................................... 125
8.2 E1 -State ................................................................................ 126
References ............................................................................................ 129
Appendix A: Conference presentations ............................................ 137
Posters .............................................................................................. 137
Talks ............................................................................................... 138
vi
List of Figures
Figure 1. Schematic of the REMPI-TOF experimental equipment. ........ 22 Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is
the 2D contour spectrum that shows clearly the different
ions formed as a function of both atomic/molecular mass
and wavenumbers. Above are REMPI spectra derived
from the contour plot for each ion observed. Mass
spectra for individual wavenumbers could also be
derived in similar fashion. ...................................................... 24 Figure 3: Experimental data (above) for the excitation g3(1)+ 
X1+ (0,0) and the simulated spectrum (below) derived
from spectroscopic constants. The experimental
spectrum also contains a single peak due to the D1
←← X1+ (0,0) excitation. Simulations can thus be of
use for peak assignments in addition to accurately
determining rotational constants. ............................................ 26 Figure 4: Energy diagram for molecular orbitals of HCl. a) Ionpair excitations. An electron is excited from the bonding
orbital of the molecule to the antibonding orbital. b)
Rydberg excitations. An electron is excited from the
non-bonding orbital to a Rydberg orbital. .............................. 28 Figure 5: Rydberg potential vs. ion-pair potential. The figure
illustrates the difference between an ion-pair state and a
Rydberg state. The average bond length of the ion–pair
state is longer than that of the Rydberg state due to the
excitation of an electron to the antibonding orbital,
giving the excited molecule semi-ionic properties. The
vibrational levels are quantized and distributed
according to the shape of the potentials.................................. 30 Figure 6: For each molecular Rydberg state there are discrete
vibrational levels. For each vibrational state there are
also discrete rotational levels. The vibrational series
depend on the shape of the potential and the rotational
vii
series depend on the energy and thus the mean bond
length of the vibrational levels. ............................................... 32 Figure 7: Franck-Condon factors. The vibrational levels are
positioned so that the probability function forms a
standing wave. It is the overlap of these probability
distributions that determines the Franck-Condon factors.
Figure from
http://www.chem.ucsb.edu/~kalju/chem126/public/elspe
ct_theory.html ......................................................................... 36 Figure 8: When gas is jet-cooled the rotational energy of individual
molecules shifts downwards, thus increasing the
probability of excitation from the lower rotational levels
compared to that from the higher ones................................... 37 Figure 9: The precession of L about the internuclear axis. The
precession forms a component  along the internuclear
axis. ............................................................................................... 39 Figure 10: Simple rotator. If S = 0 and L = 0 we only need to
consider the angular momentum of nuclear rotation N.
Therefore we have a simple rotator were N is equal to
the total angular momentum J. .............................................. 41 Figure 11: Hund‘s case a). The orbital angular momentum  and
the electronic spin  form the electronic angular
momentum . The angular momentum of the rotation
molecule N and the electronic angular momentum 
then form the total angular momentum J. .............................. 41 Figure 12: Hund‘s case b).  and N form a resultant which is called K.
The angular momenta K and S then form a resultant J. ................ 42 Figure 13: Hund‘s case c). L and S form a resultant Ja which is
coupled to the internuclear axis with a component . 
and N then form a resultant J. ................................................ 43 Figure 14: Parity. The + and – suffixes in the term symbol indicate
the parity of the rotational levels of the states. For
multiplet states the parity depends on K instead of J. ............ 44 Figure 15: Perturbation. On the left we have an average ion ratio for
the F1, ’=1 state. On the right we have the ratio for the
perturbed F1, ’=1, J’=8 rotational level. As can be
clearly seen, the perturbation to the ion-pair state causes
viii
Figure 16: Predissociation of a diatomic molecule. a)
Predissociation followed by a direct ionization. The
molecule is initially excited to a bound state which
interacts by a non-bound or a quasi-bound state. Some
of the molecules in the bound state “leap” across to the
predissociating state and are dissociated into its atomic
components. The atoms formed can themselves absorb
photon energy and ionize. b) Predissociation followed
by a resonance-enhanced ionization. In this case the
photon energy needed to excite the parent molecule
corresponds to an excited state of the atom resulting in
a resonance-enhanced excitation. .......................................... 47
Figure 17: Main ionization mechanisms of HCl. Figures a) and b)
show possible ionization channels via Rydberg (HCl*)
and ion-pair states (H+Cl-). The predissociation gateway
mechanism forming H + Cl is included. Necessary
amount of photons for ionization are shown. ...................... 114
Figure 18: (2+n) REMPI of C1 ←← X1 + (0,0) excitation. The
figure shows a diffused spectrum of the H35Cl
isotopologue. ....................................................................... 125
Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white
columns represent the P-series, the black columns the
R-series and the gray columns the S-series. An
increased I(Cl+)/I(HCl+)ratio is observed for the J’=4
rotational level. A small increase in I I(Cl+)/I(HCl+) for
the R-series at J’=4 is most likely due to an overlap
with the J’=2 peak of the S-series. ...................................... 126
Figure 20: (2+n) REMPI of E1 ←← X1 + (1,0) and V1 ←←
X1 + (14,0) excitations. The figure shows the HCl+/Cl+
ratio of individual rotational peaks...................................... 127
ix
List of Tables
Table 1: SHG crystals used for specific dyes and wavelengths of
entering photons.................................................................. 21 Table 2: State interaction parameters. ................................................... 121 Table 3: E values for the rotational peaks of the E1 ←← X1+
(1,0) and V1 ←← X1+ (14,0) excitations. ......................... 127 x
List of abbreviations
a2 = probability distribution
C = Speed of light
Deq = Dissociation energy
E = Energy
FCF = Franck-Condon factors
h = Planck constant
I = Moment of inertial
Irel = Relative intensity
J = Rotational quantum number
K = Total angular momentum apart from spin
kb = Boltzmann constant
L = Orbital angular momentum vector
L = Orbital angular momentum quantum number
m = Mass
= Reduced mass
Mw = Molecular weight
N = Population of state
P = Power
r = Internuclear distance
S = Spin vector
S = Spin quantum number
T = Temperature
TOF = Time-of-Flight
= Vibrational quantum number
= Total angular momentum vector
= Total angular momentum quantum number
osc = Oscillation frequency
e = Anharmonicity constant
= wavefunction
xi
Acknowledgements
I would like to thank my advisor Prof. Ágúst Kvaran for his guidance and
patience during my Ph.D studies.
I would also like to thank my many co-workers during this project, Victor
Huasheng Wang, Erlendur Jónsson, Dr. Andras Bodi, and other members
of the University of Iceland, Science Institute for their assistance,
encouragement and support.
The financial support of the University Research fund, University of
Iceland and the Icelandic Science foundation is greatfully acknowledged.
xiii
1
Introduction
My Ph.D. work centered on observing the relative formation of separate
molecular and atomic ion fragments via photoexcitation. It entailed
gathering experimental data by utilising REMPI or Resonance-EnhancedMulti-Photon-Ionization and analysing the data both in terms of atomic
mass and laser frequency.
This led to the development of a new method for measuring and
analysing data entailing the simultaneous collection of REMPI mass and
frequency data over a certain mass area and frequency range into a single
data matrix. This data matrix can be turned into a detailed 2D map of the
measured area using commercial software such as Igor Pro and Labview
which enables us to see important connections between formations of the
various ions (in terms of relative intensities). Thus 2D data for HX show
you how I(H+), I(X+) and I(HX+) vary with wavenumbers (hence
quantum numbers J´) and states. From this 2D map both a REMPI
spectrum of a specific atomic or molecular mass and a mass spectrum for
a specific laser frequency could be extracted as needed. This method
proved to be highly effective, both in accuracy and speed.
Three separate molecules were studied in the following order, acetylene
(C2H2), hydrogen chloride (HCl) and methyl bromide (CH3Br). By
observing the relative formation of separate atoms and molecular
fragments by photoexcitation as a function of laser power and frequency
in conjucntion with theoretical ab initio calcualtions performed by my
group members it was possible to determine the dissociation mechanics
for these molecules.
For HCl specifically, the relative intensity of Cl+/HCl+ ions that formed
via photoexcitation proved to be a highly sensitive indicator of
perturbation between Rydberg and ion-pair states for both H35Cl and
H37Cl isotopologues surpassing those previously used, such as line shifts.
A mathematical model was developed to evaluate state interaction
strengths from the relative intensity of Cl+/HCl+ ions and the interaction
strengths of several states were calculated using both this new method
and older methods which relied on line shifts and relative intensities. The
relative intensity of Cl+/HCl+ ions proved also to be a highly useful tool
in spectrum assignment, notably in rotational line assignments.
15
1.1 Acetylene (C2H2)
The UV spectroscopy, photochemistry and photophysics of acetylene
(C2H2) have been widely studied over the recent years. This is partly due
to its importance in interstellar space and cometary atmospheres, where it
is a commonly observed molecule. There it has been considered to be a
reservoir molecule for the production of carbon containing radicals
which, in turn, are involved in the formation of larger organic
compounds.1-3 Furthermore, being the simplest member of unsaturated
hydrocarbons, acetylene is a fundamental unit in various organic
photochemistry processes and synthesis work.
Photodissociation of C2H2 has been the subject of numerous experimental
investigations, among which are studies by single-1,2,4-8 , two-9,10 and
three- 2,4 photon resonance excitations. Due to the strict u ↔ g selection
for excitation per photon interaction, only ungerade Rydberg states are
accessed by one- and three- (odd number) photon excitations from the
1 +
g electronic ground state, whereas gerade Rydberg states are accessible
by two-photon (even number) excitation. Considering this and the
additional restriction on possible intersystem crossings based on the
selection rules u↔u and g↔g, it is not surprising that the mechanism
and outcome of photodissociation differs, depending on odd- or evennumber photon excitations.
Fragmentation of C2H2 into C2H and H is found to be dominant following
single and three-photon excitations.1,6,10 Thus, single-photon excitations
of the Rydberg states below the first ionization potential reveal only the
C2H product by emission spectra.6 Two distinct dissociation channels,
following single-photon excitations, have been observed7,8, showing
major differences with respect to internal energies and angular
distributions of the fragments C2H and H. In both channels the observed
decay dynamics is found to depend strongly on the excited state of the
parent molecule, C2H2*. In the case of a predissociation of the C2H2
(H1u) Rydberg state it has been proposed that it occurs via the bent
valence state A1Au.7
From less extensive two-photon excitation studies, on the other hand, both
fragmentations into C2 + H2 and into C2H + H, are found to occur.9,11 Thus, H
atoms, H2 molecules and C2 molecules in the X1g+, a3u , A1u and d3g
states have been identified by time resolved photofragment and emission
detection studies.9,11 Both the sequential bond-rupture mechanism and
concerted two-bond fission processes have been proposed to explain the C2
16
and H2 fragment formations.11 Furthermore, long-lived bent isomers of C2H2 as
well as C2H intermediates have been revealed experimentally. Tsuji et al.
concluded, from detailed REMPI analysis9, that ion fragment formations are
dominantly due to the ionization of neutral molecular fragments after
predissociation.
Because of the characteristic predissociation channels the ungerade and
gerade Rydberg states of acetylene are found to be short lived; lifetimes
range from 50 fs to more than 10 ps.4,9
More recently Matthíasson et al.12 were able to determine important
thresholds for fragmentation processes by combining ion mass-analysis
as a function of laser excitation frequencies and laser power with
DFT/STQN calculations on C2H2  C2 + H2.
1.2 Hydrogen Chloride (HCl)
Since the original work by Price on hydrogen halides13, a wealth of
spectroscopic data on HCl has been derived from absorption
spectroscopy14-17, fluorescence studies17 as well as from REMPI
experiments.18-32 Relatively intense single- and multiphoton absorption in
conjunction with electron excitations as well as rich band-structured
spectra make the molecule ideal for fundamental studies.
A large number of Rydberg states, both several low lying repulsive states as
well as the V(1+) ion-pair state have been identified. A number of spinforbidden transitions are observed, indicating that spin-orbit coupling is
important in excited states of the molecule. Perturbations due to state mixing
are widely seen both in absorption15-17 and REMPI spectra.19,20,22,24,25,27,28,32 The
perturbations appear either as line shifts16,19,20,22,25,27,28,32 or as intensity and/or
bandwidth alterations.16,19,20,22,24,25,27,28,32 Pronounced ion-pair to Rydberg state
mixings are both observed experimentally15,16,20,22,25,27,28,32,33 and predicted from
theory.33,34 Interactions between the V(1+) ion-pair state and the E(1+) state
are found to be particularly strong and to exhibit nontrivial rotational,
vibrational and electron spectroscopy. Perturbations due to Rydberg-Rydberg
mixings have also been predicted and identified.16,24 Both homogeneous (=
0)27,28,33,34 and heterogeneous (> 0)28,32,33 couplings have been reported.
Such quantitative data on molecule-photon interactions are of interest in
understanding stratospheric photochemistry as well as being relevant to the
photochemistry of planetary atmospheres and the interstellar medium.17
The excitation and subsequent ion formation mechanism of the HCl
molecule have generally been considered a two-step process, i.e. the
17
excitation of the molecule to an energetically higher Rydberg or ion-pair
state followed by its ionization. There is however evidence that a far
more complex mechanism controls the ionization of HCl molecules and
its atomic fragments.
Photofragmentation studies of HCl have revealed a large variety of
photodissociation and photoionization processes. In a detailed twophoton resonance-enhanced multiphoton ionization study, Green et al.
report HCl+, Cl+ and H+ ion formations for excitations via a large number
of  = 0 Rydberg states as well as via the V1+ ( = 0) ion-pair state,
whereas excitations via other Rydberg states are mostly found to yield
HCl+ ions.19 More detailed investigations of excitations via various
Rydberg states and the V1+ ion-pair state by use of photofragment
imaging and/or mass-resolved REMPI techniques have revealed several
ionization channels depending on the nature of the resonance excited
state.35-39 Results are largely based on an analysis of excitations via the
E1+ Rydberg state and the V1+ ion-pair state, which couple strongly to
produce the mixed (adiabatic) B1+ state with two minima.
Recently, analyses of excitations via the F1 (´=1) Rydberg state and
the V1+(´=14) state have shown characteristic effects of near-resonance
interactions on photoionization channels.39 Those studies introduced the
possibility of a model that used the I(Cl+)/I(HCl+) rate to determine the
max
interaction strength ( W12 ) of a near resonance interaction. A more
detailed analysis of excitations via low-energy triplet states has revealed
similar fragmentations due to coupling with the ion-pair state and has
introduced a model to determine the interaction strength of a nearresonance interaction.40 Those studies revealed characteristic ionization
channels which have been summarized in terms of excitations via 1)
resonance noncoupled (diabatic) Rydberg state excitations, 2) resonance
noncoupled (diabatic) ion-pair excitations and 3) dissociation of
resonance-excited Rydberg states to form H + Cl and/or H + Cl* via
predissociation of some gateway states followed by ionization.39-41
This model is supported by Kauczok et al.42 as they used velocity mapping
to determine the origins of H+ ions formed via the near-resonating lines of
F1 ←←X1+, (0,0), J´= 8 and f32 ←←X1+, (0,0), J´= 5 reported by
Kvaran et al. Their findings show that a major portion of H+ formed by these
two excitations are via the ion-pair state and it is reasonable to assume that
Cl+ is also formed by the same or similar pathways.
18
1.3 Methyl bromide (CH3Br)
The spectroscopy43-47 and photofragmentation48-54 of methyl bromide
have received considerable interest over the last decades, both
experimentally43-53 and theoretically54, for a number of reasons. Methyl
bromide as well as the chlorine and iodine containing methyl halides play
important roles both in the chemistry of the atmosphere47,55-57 and in
industry. Thus, although far less abundant than methyl chloride in the
stratosphere, methyl bromide is found to be much more efficient in ozone
depletion57 and its use is now being phased out under the Montreal
Protocol. Furthermore, bromocarbons are known to have a high global
warming potential.58 Additionally, the molecule is a simple prototype
system of a halogen containing an organic molecule and is as such well
suited for fundamental studies of photodissociation and photoionization
processes.51,54,59
Little is known about the UV spectroscopy of methyl bromide despite its
importance in various contexts. Since a pioneering work by Price43 in
1936 some absorption studies have appeared dealing with i) a weak
continuous spectrum (the A band) in the low energy region (> 180 nm;
E < 55500 cm-1)44,47,55,56 due to transitions to repulsive states54 and ii)
higher energy (< 180 nm; E > 55500 cm-1) Rydberg series and its
vibrational analysis.44-46 There has been some controversy in the literature
concerning the assignment of the higher energy band spectra. Locht et al.
recently reported on the analysis and assignments of spectra46 which
differ from earlier reports.43-45 More recently, multiphoton absorption
(REMPI) studies59 and ab initio calculations of excited states60 have been
published which help clarify the discrepancy.
Photofragmentation studies of methyl bromide can be classified into two
groups. One group focuses on the characterization of photofragments
CH3 + Br(2P3/2)/Br*(2P1/2) resulting from photodissociation in the A
band48-51,54 whereas the other group concerns the CH3+ +Br- ion-pair
formation52,53,59 in the energy region between the ion-pair formation
threshold (76695 cm-1) and the ionization energy (85031.2 cm-1 for
CH3Br+(23/2); 87615.2 cm-1 for CH3Br+(21/2)).59 To our knowledge no
other photofragmentation channels have been reported so far. Some
disagreement concerning the ion-pair formation is to be found in the
literature. Thus Xu et al.53 and Shaw et al.52 conclude that direct
excitation to the ion-pair state is the major step prior to ion-pair formation
whereas more recently Ridley et al.59 give evidence for Rydberg doorway
19
states in the photoion-pair formation analogous to observations for some
halogens containing diatomic molecules.61-65
The basic picture for the electron configuration of methyl halides is
analogous to that for hydrogen halides, such that, in the first
approximation, the symmetry notation C3v, which holds for methyl
halides, can be replaced by Cv.60 Excited state potentials for methyl
halides (CH3X; X = Cl, Br, I) as a function of the C - X bond closely
resemble those for HX molecules showing i) a number of repulsive
valence state potentials which correlate with the CH3 + Br(2P3/2)/Br*(2P
1/2) species, ii) series of Rydberg state potentials which closely resemble
the neutral and first ionic ground state potentials and iii) an ion-pair
1
A1(C3v) (1(Cv)) state with a large average internuclear distance.
Characteristic state interactions between the Rydberg and ion-pair states
are found to affect the spectroscopy and excited state dynamics for
hydrogen halides.19-21,27,28,32,39,40,66,67 It has been pointed out that
analogous effects are to be found for methyl bromide.59,60
More recently Kvaran et al.68 have reported a two-dimensional (2+n)
REMPI experiment analogous to those presented above for acetylene12
and HCl39,40,69, which helps elucidate the discrepancy concerning the
VUV spectroscopy of methyl bromide, and which also yields evidence
for new photodissociation channels via Rydberg states.
20
2
Experimental setup and analysis
method
2.1 Experimental apparatus
Tunable LASER radiation was acquired from a Coherent ScanMatePro
dye laser, or in the case of acetylene a Lumonics Hyperdye 300 dye laser,
pumped by a Lambda Physic COMPex 205 excimer LASER. The
bandwidth of the tunable LASER radiation was about 0.095 cm-1.
Depending on the frequency required, a SHG (second harmonic
generator) unit could be placed in the LASER beam pathway to
frequency double the LASER. For the second harmonic generation we
used a Sirah frequency doubler equipped with interchangeable BBO-2 or
KDP crystals, see Table 1 for details.
The LASER was directed into a vacuum chamber containing electric
platings designed to direct any ions formed down a TOF (time-of-flight)
tube. These platings consist of a single repeller which is a highly charged
positive plate and several extractors which having a lesser positive charge
serve as focal and directional lenses for the ionic beam. The LASER was
focused using either 20 cm or 30 cm focal length lenses.
Table 1: SHG crystals used for specific dyes and wavelengths of entering
photons.
Wavenumber [cm-1]
Wavelength [nm]
Dye
Crystal
22988-22124
435-452
C-440
BBO-2
22124-21186
452-472
C-460
BBO-2
21186-20408
472-490
C-480
BBO-2
20408-18622
490-537
C-503
BBO-2
18622-17637
537-567
R-540
BBO-2
17637-16750
567-597
R-590
KDP-R6G
Diagonally to the LASER beam path, in line with the focus point, a
nozzle sprayed gas into the vacuum chamber with regular intervals, thus
21
creating a jet-cooled stream of molecular particles in the focal point of
the LASER. Ionization chamber was pumped by a diffusion pump backed
by an Edwards mechanical pump whereas the TOF tube was pumped by a
Pfeiffer turbo pump also backed by an Edwards mechanical pump. On
top of the diffusion pump, located between the mechanical pump and the
ionization chamber, were cooling rods filled with liquid nitrogen.
An acetylene gas sample was acquired from Linde gas (AAS Acetylene
2.6). Pure acetylene or mixtures of C2H2 and argon (typically in ratios
ranging from 1:1 to 1:4 = C2H2:Ar) were pumped through a 500 m
pulsed nozzle from a typical total backing pressure of about 1.0 – 1.5 bar
into the ionization chamber. The pressure in the ionization chamber was
lower than 10-5 mbar during experiments. The distance between the
nozzle and the center between the repeller and the extractor was about 6
cm. The nozzle was held open for about 200 s and the LASER beam
was typically fired about 450 s after opening the nozzle.
Figure 1. Schematic of the REMPI-TOF experimental equipment.
HCl and CH3Br gas samples were acquired from Merck-Schuchardt,
>99.5% purity both. They were pumped through a 500 m pulsed nozzle
from a typical total backing pressure of about 1.0–1.5 bar into an
ionization chamber. The pressure in the ionization chamber was lower
than 10-6 mbar during experiments. The nozzle was held open for about
200 s and the LASER beam was typically fired about 500 s after
opening the nozzle.
22
REMPI-TOF spectra for jet-cooled gas were acquired by detecting ions
formed in the focal point that had been directed through a TOF tube, on a
MCP (micro channel plate). LeCroy 9310A, 400 MHz storage
oscilloscope was used to gather the data from the MCP in digital format.
Typical repetition rates were 50-100 pulses for each frequency point.
Figure 1 shows a schematic of the experimental setup.
Information on the power dependence of the ion signals was generally
acquired by systematically reducing the laser power by directing the laser
through different numbers of quartz windows which reflected a part of
the laser beam. Each data point was acquired by averaging over 1000
pulses. The reflection precentage of each quartz window was calibrated
at about 8.4%. During a single measurement run one window was added
in the path of the laser beam after each 1000 pulses up to a maximum of
six windows at which point they where removed again one at a time
every 1000 pulses. The laser power was measured before and after every
measurement run and should optimally remain unchanged. To insure
accuracy at least three measurement runs were preformed for each ion
signal measured. Information on the power dependence of the ion signals
was generally acquired by averaging over approximately 1000 pulses.
2.2 Analysis Method
Using the equipment described we were able to measure simultaneously
the formation of all atomic and molecular ions within a certain mass
range as a function of laser frequency and gather this data into a single
data matrix.
To do so we used Labview version 8.0. A program was created by
Erlendur Jónsson70 that gathered the summed data from the oscilloscope
into a text file that included the wavenumber of the excitation, the mass
data reading for each wavenumber and an integration over a certain mass
area for each wavenumber.
Igor Pro version 5.071 was used to process this text file to create a 2D
contour plot of the measured area. REMPI spectra for specific atomic or
molecular mass could then be extracted from the 2D image, in addition to
mass spectra for specific wavenumbers. Figure 2 shows a 2D contour
plot and samples of the rotational spectra of HCl that were extracted
from the 2D contour plot.
23
Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is the 2D
contour spectrum that shows clearly the different ions formed as a function of
both atomic/molecular mass and wavenumbers. Above are REMPI spectra
derived from the contour plot for each ion observed. Mass spectra for individual
wavenumbers could also be derived in similar fashion.
24
This analysis method enables us to see important connections between
formations of the various ions via REMPI (in terms of relative intensities) as
the 2D data for HCl show you how I(H+), I(35Cl+), I(H35Cl+), I(37Cl+) and
I(H37Cl+) vary with wavenumbers (hence quantum numbers J´) and states. It
proved to be quite accurate in observing mass peaks that previously went
undetected due to overlap or that were otherwise obscured allowing for a more
robost assignment of rotational spectra. It also allowed us to discern if 35/37Cl+
signals originated from the Rydberg state rotational line in question or if it was
due to overlap from a nearby ion-pair state rotational line. This last proved
highly valuable in our studies on photofragmentations.
2.2.1 Simulations
Gathered REMPI spectra (such as those shown in figure 2) can be
simulated by a quantum mechanical simulation using Igor Pro 5.0. A
macro (small program or script that is run inside Igor Pro) was used to
simulate rotational spectra by using spectroscopic parameters. The
simulation determines relative rotational line positions from first- and
second-order rotational constants (B and D) for the excited and ground
state. It also determines the relative intensity of the rovibrational lines by
taking account of the ground state population and degeneracy.27
The experimental spectrum was displayed on a screen with the simulated
spectrum. Realistic rotational parameters were then put into the macro and
the simulated spectrum was generated. Finally the rotational constants were
changed until a reasonable fit to experimental data was reached. In some
cases a least squares analysis could be used to assist with the simulation, as
was done in the case of C2H2. However the final simulation was always done
by a visual comparison of the spectra as in some cases the least square
analysis gives an inferior result due to computational errors. These errors
were typically due to the program having too much emphasis on the
bandwidth and shape of the rotational peaks and too little emphasis on peak
positions, resulting in the center of the simulated peaks being shifted away
from the center of the measured peaks.
Simulations like the one shown in figure 3, which is a simulation of the
g3(1)+ ←← X1+ (0,0) excitation, could be used to accurately determine
rotational constants of the simulated spectra. They could also be useful
for line assignments. From the calculated spectra in figure 3 it can clearly
be seen that the experimental spectra contain a rotational peak outside of
the g3(1)+ ←← X1+ (0,0) excitation, which was later found to be a part
of the D1 ←← X1+ (0,0) excitation. In addition, when searching for
25
line perturbations, simulations like these can also be of moderate use as
subtle line shifts become more obvious.
1.4
Experimental
1
D  ; R-line ; J'=1
1.2
1.0
3
J'=1
0.8
5
Calculated
0.6
7
0.4
82508
82512
82516
-1
2xh[cm ]
82520
Figure 3: Experimental data (above) for the excitation g3(1)+  X1+ (0,0) and
the simulated spectrum (below) derived from spectroscopic constants. The
experimental spectrum also contains a single peak due to the D1 ←← X1+
(0,0) excitation. Simulations can thus be of use for peak assignments in addition
to accurately determining rotational constants.
2.2.2 Time of flight analysis
When a molecule is ionized in an electric field it gains momentum in the
direction of the field. The relationship between the atomic or molecular
mass of the ion (Mw) and the time-of-flight (TOF) for our equipment is
TOF = a M w  b
(1)
The constants a and b are experimental constants that vary between
experiments which must be evaluated for each measurement and Mw is
the molecular weight of the ions formed from the sample injected into the
gas chamber. Using equation (1) it was easy to evaluate the atomic mass
of ions formed by REMPI as there were generally some known peak
formations due to impurities and/or background gas in the vacuum
chamber, such as C+ and C2+, which could be used for calibration.
26
3
Theoretical considerations
3.1 Electronic spectroscopy of diatomic
molecules72-74
The quantum energy levels of a molecule can be broken down into three
distinct parts. The electronic energy levels, which arise from the energy
of different electron configurations, the vibrational energy levels, which
correspond to the allowed energy for vibrations of molecular bonds and
the rotational energy levels, which correspond to the allowed rotational
energy of the molecule in question.
The approximate order of magnitude for excitations within these energy
levels is:
Eelec ≈ Evib *103 ≈ Erot *106
(2)
They are also interconnected in the sense that each vibrational state has a
series of rotational levels and each electronic state has a series of
vibrational levels. Therefore, the total energy of an electronic excitation
can be expressed as:
totalEelecEvibErot
3.1.1 Electronic energy levels.
Electronic excitation occurs when an electron is excited to an energetically
higher molecular orbital from its ground state or energetically lower orbital.
A molecular Rydberg state is composed of atom like orbitals with
primary quantum numbers higher than those of the ground state. During
Rydberg excitation the electron in the highest occupied molecular orbital
(HOMO) is excited into some energetically higher Rydberg orbitals
depending on the frequency used for excitation.
27
An ion-pair state is formed when an electron of the bonding electron pair
is excited into the antibonding orbital (* ←← Figure 4 gives an
example using HCl.
4s
4s


1s
1s


3p
3p


3s
3s
a)
b)
Figure 4: Energy diagram for molecular orbitals of HCl. a) Ion-pair excitations.
An electron is excited from the bonding orbital of the molecule to the
antibonding orbital. b) Rydberg excitations. An electron is excited from the nonbonding orbital to a Rydberg orbital.
As the antibonding orbitals are located away from the center of the
molecule this weakens the molecular bond and in some cases may cause
it to break. However for diatomic molecules with a difference in
electronegativity the antibonding electron is attracted to the atom with the
higher electronegativity. In the case of HCl this means that the
antibonding electron is attracted to the Cl atom, causing the atoms to
attain ion-like properties (H+ and Cl-) and remain bonded through
electrostatic properties. Nevertheless, the ion-pair bond is both weaker
and longer than a regular bond.
For a single-photon excitation, the total electronic angular momentum of
the electron must remain the same or change by only one integer,
according to the electronic excitation selection rule
0, ±1
28

For multiphoton excitations, as each photon must fulfil the selection rule,
this rule is applied for each photon used in the excitation, resulting in
0, ±1, ±2 ... ±n


where n is the number of photons in the excitations. Thus multiphoton
excitations open up several possible excitation paths otherwise
undetectable. For example, the ground state of HCl is a X1 state, thus for
single-photon excitations only  and  states are accessible in HCl.
However, for two-photon excitations  states become accessible in
addition to the  and  states.
3.1.2 Vibrational energy levels
We have discussed the excitation of electrons in a molecule. The next
effect we need to consider is the vibration of the molecular bond.
A molecular bond is formed from the positive overlap of two atomic
wavefunctions. The length of the bond is dictated by the attracting
properties of the electrons of one atom to the nucleus of the other and the
mutual repulsive forces of the electrons and the nuclei of each atom. As
such there must be an internuclear distance where the attractive and
repulsive forces of the atoms reach equilibrium.
This internuclear distance, called the bond length of the molecule,
corresponds to the bottom of the potential well. Pushing or pulling the
atoms away from that optimal bond length increases the potential energy
of the molecule.
Figure 5 illustrates the difference between Rydberg states and ion-pair
states. The bond length of the Rydberg state is smaller than that of the
ion-pair state, in addition the energy gap is generally higher between
vibrational levels of the Rydberg state than for the ion-pair state as they
are quantized and distributed according to the shape of the potential.
A simple harmonic oscillator is a useful approximation for the vibrational
energies. In the simple harmonic model they are defined as
½osc cm-1 
where  is the vibrational quantum number. In equation (6) the energy
difference between adjacent vibrational levels is equal to the oscillation
frequency osc and the vibrational energy cannot be zero.
29
Energy
Ion-pair
Potential
Rydberg
Potential
Vibrational levels
Internuclear distance
Figure 5: Rydberg potential vs. ion-pair potential. The figure illustrates the
difference between an ion-pair state and a Rydberg state. The average bond
length of the ion–pair state is longer than that of the Rydberg state due to the
excitation of an electron to the antibonding orbital, giving the excited molecule
semi-ionic properties. The vibrational levels are quantized and distributed
according to the shape of the potentials.
However, real molecules do not follow a simple harmonic path. The
repulsive forces between electrons build up faster than the attractive force
between the electrons and the nucleus when the atoms are pressed
together and similarly they diminish slower when they are pulled apart.
Therefore if the atoms move too far apart, which can happen if the
vibrational energy reaches a certain amount, the bond between them will
break and the molecule will dissociate into atoms. So while the simple
harmonic oscillator approximation is useful as a tool, the deviations from
the simple oscillator need to be taken into account for real molecules. An
expression that fits to a good approximation is the Morse function:


U (r )  Deq 1  expareq  r 
30
2


where a is a constant for a particular molecule, req is the bond length at
equilibrium, r is the bond length and Deq is the dissociation energy. By
using this potential energy in the Schrödinger equation, the allowed
vibrational bands are found to be
v½e- + ½)2 ee

Where e is the oscillation frequency and ee is the anhermonicity
constant.
3.1.3 Rotational energy levels
The rotational energy of a molecule is inversely proportional to its
moment of inertia. By looking at a rigid diatomic molecule we can see
that its moment of inertia can be expressed as:
I
m1 m2 2
r0  r02  
m1  m2

where m1 and m2 are the mass of each atom,  is the reduced mass of the
system and r0 the internuclear distance between the atoms.
By solving the Schrödinger equation for a diatomic system it can
be shown that the allowed rotational energy levels for a rigid diatomic
molecule can be expressed as:
EJ 
h2
8 2 I
J ( J  1) Joules 
m 2 kg
) and I is the moment of
where h is the Planck constant (6,63*10-34
s
inertia. J is the rotational quantum number and can only take integer values
of zero and higher. This restriction to integer values comes directly from
the Schrödinger equation and it is this restriction that introduces the discrete
rotational levels observed in spectroscopy, see figure 6.
31
Energy
Rydberg
Potential
Vibrational levels
Rotational levels
Internuclear distance
Figure 6: For each molecular Rydberg state there are discrete vibrational levels.
For each vibrational state there are also discrete rotational levels. The vibrational
series depend on the shape of the potential and the rotational series depend on
the energy and thus the mean bond length of the vibrational levels.
In this work I use wavenumbers [cm-1] instead of Joules [J]. To compensate for
this common practise in spectroscopy, equation (10) becomes:
EJ
h2
j 

J ( J  1) cm-1
hc 8 2 Ic

where c is the speed of light in cm s-1. This equation is usually
abbreviated to:
 j  BJ ( J  1) cm-1 
where B is the rotational constant that is given by:
32
h

8 I B c
B
2

From equation (12) it can be seen that the energy of the rotational levels will
gradually increase as J increases and that the energy difference between
adjacent rotational levels will also increase by 2B for each level of J.
At this point it should be stated that the above only holds for an ideal
rigid rotor. In reality the molecules are not completely rigid. As J
increases, the distance between the atoms increases to some degree. This
is somewhat like spinning a ball fastened to a rubber string. As you spin
the ball faster, the string lengthens. This causes the moment of inertia of
the molecules to diminish and introduces an effect called centrifugal
distortion. To correct for this the centrifugal distortion constant is
introduced and equation (12) becomes
J= BJ(J+1) – DJ2 (J+1)2 cm-1

where D is defined as:
D
h3

32 4 I 2 r 2 kc

These two values (B and D) usually suffice for modern spectroscopy
fitting, since higher order fitting parameters have negligible effect.
For a single-photon excitation, the angular momentum of the molecule
must change by one, according to the rotational selection rule
Jif
Jif≠
For a multiphoton excitation, as each photon must fulfil the selection rule,
this rule is applied for each photon used in the excitation, resulting in
For
when n 
J when n 
33
etc
For≠
Jn
where n is the number of photons used for the excitation. Thus, as
excitation is possible between more rotational levels, multiphoton
excitations introduce additional line series for each vibrational level
within a state.
3.2 The intensity of electronic excitation
spectroscopy lines72-74
The intensity of absorption spectroscopic lines results from a combination of
several factors. Most notable are the electron transition probabilities, the
Frank-Condon principle and the Boltzmann distribution. The first two are
due to molecular wave functions. Using the Born-Oppenheimer
approximation we can treat a molecular wave function as a combination of
an electronic wave function and a nuclear wave function. The Boltzmann
distribution is a property-of-state population and is therefore affected by the
temperature of the measured sample.
The power of the excitation source also affects the intensity of the
spectroscopic lines. This effect is however separate from the intrinsic
properties of molecules and is simply due to an increased excitation rate
from the higher density of photons.
3.2.1 Transition probabilities
The transition probabilities of electronic excitation is one of the main
properties that influence the intensity of spectroscopic lines. Transition
probabilities (a2) describe the probability of an excitation between
electronic states and are defined as
a 2  (  m  n d e ) 2  

where  is dipole moment of the molecule, m and n are the molecular
wavefunctions and de is the volume element. The wavefunction can be
regarded as a combination of electron wavefunctions, vibrational wavefunctions, rotational wavefunctions and even translational wavefunctions.
34
   e v r t  

For rovibrational excitations the rotational and translational
wavefunctions as considered to be constants. A common approximation
is also to consider the electronic wavefunction as a constant which
depends on the characteristics of the ground and excited state. As such
the transition probability of rovibrational excitations can be defined as
a 2  (  v '  v '' dr ) 2  

This gives rise to the Frank-Condon factors (FCF) which are transition
probabilities proportional to the overlap of the vibrational wave functions
in the upper and lower vibrational states.
The FCF influence on intensity varies with vibrational levels depending
on the wavefunction overlap and remains the same for all rotational
excitations within the same vibrational excitation to a first approximation.
In figure 4 we see vibrational levels of two fictional states, E0 and E1. As
electronic excitations are not influenced by vibrational selection rules,
excitation from E0 (’=0) to any vibrational level of E1 is allowed as long
as there is a non-zero chance that the internuclear distance is the same for
the E1 and E0 states. In this case excitation between the ground
vibrational states of E0 and E1 is highly unlikely, whereas excitation
between the ground vibrational state of E0 and ’=2-5 of E1 is highly
likely.
3.2.2 Boltzmann distribution
The second property that influences line intensities is the population of
the ground state as the rotational population of the ground state
influences the number of molecules that are available for a specific
excitation. The Boltzmann distribution is defined as
  EJ
NJ
 exp
N0
 k bT



(19)
where N0 is the total number of particles in the ground state, NJ is the
number of states having the energy EJ, kb is the Boltzmann constant (1.38
x 10-23 m2kgs-2K-1) and T is the temperature.
35
Figure 7: Franck-Condon factors. The vibrational levels are positioned so that
the probability function forms a standing wave. It is the overlap of these
probability distributions that determines the Franck-Condon factors. Figure from
http://www.chem.ucsb.edu/~kalju/chem126/public/elspect_theory.html
Therefore, as a sample is cooled down, more particles will occupy the
lower rotational levels of the ground state, thus increasing the chance of
excitation to the lower rotational levels of the excited state, while
decreasing it for the higher rotational levels. In figure 8 we see an
example of this using a fictional distribution. In the hot gas sample we
would expect to see rotational peaks originating from the J’=0 to at least
the J’=5 rotational level. For the cold sample however, only excitation
36
origination from the J’=0 to the J’=2 rotational levels would be expected.
Thus cold samples show far fewer rotational lines than hot samples.
This effect is very useful in spectroscopy as it allows for different degrees of
spectrum complexity. Cold samples have few rotational lines and therefore
do not offer the same amount of data, yet they are simpler and easier to
assign. Hot samples have more rotational lines and more data, but are more
complex to assign. Thus by varying the rotational temperature of a gas
sample and comparing, very useful information is gained.
Rotational levels
5
4
3
2
1
0
Hot gas
Cold gas
Figure 8: When gas is jet-cooled the rotational energy of individual molecules
shifts downwards, thus increasing the probability of excitation from the lower
rotational levels compared to that from the higher ones.
3.2.3 Laser power dependence
Ion intensities (I(M+)) vary with the laser power (Plaser), the number of
photons needed to ionize (n) and the transition probabilities as discussed
above. The total ion intensity can be expressed as
Plasern 

where  is a proportionality constant depending on the transition
probability. From equation (20) the following expression can be derived:
37
rel
lognlog Plaser + C


rel
where Plaser is proportional to the laser power. From this equation it can
be seen that the number of photons needed for excitation can be derived
from a logI(M+) vs. logP plot. This permits an easy extraction of photon
numbers and gives valuable information concerning excitation and
ionization pathways.
3.2.4 Multiphoton excitation intensities
These previously mentioned properties form a basis for the intensity of
rovibrational lines. For a two-photon resonance excitation followed by
ionization, the intensities are proportional to the products of the cross
sections of two major steps, a) the resonance excitation and b)
photoionization. According to Kvaran et al.25, the resonance excitation is
proportional to a function S´´´(J, , ||, ±) which depends on the
difference of the angular momentum quantum numbers J and  as
well as the parallel (||) and perpendicular (±) transition dipole moments
between the two states, where || equals J←J transitions and ± equals J
±1 ← J transitions. The transition strengths for one-, two- and threephoton excitations have been formulated in terms of Hönl-London type
approximations for diatomic molecules.72,75,76
The resonance excitation is also proportional to a function C(v’,v’’). In
the case of a Boltzmann distribution, C(v’,v’’) can be expressed as
C(v’,v’’) = KF(v’,v’’)Pn2(v´) 
where K is a parameter depending on the electronic structure of the
molecule, geometrical factors and sample concentrations, F(v´,v´´) is the
Franck-Condon factor for the transition v´←v´´, P is the laser power and
n is the number of photons necessary to complete the ionization and
2(v´) is the ionization cross section which is a slowly varying function
with laser energy.
Thus by taking the degeneracy (g(J´´)) of the ground state rotational
energy levels (E(J´´)) into account, the relative line intensity is defined as
I rel  C(v´, v´´)g(J´´)Sv´v´´e
38
  E ( J ´´) 


 kT 


3.3 Total angular momentum and
Hund’s cases72
The total electronic angular momentum is composed of the electron spin
angular momentum and the orbital angular momentum. An electron moving in
its orbital is said to possess orbital angular momentum. For a diatomic
molecule this momentum is quantized and expressed as L and has the
magnitude
|L|  L( L  1)  
Unless L = 0 the orbital angular momentum vector L precesses about the
internuclear axis of the molecule as figure 9 shows.
L

Figure 9: The precession of L about the internuclear axis. The precession forms
a component  along the internuclear axis.
The angular momentum vector  is the component of the orbital angular
momentum along the internuclear axis with a magnitude of.
ħ


For each given value of the quantum number L the quantum number
can take the values
 = 0, 1, 2, ... , L. (26)
39
So for each value of L there are L+1 distinct states with different energy.
The molecular state designations , ,  and  represent  values of 0,
1, 2 and 3 respectively.
The electron which orbits around the molecule is also spinning about an
axis forming a spin orbit vector S which has the magnitude
|S|  S ( S  1)  

Here the corresponding quantum number S can take integer or half
integer values depending on whether there is an odd or even number of
electrons. S then precesses about the internuclear axis (much in the same
way as L) with a constant component with amagnitude
ħ


Where  can take the values
 = S, S-1, S-3, ... -S

As such  can take 2S+1 different values and can also take negative values.
These two elements of electron motion added together form the total
angular momentum of the electrons:


The molecule’s angular momenta, electron spin, electronic orbital angular
momentum and the angular momentum of nuclear rotation form together a
resultant J which is the total angular momentum of the molecule.
For 1 states the spin and angular momenta are zero. Therefore the total
angular momentum is the same as the angular momentum of nuclear rotation
and we have a simple rotator as shown in figure 10. For states where  and 
are nonzero we have special cases which are called Hund’s cases.
3.3.1 Hund’s case a)
For Hund’s case a), the interaction of the nuclear rotation with the
electronic motion is considered to be weak (both spin and orbital).
However, the coupling of the electronic motion with the line joining the
nuclei is considered to be strong. The electronic angular momentum  is
therefore well defined even in rotating molecules.
40
N
J
Figure 10: Simple rotator. If S = 0 and L = 0 we only need to consider the
angular momentum of nuclear rotation N. Therefore we have a simple rotator
were N is equal to the total angular momentum J.
The angular momentum of the rotating molecule N and the electronic angular
momentum  then form the total angular momentum J as shown in Figure 11.
J
N



Figure 11: Hund‘s case a). The orbital angular momentum  and the electronic spin 
form the electronic angular momentum . The angular momentum of the rotation
molecule N and the electronic angular momentum  then form the total angular
momentum J.
Since it is obvious that J cannot be smaller than  we get
J


and thus, levels with J <  do not occur.
41
3.3.2 Hund’s case b)
When L = 0 and S ≠ 0, a weak or zero coupling of the internuclear axis
with the spin vector S occurs which is characteristic of Hund’s case b). In
this case  and N form a resultant which is called K which is the total
angular momentum apart from spin. The corresponding quantum number
K can take the values
K = , +1, +2 ....
(32)
The angular momenta K and S then form a resultant J which is the total
angular momentum, see Figure 12.
S
J
K
N

Figure 12: Hund‘s case b).  and N form a resultant which is called K. The
angular momenta K and S then form a resultant J.
The possible values of J are therefore
J = (K+S), (K+S-1), ... , (K-S)

Thus in general, every level with a given K has 2S+1 components. This
appears as peak splitting in rotational spectra. Note that for singlet states
the distinction between cases a) and b) are pointless, as S=0, = and
therefore K=J.
3.3.3 Hund’s case c)
In some cases the interaction of L and S may be stronger than the coupling
with the internuclear axis. In these cases  and  are not defined. Instead L
and S form a resultant Ja which is coupled to the internuclear axis by a
component .  and N then form a resultant J, see Figure 13.
42
J
N

L
Ja
S
Figure 13: Hund‘s case c). L and S form a resultant Ja which is coupled to the
internuclear axis with a component .  and N then form a resultant J.
Hund’s cases a), b) and c) are the most common Hund’s cases. There are
two more, d) and e); however, they are of lesser importance for the scope
of this dissertation.
3.4 Symmetry properties72
The symmetry properties of rotational levels are important for
spectroscopic work. The rigorous selection rule which states that
excitations can only occur between levels of the same symmetry can be
of great help in assigning spectroscopic lines.
The symmetry of rotational levels is a property of their eigenfunctions. If
the eigenfunction of a rigid rotor remains unchanged when reflected at its
origin by replacing  by + and  by - it is considered to be in a
positive electronic state. Here  is the azimuth of the line connecting the
mass point to the origin and  is the angle between this line and the z
axis. Should the eigenfunction change sign it is considered to be in a
negative electronic state.
Rotator functions remain unchanged for even values of J but change sign for
odd values of J. This characteristic is called parity and rotational levels can be
assigned a + or – parity depending on the symmetry properties.
43
3.4.1 Parity of rotational levels
For states that have = 0 and S = 0 the parity of the rotational levels
switches between being positive or negative depending on whether J is
even or odd. For 1+ states the first level has a positive parity. For 1states the reverse is true and the first level has a negative parity. The same
holds for states were = 0 and S ≠ 0, however here the parity depends on
K rather than J.
For states were  ≠ 0 the rotational levels have both a positive and
negative parity, for which there is a small energy difference. See Figure
14 for further clarification.
K
0
1
2
3
4
1+
+
-
+
-
+
-
0
1
2
3
4
5
+
2+
3+
5
K
0
1
2
3
4
1-
-
+
-
+
-
+
0
1
2
3
4
5
-
+ +
- -
J
- -
+ +
- -
+ +
- -
½
½
3/2
3/2
5/2
5/2
7/2
7/2
9/2
9/2
11/2
+
- - -
+ + +
- - -
+ + +
- - -
1
012
123
234
345
456 J
J
2-
3-
+ +
- -
+ +
½
3/2
3/2
5/2
5/2
7/2
7/2
9/2
9/2
11/2
+ + +
- - -
+ + +
- - -
+ + +
012
123
234
345
½
-
1
5
J
J
456 J
Figure 14: Parity. The + and – suffixes in the term symbol indicate the parity of the
rotational levels of the states. For multiplet states the parity depends on K instead of J.
3.4.2 Parity selection rules
For single photons, excitation may only occur between rotational levels
with opposite parity.
but not or
For two-photon excitation, this turns into
andbut not
and for three-photon excitation, it again turns to
+  - but not + + or - thus only excitations between rotational levels of the same parity is
allowed for an even number of photons and excitation between rotational
levels of opposite parity is allowed for an odd number of photons.
44
3.5 Perturbations72
Sometimes a rotational spectrum can show a deviation from an otherwise
smooth course. This deviation is generally caused by a perturbation. A
perturbation can occur when rotational levels with the same J’ for different
electronic states are close to each other. It is characterized by a shift from the
expected line position and/or a change in the line intensity of the perturbed
lines. Perturbations where the vibrational level has been shifted have also
been observed; those are known as vibrational perturbations and are outside
the scope of this work.
3.5.1 Rotational perturbations
When two rotational levels with the same J’ are energetically close to each
other it is possible for them to be perturbed, causing them to separate in
energy and receive spectroscopic characteristics from each other.
1.2
F, v´=1
HCl+
X, v´=0
d)
1
I(M+)/I1(HiCl+)
0.8
0.6
H+
Cl+
0.4
0.2
0
J´  8 / i = 35
J´  8 / i = 37
J´=8 / i = 35
J´=8 / i = 37
Fig.3d
Figure 15: Perturbation. On the left we have an average ion ratio for the F1,
’=1 state. On the right we have the ratio for the perturbed F1, ’=1, J’=8
rotational level. As can be clearly seen, the perturbation to the ion-pair state
causes considerable changes to the ratio of H+ and Cl+ vs. HCl+ ion formation for
both the 35Cl and 37Cl isotopes.
45
As an example, the F1, ’ = 1, J’ = 8 and the V1, ’ = 14, J’ = 8 rotational
levels of the HCl molecule are very close energetically. Due to this, the
corresponding Rydberg rotational peak (for the F1state) shows a mass
spectrum that has ion-pair state (V1) characteristics and vice versa, see Figure
15. In addition, the energy difference between J’ = 7 and J’ = 8 and also
between J’ = 8 and J’ = 9 for both states is different from what one would
expect from a non-perturbed progression of rotational lines, whereas the
difference is in accordance with a shift due to perturbation.39
This does not mean that any rotational level that is energetically close to
another is perturbed. The perturbation can only occur between specific
rotational levels as governed by the selection rules.
3.5.2 Perturbation selection rules
1) Both states must have the same total angular momentum J; J = 0
2) Both states must have the same multiplicity; S = 0
3) The  value of the two states must only differ by 0 or ±1;  = 0 , ±1
4) Both states must have the same parity, either both positive or both
negative; + // 5) For molecules with identical nuclei, both states must have the same
symmetry in the nuclei; s // a
Rules 1, 4 and 5 are perfectly rigorous. The second rule holds only
approximately as perturbations between states of different multiplicity
increase in magnitude with increasing multiplet splitting similarly to
transitions with radiation. The third rule holds only when  is defined,
Hund’s case a) and b). For Hund’s case c) the total angular momentum
is used instead.
3.6 Predissociation72
Predissociation is a fragmentation of a molecule into its atoms or smaller
molecular fragments. It can occur through an interaction of a bound state
with an unbound or quasi-bound state. Fragmentation can also occur via
direct excitation to an unbound or quasi-bound state in which case it is
simply referred to as dissociation.
Predissociation can be detected in a rotational spectrum by a sudden
uncharacteristic broadening of lines. This corresponds to the shortening of
the lifetime of the rotational levels due to the molecule predissociating into
46
smaller atomic or molecular fragments. The predissociation of a molecule
can be followed by an excitation of the fragments, either through direct
ionization or by a resonance-enhanced ionization, see Figure 16 a) and b).
a)
b)
A+
B+
A+
B+
A#
AB#
AB#
A+B
AB
A+B
AB
Figure 16: Predissociation of a diatomic molecule. a) Predissociation followed
by a direct ionization. The molecule is initially excited to a bound state which
interacts by a non-bound or a quasi-bound state. Some of the molecules in the
bound state “leap” across to the predissociating state and are dissociated into its
atomic components. The atoms formed can themselves absorb photon energy
and ionize. b) Predissociation followed by a resonance-enhanced ionization. In
this case the photon energy needed to excite the parent molecule corresponds to
an excited state of the atom resulting in a resonance-enhanced excitation.
47
4
Published papers
International Journals
Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran.
Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35,
37: State interactions, photofragmentations and energetics of high energy
Rydberg states. Journal of Chemical Physics, 134, 164302, 2011.
Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras
Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation
Channels via Rydberg States. Journal of Physical Chemistry A, 114,
9991, 2010.
Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional
(2+n) REMPI of HCl: State interactions and photorupture channels via
low energy triplet Rydberg states. Journal of Chemical Physics, 131,
044324, 2009.
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two Dimensional
(2+n) REMPI of HCl: Observation of a new electronic state, Journal of
Molecular Spectroscopy, available online, 2009.
Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi,
Erlendur Jónsson, Two dimensional (2+n) resonance enhanced
multiphoton ionisation of HCl: Photorupture channels via the F-1
Delta(2) Rydberg state and ab initio spectra, Journal of Chemical
Physics, 129(16), 164313, 2008.
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of
acetylene: Gerade Rydberg states and photorupture channels, Chemical
Physiscs Letters, 458 (1-2), 58 (2008).
49
Icelandic Journals
Kristján Matthíasson, Victor Huasheng Wang, Ágúst Kvaran.
Massagreining í kjölfar ljósgleypni: Víxlverkanir milli örvaðra ástanda
uppgötvaðar. "Tímarit um raunvísindi og stærðfræði", 2011.
Ágúst Kvaran, Victor Huasheng Wang og Kristján Matthíasson, Tveggja
ljóseinda gleypni acetylens, "Tímarit um raunvísindi og stærðfræði", 1.
hefti, 2007, bls. 41-44.
50
Paper I
Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran.
Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35,
37: State interactions, photofragmentations and energetics of high energy
Rydberg states. Journal of Chemical Physics, 134, 164302, 2011.
51
THE JOURNAL OF CHEMICAL PHYSICS 134, 164302 (2011)
Two-dimensional resonance enhanced multiphoton ionization of Hi Cl;
i = 35, 37: State interactions, photofragmentations and
energetics of high energy Rydberg states
Kristján Matthíasson, Jingming Long, Huasheng Wang, and Ágúst Kvarana)
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
(Received 8 February 2011; accepted 5 March 2011; published online 22 April 2011)
Mass spectra were recorded for (2 + n) resonance enhanced multiphoton ionization (REMPI) of
HCl as a function of resonance excitation energy in the 88865-89285 cm−1 region to obtain twodimensional REMPI data. Band spectra due to two-photon resonance transitions to number of
Rydberg states (�� = 0, 1, and 2) and the ion-pair state V(1 � + (�� = 0)) for H35 Cl and H37 Cl
were identified, assigned, and analyzed with respect to Rydberg to ion-pair interactions. Perturbations show as line-, hence energy level-, shifts, as well as ion signal intensity variations with rotational quantum numbers, J� , which, together, allowed determination of parameters relevant to the
nature and strength of the state interactions as well as dissociation and ionization processes. Whereas
near-resonance, level-to-level, interactions are found to be dominant in heterogeneous state interactions (�� �= 0) significant off-resonance interactions are observed in homogeneous interactions (��
= 0). The alterations in Cl+ and HCl+ signal intensities prove to be very useful for spectra assignments. Data relevant to excitations to the j3 �(0+ ) Rydberg states and comparison with (3 + n)
REMPI spectra allowed reassignment of corresponding spectra peaks. A band previously assigned to
an � = 0 Rydberg state was reassigned to an � = 2 state (ν 0 = 88957.6 cm−1 ). © 2011 American
Institute of Physics. [doi:10.1063/1.3580876]
I. INTRODUCTION
Since the original work by Price on the hydrogen
halides,1 a wealth of spectroscopic data on HCl has been derived from absorption spectroscopy,2–5 fluorescence studies5
as well as from resonance enhanced multiphoton ionization (REMPI) experiments.6–20 Relatively intense singleand multiphoton absorption in conjunction with electron
excitations as well as rich band structured spectra make the
molecule ideal for fundamental studies. A large number of
Rydberg states, several low-lying repulsive states as well as
the V(1 � + ) ion-pair state have been identified. A number of
spin-forbidden transitions are observed, indicating that spin–
orbit coupling is important in excited states of the molecule.
Perturbations due to state mixing are widely seen both in
absorption3–5 and REMPI spectra.7, 8, 10, 12, 13, 15, 16, 20 The
perturbations appear either as line shifts4, 7, 8, 10, 13, 15, 16, 20 or
as intensity and/or bandwidth alterations.4, 7, 8, 10, 12, 13, 15, 16, 20
Pronounced ion-pair to Rydberg state mixings are both
observed experimentally3, 4, 8, 10, 13, 15, 16, 20, 21 and predicted
from theory.21, 22 Interactions between the V(1 � + ) ion-pair
state and the E(1 � + ) state are found to be particularly strong
and to exhibit nontrivial rotational, vibrational, and electron
spectroscopy due to a production of a mixed (adiabatic)
B1 � + state with two minima. Perturbations due to Rydberg–
Rydberg mixings have also been predicted and identified.4, 12
Both homogeneous (�� = 0)15, 16, 21, 22 and heterogeneous
a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Permanent address: Science Institute, University of Iceland,
Dunhagi 3, 107 Reykjavík, Iceland, Tel: +354-525-4672/4800, Fax: +354552-8911.
0021-9606/2011/134(16)/164302/8/$30.00
(�� �= 0)16, 20, 21 couplings have been reported. Such quantitative data on molecule–photon interactions are of interest in
understanding stratospheric photochemistry as well as being
relevant to the photochemistry of planetary atmospheres and
the interstellar medium.5
Photofragment studies of HCl have revealed a large variety of photodissociation and photoionization processes. In
a detailed two-photon resonance enhanced multiphoton ionization study, Green et al. report HCl+ , Cl+ , and H+ ion formations for excitations via large number of � = 0 Rydberg
states as well as via the V1 � + (� = 0) ion-pair state, whereas
excitations via other Rydberg states are mostly found to yield
HCl+ ions.7 More detailed investigations of excitations via
various Rydberg states and the V1 � + ion-pair state by use of
photofragment imaging and/or mass-resolved REMPI techniques have revealed several ionization channels depending
on the nature of the resonance excited state.23–30 The number of REMPI studies performed by our group for resonance
excitations to the F1 �2 Rydberg state16, 27 and several triplet
Rydberg states16, 27 as well as the V1 � + ion-pair states have
revealed near-resonance interactions between the Rydberg
and the ion-pair states. This shows as relative ion signal alterations in all cases27, 28, 30 and/or as line shifts in all cases
except for the weakest interactions.16, 20, 29 Data analysis has
allowed determination of interaction strength. The resonance
interpretation has been confirmed by proton formation studies for REMPI via the F1 �2 (v� = 1, J� = 8) and f3 �2 (v�
= 0, J� = 2–6) Rydberg states using three-dimensional velocity mapping.29 All in all REMPI photofragmentation studies of HCl have revealed characteristic ionization channels
which have been summarized in terms of excitations via (1)
134, 164302-1
© 2011 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
164302-2
Matthíasson et al.
excitations via resonance noncoupled (diabatic) Rydberg state
excitations, (2) excitations via resonance noncoupled (diabatic) ion-pair excitations, and (3) dissociation channels involving dissociation and/or photodissociation of resonance
excited Rydberg states.28
In this paper, we use a two-dimensional (2D) REMPI
data, obtained by recording ion mass spectra as a function of
laser frequency, to study the state interactions and photofragmentation dynamics of HCl following two-photon resonance
excitations to the triplet Rydberg states j3 � (0+ ) (ν � = 0),
j3 � − 1 (ν � = 0), the V1 � + (ν � = 20, 21) ion-pair states as well
as to Rydberg states, named A and B here, which band origins are at ν 0 = 88948.4 cm−1 ν 0 = 88959.9 cm−1 , respectively, according to Green et al.9 Rotational line shifts and
quantum level dependent ion signal intensities, due to perturbation effects, are observed for the H35 Cl and/or H37 Cl isotopomers. By a combined analysis of the line shifts and signal
intensities, interaction strengths, fractional state mixings, and
parameters relevant to dissociation and ionization processes
were evaluated. The perturbation observations as well as comparison of (2 + n) and (3 + n) REMPI data proved to be very
helpful for assigning spectra bands. Lines due to transitions to
the j3 � (0+ ) (ν � = 0) and the A states were reassigned. The ν 0
= 88948.4 cm−1 band, previously assigned to an � = 0 state
was reassigned to an � = 2 state.
J. Chem. Phys. 134, 164302 (2011)
mass spectra. Mass spectra were typically recorded in 0.05 or
0.1 cm−1 laser wavenumber steps to obtain 2D REMPI spectra. REMPI spectra for certain ions as a function of excitation
wavenumber (1D REMPI) were obtained by integrating mass
signal intensities for the particular ion. Care was taken to
prevent saturation effects as well as power broadening by
minimizing laser power. Laser calibration was performed by
recording an optogalvanic spectrum, obtained from a built-in
Neon cell, simultaneously with the recording of the REMPI
spectra. Line positions were also compared with the strongest
hydrogen chloride rotational lines reported by Green et al.9
The accuracy of the calibration was found to be about
±1.0 cm−1 on a two-photon wavenumber scale. Intensity
drifts during the scan were taken into account, and spectral intensities were corrected accordingly. Experimental conditions
for the three-photon excitation are described in Ref. 20.
III. RESULTS AND ANALYSIS
A. REMPI spectra and relative ion signals for the
j 3 − 1 ←← X 1 + (0, 0) transitions
Figure 1 shows 2D-REMPI contour (below) and corresponding 1D-REMPI spectra (above) for the narrow spectral region of 88990–89080 cm−1 . The figure shows Q lines
II. EXPERIMENTAL
Two-dimensional REMPI data for jet cooled HCl gas
were recorded. Ions were directed into a time-of-flight tube
and detected by a microchannel plate (MCP) detector to
record the ion yield as a function of mass and laser radiation
wavenumber. The apparatus used is similar to that described
elsewhere.19, 30, 31 Tunable excitation radiation in the 224.0
–225.0 nm wavelength region was generated by an Excimer
laser-pumped dye laser system, using a Lambda Physik
COMPex 205 Excimer laser and a Coherent ScanMatePro
dye laser. The dye C-440 was used and frequency doubling
obtained with a BBO-2 crystal. The repetition rate was
typically 10 Hz. The bandwidth of the dye laser beam was
about 0.095 cm−1 . Typical laser intensity used was 0.1
–0.3 mJ/pulse. The radiation was focused into an ionization
chamber between a repeller and an extractor plate. We
operated the jet in conditions that limited cooling in order
not to lose transitions from high rotational levels. Thus,
an undiluted, pure HCl gas sample (Merck-Schuchardt
OHG; purity >99.5%) was used. It was pumped through a
500 μm pulsed nozzle from a typical total backing pressure of about 2.0–2.5 bar into the ionization chamber.
The pressure in the ionization chamber was lower than
10−6 mbar during experiments. The nozzle was kept open
for about 200 μs and the laser beam was typically fired
500 μs after opening the nozzle. Ions were extracted into
a time-of-flight tube and focused onto a MCP detector, of
which the signal was fed into a LeCroy 9310 A, 400 MHz
storage oscilloscope and/or a LeCroy WaveSurfer 44MXs-A,
400 MHz storage oscilloscope as a function of flight time.
Average signal levels were evaluated and recorded for a fixed
number of laser pulses (typically 100 pulses) to obtain the
FIG. 1. 2D-(2 + n) REMPI spectra (below) and corresponding 1D REMPI
spectra (above) for H+ , 35 Cl+ , H35 Cl+ , 37 Cl+ , and H37 Cl+ derived from
HCl with isotope ratios in natural abundance for the two-photon excitation region of 88990– 89080 cm−1 . Assignments for the Q line series of
the j3 � 1 ←← X1 � + (0, 0) (H35 Cl and H37 Cl: solid lines) and V1 � +
←← X 1 � + (20, 0) (H35 Cl: solid lines; H37 Cl: broken lines) spectra are
shown. J = J� —numbers are indicated in the figure.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
164302-3
J. Chem. Phys. 134, 164302 (2011)
2D-REMPI of HCl
rotational energy levels for the ground electronic state [see
Fig. 2(a)]. This is a characteristic for a near-resonance levelto-level rotational interaction between the Rydberg state (1)
and the V(1 � + ) ion-pair state (2).16, 20 The smallest spacing between rotational energy levels of the two states for the
same J� quantum numbers (�EJ � = E1 (J� )–E2 (J� )) is found to
be for J� = 2 and 3 for the V(v� = 20) state (see Table I).
First order unshifted energy levels, both for the j3 � − 1 (1)
and the V(1 S+ ) (2) states, E1 0 (J� ) and E2 0 (J� ), respectively,
were derived from the linear fits for �E J� , J� −1 versus J� [see
Fig. 2(a)] and the energy level values for unshifted levels.
From these and energies of perturbed levels (E(J� )) interaction strengths (W12 ) could be derived as a function of J� from
1
1 0 �
2
E 1 (J ) + E 20 (J � )
W12 (J � ) =
4
2
1/2
2
2
− E 1 (J � )
− E 10 (J � ) − E 20 (J � )
. (1)
The interaction strength parameter, W� 12 was derived
from the expression W12 (J� ) = W� 12 (J� (J� +1))1/2 which holds
for a heterogeneous interaction (�� �= 0) (see Table II).
The fractional contributions to the state mixing [c12 for the
Rydberg state (1) and c22 for the ion-pair state (2)] are now
easily derived from W12 and the energy difference �EJ �
= E1 (J� ) –E2 (J� ) as
(�E J � )2 − 4 (W12 )2
1
(2)
c12 = +
; c22 = 1 − c12 .
2
2 |�E J � |
FIG. 2. H35 Cl: Spacings between rotational levels (�EJ � , J� −1 ) as a function
of J� for the j3 � − (1) (a) and j3 � − (0+ ) (b) Rydberg states for H35 Cl derived
from Q rotational lines.
due to the transitions j3 � − 1 ←← X1 � + (0, 0) and V1 � +
←← X1 � + (20, 0), for the H35 Cl and H37 Cl isotopomers and
their ion fragments.
Small but significant shift of peaks due to transitions
to J� = 2 and 3 levels is observed. This shows as deviation in energy level spacings (�EJ � , J� −1 = E(J� )−E(J� −1))
from linearity for the corresponding rotational energy levels (E(J� )) derived from measured peak positions and known
Significant enhancement of the relative Cl+ signals
(I(35 Cl+ )/I(H35 Cl+ )) and I(37 Cl+ )/I(H37 Cl+ )) is observed
for j3 � − 1 ←← X1 � + , (0, 0), Q lines, J� = 2 [see
Figs. 3(a) and 3(b)] also characteristic for the near-resonance
interaction.16, 20, 27 The H37 Cl isotopomer shows considerably
larger intensity ratio than the H35 Cl isotopomer. An expression for I(Cl+ )/I(HCl+ ) as a function of the mixing fraction,
c22 , based on ionization processes following resonance excitation, has been derived,28
α γ + c22 (1 − γ )
I (Cl+ )
+ =
I (HCl )
1 − c22
,
(3)
I (Cl+ ) = α2 c22 + β1 c12 ;
I (HCl+ ) = α1 c12 + β2 c22
TABLE I. �EJ � relevant to near-resonance interactions for j3 � − 1 ↔ V1 � + ,ν � = 20, j3 � − (0+ ) ↔ V1 � + ,ν � = 20, 21, State A ↔ V1 � + ,ν � = 20, and State
B ↔ V1 � + ,ν � = 20.
�Ej� = E(j3 � − 1 ; ν � = 0)
–E(V1 � + ; ν � = 20)
J�
0
1
2
3
4
5
6
H35 Cl
− 62.2
− 20.6
40.2
108.2
187.3
279.0
�Ej� = E(j3 � −. (0+ ); ν � = 0)
–E(V1 � + ; ν � = 20/21)
�Ej� = E(State A)
–E(V1 � + ; ν � = 20)
�Ej� = E(State B)
–E(V1 � + ; ν � = 20)
H37 Cl
H35 Cl (ν � = 20/21)
H37 Cl (ν � = 20/21)
H35 Cl
H35 Cl
− 55.7
− 14.7
47.9
115.1
192.1
196.4/−304.3
208.9/−311.6
232.4/−284.2
271.6/−245.1
322.5/−193.8
384.2/−129.6
457.4/–71
214.8/–316.1
215,4/–305.7
238.2/–280.6
278.9/–241.7
328.9/–190.4
394.0/–130.7
462.6/–65
− 96.6
− 62.0
− 22.0
26.0
88.0
− 92.7
− 59.3
− 13.8
45.4
117.2
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164302-4
J. Chem. Phys. 134, 164302 (2011)
Matthíasson et al.
TABLE II. Parameter values, relevant to state mixing, derived from peak shifts and intensity ratios
(I (i Cl+ )/I (Hi Cl+ )) as a function of J� . See definitions of parameters in the text.
j3 � − 1 ; ν � = 0
Isotopomers
J�
closest resonances
|�E(J� res )|(cm−1 )
W12 (cm−1 )
� (cm−1 )
W12
c12 (c22 )
γ
α
(J�
res )
j3 � − (0+ ); ν � = 0
State B
H35 Cl
H37 Cl
H35 Cl
H37 Cl
H35 Cl
2
20.6
6.5
2.7
0.89(0.11)
0.004
3.5
2
14.7
5.8
2.4
0.81(0.19)
0.003
4.2
7(6)
? (71)a,b
25
...
0.88(0.12)
(0.031)c
(2.1)c
6(7)
65(?)a,b
25
...
0.82(0.18)
0.013
4.0
4
13.8
2.7
0.6
0.96(0.04)
0.002
3.1
a
Values for J� = 7 could not be determined since rotational peaks due to transitions to V(v� = 21, J� = 7) were not observed.
b
Values for J� = 6 were derived from observations of weak and broad rotational lines in the Q series due to transitions to
V(v� = 21, J� = 6) at 89317.4 cm−1 and 89311.1 cm−1 for H35 Cl and H37 Cl, respectively.
c
Parameters are uncertain due to overlap of spectra peaks for transitions to J� = 6 and 8. The γ value is an upper limit value.
The α value is a lower limit value.
where α( = α 2 /α 1 ) measures the relative rate of the two
major/characteristic ionization channels, i.e., for the Cl+
formation for excitation from the diabatic ion-pair state (α 2 )
to the HCl+ formation from the diabatic Rydberg state (α 1 ).
Here, γ (=β 1 /α 2 ) represents the rate of Cl+ formation via the
diabatic Rydberg state (β 1 ; referred to as the “dissociative
channel” in Ref. 28) to that of its formation from the diabatic
ion-pair state (α 2 ), which is one of the major/characteristic
ionization channels. Hence, γ is a relative measure of the importance of the “dissociative channel.” Expression (3) allows
the relative ion signals as a function of J� to be fitted to derive
α and γ [Figs. 3(a) and 3(b) and Table II]. The larger Cl+
FIG. 3. Relative ion signal intensities, I(i Cl+ )/I(Hi Cl+ ) (i = 35 and 37) vs J� derived from Q rotational lines of REMPI spectra due to resonance transitions
to Rydberg states (gray columns) and simulations, assuming J� level-to-level interactions between the Rydberg states and the V1 � + (v� = 20, 21) states (white
and black columns): (a) H35 Cl, j3 � − 1 ↔ V1 � + (v� = 20) interactions, (b) H37 Cl, j3 � − 1 ↔ V1 � + (v� = 20) interactions, (c) H35 Cl, j3 � − (0+ ) ↔ V1 � + [v�
= 20 (white columns) and v� = 21 (black columns)] interactions, and (d) H37 Cl, j3 � − (0+ ) ↔ V1 � + [v� = 20 (white columns) and v� = 21 (black columns)]
interactions.
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164302-5
2D-REMPI of HCl
J. Chem. Phys. 134, 164302 (2011)
FIG. 4. (a) and (b) 2D-(2 + n) REMPI spectra (below) and corresponding 1D REMPI spectra (above) for H+ , 35 Cl+ , H35 Cl+ , 37 Cl+ , and H37 Cl+ derived
from HCl with isotope ratios in natural abundance for the two-photon excitation regions of 89264–89285 cm−1 (a) and 89235–89265 cm−1 (b). Assignments
for the Q line series of the j3 � − (0+ ) ←← X1 � + (0, 0) (H35 Cl and H37 Cl) spectra are shown. The intensities of the 1D REMPI spectra in the 89235
–89265 cm−1 spectral region (b) have been multiplied by factor 4 with respect to the corresponding intensities in 89264–89285 cm−1 spectral region (a).
(c) 1D-(3 + n) REMPI spectrum for total ionization of HCl for the three-photon excitation region of 89295–89430 cm−1 . Assignments for the j3 � − (0+ )
←← X1 � + (0, 0) and l3 �3 ←← X1 � + (0, 0) transitions (H35 Cl and H37 Cl) are shown. J = J� —numbers are indicated in the figures.
fragmentation observed for H37 Cl compared to that for H35 Cl
can be understood by comparison of the derived parameters
listed in Table II. Whereas the interaction strengths are comparable, for the two isotopomers the ion-pair mixing fraction
(c22 ) is significantly larger for H37 Cl (c22 = 0.19) than for H35 Cl
(c22 = 0.11). This is primarily due to the smaller energy gap
(�EJ � = 14.7 cm−1 ) between the mixing rotational states for
H37 Cl compared to that for H35 Cl (�EJ � = 20.6 cm−1 ). The
gamma values (γ ) obtained, both for the H35 Cl (γ = 0.004)
and the H37 Cl (γ = 0.003) isotopomers are small values and
comparable to those obtained before for the triplet states f3 �1
and g3 � +28, 30 indicating a small, but non-negligible contribution of the dissociation channels to the Cl+ signal. Judging
from a coupling scheme given by Alexander et al.32 this could
be formed after a direct predissociation of the j3 � − 1 state by
spin–orbit coupling with the repulsive t3 � + 1 state and/or after predissociation of nearby Rydberg states (1 �, 3 �2 ) which
could act as gateways via S/O coupling with the j3 � − 1 states.
B. REMPI spectra and relative ion signals for the
j 3 − (0+ ) ←← X 1 + (0, 0) transitions
Figures 4(a) and 4(b) show 2D and 1D (2 + n)
REMPI spectra for the narrow excitation region of 89235–
89285 cm−1 . The figures show the Q lines due to the j3 � − (0+ )
←← X1 � + (0, 0) resonance transitions for H35 Cl and H37 Cl.
Total 1D (3 + n) REMPI spectrum is shown in Fig. 4(c) for
the spectral region 89300–89430 cm−1 . It shows R lines for
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164302-6
J. Chem. Phys. 134, 164302 (2011)
Matthíasson et al.
TABLE III. Rotational lines for the j3 � − (0+ ) ←← X1 � + (0, 0) transitions (HCl). The line positions are common to H35 Cl and H37 Cl except for
the Q lines, J� = 6 and 7, in which case the values for H37 Cl are inside
brackets.
j3 � − (0+ ) ←← X1 � + (0, 0)
J�
O
Q
0
1
2
3
4
5
6
89219.6
89176.2
89131.4
89282.0
89280.5
89277.3
89272.1
89266.8
89259.0
89246.3
(89244.7)
89261.1
(89259.9)
89246.3
89237.1
7
8
9
S
89340.1
89377.3
89412.8
89446.7
89475.9
the same electronic transitions as well as peaks due to transitions to the l3 �3 state.20 Clear gap between the J� = 6 and
J� = 7 rotational lines is observed for the R lines. This gap
corresponds to the smallest spacing between observed rotational energy levels for the j3 � − (0+ ) (ν � = 0) and rotational
energy levels for the V1 � + (ν � = 21) states for equal J� values (see Table I) suggesting a near-resonance interaction between the two states.16, 20, 27 Comparison of peak positions in
(3 + n) and (2 + n) REMPI spectra and relative intensities of
ion peaks, allowed assignment of the Q line rotational peaks
both for H35 Cl and H37 Cl in the (2 + n) REMPI spectrum. Irregular arrangement of peaks, with respect to J� numbering, is
seen for J� = 5–9 [see Fig. 4(b)] and enhanced intensity ratios
(I(i Cl+ )/I(Hi Cl+ )) are observed for transitions to J� = 6 and
7 [Figs. 3(c) and 3(d)]. See also Table III. Peak assignments
differ from earlier assignments.9, 20
Analogous and relatively large deviation in energy level
spacings (�EJ � , J� −1 ) from linearity is clearly seen both for
H35 Cl and H37 Cl [see Fig. 2(b)]. This allowed the interaction
strengths (W12 ) to be evaluated for J� = 5–8 analogous to that
described before. A relatively large interaction strength value
of about 25 ± 3 cm−1 was obtained both for H35 Cl and H37 Cl
independent of J� as to be expected for homogeneous interactions (Table II). Despite difference in line assignments this
value is comparable to that reported earlier in Ref. 20 (W12
= 20 ± 4 cm−1 ). The large homogeneous interaction strength
results in off-resonance interactions between J� states showing as significant mixing contribution for the ion-pair state
(c22 ) over a wide range of J� states, both for V(v� = 20) and
V(v� = 21). This results in significant contributions to the ion
ratios from off-resonance interactions according to Eq. (3).
Mixing contributions from vibrational states further away in
energy (v� < 20 and v� > 21), on the other hand, are negligible,
assuming the interaction strength (W12 ) to be comparable.
Assuming, to a first approximation, that the ion intensity
ratio is a sum of contributions due to interactions from the V(v�
= 20) and V(v� = 21) states for common α and γ parameters
I(37 Cl+ )/I(H37 Cl+ ) can be expressed as
I (Cl+ )
=α
I (HCl+ )
2
2
γ + c2,20
γ + c2,21
(1 − γ )
(1 − γ )
+
,
2
2
1 − c2,20
1 − c2,21
(4)
2
2
and c2,21
are the fractional mixing contributions
where c2,20
for V(v� = 20) and V(v� = 21), respectively. Figure 3(d) shows
least square fit of the data for I(37 Cl+ )/I(H37 Cl+ ) versus J� as
well as the V(v� = 20) and V(v� = 21) contributions for the α
and γ parameters listed in Table II. The calculations are limited to J� < 7 since rotational lines for higher J� , hence energy
levels, for V(v� = 21) could not be observed. Due to uncertainty in the ion-ratio value for J� = 6 because of overlap of
Q line peaks for J� = 6 and 8 analogous least square analyses
could not be performed for H35 Cl [Fig. 3(c)]. The characteristic large and J� -independent ion intensity ratios for J� < 5,
observed both for H35 Cl and H37 Cl result in a relatively large
γ factor, an order of magnitude bigger than those determined
for other triplet states, �� > 0 mentioned before. This suggests
that the “dissociation channels” are of greater importance. As
mentioned before the small contributions to the dissociation
channels for the other triplet states has been interpreted as being due to predissociation via gateway states.28 Based on the
coupling schemes given by Alexander et al.32 such channels
for the j3 � − states are limited. The “enhanced” importance
of “dissociation channels” therefore could be due to an opening of a dissociation channel via photoexcitation to an inner
wall of a bound excited Rydberg state above the dissociation
limit.28
C. REMPI spectra and relative ion signals for the
A ←← X 1 + (0, 0) and B ←← X 1 + (0, 0) transitions
Figure 5 shows 1D-REMPI spectra for the narrow spectral region of 88865–88985 cm−1 . The
figure shows the Q lines due to the transitions A
←← X 1 � + (0, 0) and B ←← X 1 � + (0, 0) both for
the H35 Cl+ and H37 Cl+ ions and corresponding ion fragments. Also it shows rotational lines due to the transitions
j3 � − 1 ←← X1 � + (0, 0), � ≤ 2 ←← X1 � + (0, 0), and
V1 � + ←←X1 � + (20, 0).
Slight but significant enhancement in spacing between
rotational levels J� = 5 and 4 is observed for the B state and
clear increase in the relative 35 Cl+ signal intensity is detected
for the B ←← X 1 � + (0, 0), J� = 4 transition (see Fig. 6). This
corresponds to the smallest spacing between observed rotational energy levels of the B and the V1 � + (ν � = 20) states for
equal J� values for J� = 4 (see Table I) due to a near-resonance
interaction between the two states.16, 20, 27 Analysis of the line
shifts allowed evaluation of W12 = 2.7 cm−1 (W� 12 = 0.6
cm−1 ) for J� = 4 for H35 Cl. Good consistency in calculated
and experimental values for the ion ratios I(35 Cl+ )/I(H35 Cl+ )
was obtained for γ = 0.002 and α = 3.1 (Fig. 6 and Table II).
The B state has been assigned as an � = 2 state.9 The low
γ value of 0.002 resembles those observed earlier for triplet
states (see above and Ref. 28) which indicates that the B state
is a 3 �2 state.
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164302-7
J. Chem. Phys. 134, 164302 (2011)
2D-REMPI of HCl
3 −
State A , Q
6 [4]
5 [3]
j Σ (1), v'=0 ,
4 [2]
3 [1]
2 [0]
3
State B , Q
6
7
8
5
2
Q
P
1
Ω≤2,Q
4
2 6
3
5
1 42
37
H Cl
1 +
V Σ , v'=20 , Q
5
5
37
4
Cl
+
+
4
35
H Cl
35
Cl
+
+
+
H
88880
88900
88920
[cm-1 ]
88940
88960
88980
FIG. 5. 1D-(2 + n) REMPI spectra for H+ , 35 Cl+ , H35 Cl+ , 37 Cl+ , and H37 Cl+ derived from HCl with isotope ratios in natural abundance for the two-photon
excitation region of 88865–88985 cm−1 . Assignments for A ←← X 1 � + (0, 0), B ←← X 1 � + (0, 0), j3 � − 1 ←← X1 � + (0, 0), and �� ≤ 2 ←← X1 � +
(0, 0) spectra (H35 Cl and H37 Cl) are shown. Assignments for V1 � + ←← X1 � + (20, 0) are shown for H35 Cl as solid lines and for H37 Cl as broken lines.
Assignments from Ref. 9 for A ←← X 1 � + (0, 0) are in brackets. J = J� —numbers are indicated in the figure.
The spectral peaks due to the A ←← X 1 � + (0, 0) transition are marked according to the assignment given by Green
et al.9 with numbers inside brackets in Fig. 5. These have been
reassigned based on our analysis of the 2D REMPI data, as
shown in the figure, for reasons which will now be discussed.
Both the A and the B spectra show characteristic drops
in peak intensities for the parent ions (H35 Cl+ and H37 Cl+ )
�
as J increases. The intensities for the B-spectra, reach minima for the resonance perturbed levels J� = 4. As a matter of
fact that peak is hardly observable for H37 Cl+ . Similarly, the
A-spectra show either no peaks or very weak peaks9 corresponding to the J� = 2 assignment given by Green et al. both
for H35 Cl and H37 Cl. This is characteristic for near-resonance
interactions with the ion-pair state V(1 � + )20 , which in this
case must be for v� = 20. Both for the B and the A states the
closes rotational levels, in energy, which belong to the V(v�
= 20) state are those for J� = 4 (see Fig. 5). The spacing,
�EJ� = 4 , for the A state (H35 Cl) is about 22.0 cm−1 (see Table I for the B state). It can, therefore, be concluded that the
peaks assigned as J� = 2 for the A spectrum are in fact due
to transitions to J� = 4 levels. This puts the first peaks in
the line series as J� = 2, suggesting that the A state is an �
= 2 state. Other peaks in the A spectrum are reassigned accordingly in Fig. 5. Furthermore, there are no significant Cl+
masses detected for any of the rotational transitions in the A
←← X 1 � + (0, 0) system which would be expected if the A
state was an � = 0 state.27 Whereas the previous assignment
gives a low rotational constant , B� , of 5.7941 cm−1 for the A
state, which certainly might be expected if it was an �� = 0
state,15, 16 our reassignment gives B� = 9.08 cm−1 , which is
typical for a Rydberg state with weak or negligible Rydbergvalence state mixing. Further analysis of the A state spectrum,
based on the new assignment gives D� = 0.0185 cm−1 and ν 0
= 88957.6 cm−1 . For comparison, B� = 8.954 cm−1 and D�
= −0.0042539 cm−1 for the B state, which has been assigned
as an �� = 2 state.9
IV. CONCLUSIONS
FIG. 6. Relative ion signal intensities, I(35 Cl+ )/I(H35 Cl+ ) vs J� derived from
Q rotational lines of REMPI spectra due to resonance transitions to the �� = 2
(88959.9 cm−1 ) (B) state (gray columns) and simulations, assuming J� levelto-level interactions between the Rydberg state and the V1 � + (v� = 20) state
(white columns).
Two-dimensional (2 + n) REMPI data for HCl, obtained
by recording ion mass spectra as a function of the laser frequency, were recorded for the two-photon resonance excitation region 88865– 89285 cm−1 . Spectra for H35 Cl and H37 Cl,
due to resonance transitions to the ion-pair states V1 � + (ν �
= 20, 21) and four Rydberg states, j3 � − (0+ )(ν � = 0),
j3 � − 1 (ν � = 0) and states centered at = 88957.6 cm−1 (A)
and 88959.9 cm−1 (B) for H35 Cl were studied. A combined
analysis of rotational line shifts and ion signal intensities
was performed, developed, and used to derive information
relevant to state interactions strengths, photofragmentation
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164302-8
channels, rotational energy characterization, and/or state assignments.
Interaction strengths, W12 , and fractional state
mixing (c12 /c22 ) due to Rydberg to ion-pair (V1 � + (v�
= 20, 21)) state interactions were evaluated for the
Rydberg states j3 � − (0+ )(ν � = 0), j3 � − 1 (ν � = 0) for
Hi Cl; i = 35, 37 and for the B state (H35 Cl) from rotational line shift analysis. Enhancements in relative
Cl+ ion intensities, I(i Cl+ )/I(Hi Cl+ ), are observed in
all cases for J� levels corresponding to near-resonance
interactions. Data for intensity ratios as a function of J�
were compared to model expressions which take account of
the major ion formation channels following excitations to the
Rydberg states, state interactions as well as dissociation channels. The observations for the j3 � − 1 (ν �
= 0) and the B states could be interpreted as being due
to level-to-level interactions between the Rydberg states and
the V(v� = 20) states, whereas interactions both with V(v� = 20
and 21) needed to be taken account of to explain the observation for the j3 � − (0+ )(ν � = 0) states. Fit analysis gave parameters which measure the importance of dissociation (predissociation and/or photodissociation) channels in the ionization
processes. The weight of dissociation channels are found to
be significantly larger for the �� = 0 states (j3 � − (0+ )) than
for the �� = 1, 2 states which have been studied.
Relative ion signals as a function of J� proved to be useful guide to assigning rotational peak spectra and allowed
reassignments of the spectra due to the transitions to the
j3 � − (0+ )(ν � = 0) and the A (ν 0 = 88957.6 cm−1 ) state. The
A state was characterized as an �� = 2 state with rotational
parameters B� = 9.08 cm−1 and D� = 0.0185 cm−1 .
ACKNOWLEDGMENTS
The financial support of the University Research Fund,
University of Iceland, the Icelandic Science Foundation
as well as the Norwegian Research Council is gratefully
acknowledged.
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27 Á. Kvaran, K. Matthíasson, H. Wang, A. Bodi, and E. Jonsson, J. Chem.
Phys. 129(17), 164313 (2008).
28 A. Kvaran, K. Matthiasson, and H. Wang, J. Chem. Phys. 131(4), 044324
(2009).
29 S. Kauczok, C. Maul, A. I. Chichinin, and K.-H. Gericke, J. Chem. Phys.
133, 024301 (2010).
30 K. Matthiasson, H. Wang, and A. Kvaran, J. Mol. Spectros. 255(1), 1
(2009).
31 Á. Kvaran, K. Matthíasson, and H. Wang, Physical Chemistry; An Indian
Journal 1(1), 11 (2006).
32 M. H. Alexander, X. N. Li, R. Liyanage, and R. J. Gordon, Chem. Phys.
231(2–3), 331 (1998).
3 S.
4 D.
5 J.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
Paper II
Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras
Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation
Channels via Rydberg States. Journal of Physical Chemistry A, 114,
9991, 2010.
61
J. Phys. Chem. A 2010, 114, 9991–9998
9991
Two-Dimensional (2+n) REMPI of CH3Br: Photodissociation Channels via Rydberg States
Ágúst Kvaran,* Huasheng Wang, and Kristján Matthı́asson
Science Institute, UniVersity of Iceland, Dunhagi 3, 107 ReykjaVı́k, Iceland
Andras Bodi
Molecular Dynamics Group, Paul Scherrer Institut, 5232 Villigen, Switzerland
ReceiVed: May 6, 2010; ReVised Manuscript ReceiVed: August 3, 2010
(2+n) resonance enhanced multiphoton ionization (REMPI) spectra of CH3Br for the masses H+, CHm+,
i
Br+, HiBr+, and CHmiBr+ (m ) 0-3; i ) 79, 81) have been recorded in the 66 000-81 000 cm-1 resonance
energy range. Signals due to resonance transitions from the zero vibrational energy level of the ground state
CH3Br to a number of Rydberg states [Ωc]nl;ω (Ωc ) 3/2, 1/2; ω ) 0, 2; l ) 1(p), 2(d)) and various vibrational
states were identified. C(3P) and C*(1D) atom and HBr intermediate production, detected by (2+1) REMPI,
most probably is due to photodissociation of CH3Br via two-photon excitations to Rydberg states followed
by an unusual breaking of four bonds and formation of two bonds to give the fragments H2 + C/C* + HBr
prior to ionization. This observation is supported by REMPI observations as well as potential energy surface
(PES) ab initio calculations. Bromine atom production by photodissociation channels via two-photon excitation
to Rydberg states is identified by detecting bromine atom (2+1) REMPI.
Introduction
Spectroscopy1–6 and photofragmentation7–13 of methyl bromide has received considerable interest over the last decades,
both experimentally1–12 and theoretically,13 for a number of
reasons. Methyl bromide as well as the chlorine and iodine
containing methyl halides play important roles both in the
chemistry of the atmosphere6,14–16 and in industry. Thus, although
far less abundant than methyl chloride in the stratosphere, methyl
bromide is found to be much more efficient in ozone depletion16
and is now being phased out under the Montreal Protocol.
Furthermore, bromocarbons are known to have a high global
warming potential.17 Additionally, the molecule is a simple
prototype system of a halogen containing organic molecule for
fundamental studies of photodissociation and photoionization
processes.10,13,18
Little is known about the UV spectroscopy of methyl bromide
despite its importance in various contexts. Since a pioneering
work by Price1 in 1936 some absorption studies have appeared
dealing with (i) a weak continuous spectrum (the A band) in
j < 55 500 cm-1)2,6,14,15
the low energy region (λ > 180 nm; E
due to transitions to repulsive states13 and (ii) higher energy (λ
-1
j > 55 500 cm ) Rydberg series and its vibrational
< 180 nm; E
analysis.2–5 There has been some controversy in the literature
concerning the assignment of the higher energy band spectra.
Locht et al. recently reported analysis and assignments of
spectra4,5 that differ from earlier reports.1–3 More recently,
however, multiphoton absorption (REMPI) studies18 and ab
initio calculations of excited states19 have been published that
help clarify the discrepancy.
Photofragmentation studies of methyl bromide can be classified into two groups. One group focuses on the characterization
of photofragments CH3 + Br(2P3/2)/Br*(2P1/2) resulting from
photodissociation in the A band7–10,13 whereas the other group
* Author for correspondence. Phone: +354-525-4694 (A.K.’s office),
+354-525-4800 (main office). Fax: +354-552-8911 (main office). E-mail:
[email protected]. Homepage: http://www.hi.is/∼agust/.
concerns the CH3+ + Br- ion-pair formation11,12,18 in the energy
region between the ion-pair formation threshold (76 695 cm-1)
and the ionization energy (85 031.2 cm-1 for CH3Br+(2Π3/2);
87 615.2 cm-1 for CH3Br+(2Π1/2)).18 To our knowledge no other
photofragmentation channels have been reported so far. Some
disagreement concerning the ion-pair formation is to be found
in the literature. Thus Xu et al.12 and Shaw et al.11 conclude
that direct excitation to the ion-pair state is the major step prior
to ion-pair formation whereas more recently Ridley et al.18 give
evidence for Rydberg doorway states in the photoion pair
formation analogous to observations for some halogen containing diatomic molecules.20–24
The basic picture for the electron configuration of the methyl
halides is analogous to that for the hydrogen halides, such that,
in the first approximation, the symmetry notation C3V, which
holds for the methyl halides, can be replaced by C∞V.19 Excited
state potentials for the methyl halides (CH3X; X ) Cl, Br, I) as
a function of the C-X bond closely resemble those for the HX
molecules showing (i) a number of repulsive valence state
potentials that correlate with the CH3 + Br(2P3/2)/Br*(2P1/2)
species, (ii) a series of Rydberg state potentials that closely
resemble the neutral and first ionic ground state potentials, and
(iii) an ion-pair 1A1(C3V) (1Σ(C∞V)) state with large average
internuclear distance. Characteristic state interactions between
Rydberg and the ion-pair states are found to affect the
spectroscopy and excited state dynamics for the hydrogen
halides.25–34 It has been pointed out that analogous effects are
to be found for methyl bromide.18,19
In this paper we report a two-dimensional (2+n) REMPI
experiment analogous to those presented before for acetylene35
and HCl,25,34,36 which helps elucidate the discrepancy concerning
the VUV spectroscopy of methyl bromide, and which also yields
evidence for new photodissociation channels via Rydberg states.
First, it allows us to assign several new vibronic bands and to
confirm the assignment by Causley and Russel based on single
photon absorption data.2 Second, C atom and HBr molecule
REMPI signals in the 2D REMPI data show that CH3Br Rydberg
10.1021/jp104128j  2010 American Chemical Society
Published on Web 08/20/2010
9992 J. Phys. Chem. A, Vol. 114, No. 37, 2010
states may photodissociate to form H2 + C(3P)/C*(1D) + HBr.
Third, strong bromine atom REMPI signals following twophoton excitation to Rydberg states as well as power dependence
analysis of the signals is indicative of important predissociation
channels leading to Br(2P3/2) and Br*(2P1/2).
Experimental Section
The apparatus used has been described elsewhere, and only
a brief overview is given here.25,34–36 Mass spectra for masses
1 amu (H+) to 96 amu (CH381Br+) were recorded for the twophoton excitation region 66 000-81 500 cm-1 (one-photon
wavelength region 245-303 nm. Tunable excitation radiation
was generated by Excimer laser-pumped dye laser systems,
using a Lambda Physik COMPex 205 Excimer laser and a
Coherent ScanMatePro dye laser at a typical repetition rate of
10 Hz. Dyes R610, R590, R540A, and C503 were used and
frequency doubling performed with KDP and BBO-2 crystals.
The bandwidth of the dye laser beam was about 0.095 cm-1.
The typical laser intensity used was 0.1-0.3 mJ/pulse. Undiluted, pure CH3Br gas sample (Merck Schuchardt; purity 99.5%)
was used. It was pumped through a 500 µm pulsed nozzle from
a typical total backing pressure of about 1.0-1.5 bar into an
ionization chamber. The pressure in the ionization chamber was
lower than 10-6 mbar during experiments. The nozzle was kept
open for about 200 µs, and the laser beam was typically fired
500 µs after the nozzle was opened. Ions were extracted into a
time-of-flight tube and directed on an MCP detector, whose
signal was fed into a LeCroy 9310A, 400 MHz storage
oscilloscope, to record the time-of-flight distributions. The
average signal levels were evaluated and recorded for a fixed
number of laser pulses (typically 100 pulses) to obtain the mass
spectra. Mass spectra were typically recorded in 0.1 or 0.2 cm-1
laser wavenumber steps to obtain 2D REMPI spectra. REMPI
spectra for certain ions as a function of excitation wavenumber
(1D REMPI) were obtained by integrating signal intensities for
the time-of-flight ranges corresponding to the particular ion
mass. The power dependence of the ion signal was determined
by averaging for ca. 1000 pulses, after bypassing a different
number of quartz windows to reduce power. Care was taken to
prevent saturation effects as well as power broadening by
minimizing laser power. Laser calibration was performed by
recording an optogalvanic spectrum, obtained from a built-in
neon cell, simultaneously with the recording of the REMPI
spectra. The accuracy of the calibration was found to be about
(2.0 cm-1 on a two-photon wavenumber scale. Intensities were
corrected for laser power and drifts during the scans. Overall
spectra are composed of several shorter scans, each of which
were normalized to the square of the laser intensity, which
corresponds to a power dependence of (2+1)REMPI under
steady-state conditions. These scans are then normalized to each
other using the intensities of bands that are common to
neighboring sections. However, some uncertainties in the relative
intensities of the bands remain.
Results and Analysis
Mass and REMPI Spectra. Figure 1a shows a typical mass
spectrum recorded at the 66 022 cm-1 two-photon laser excitation corresponding to the [3/2]5p;0 Rydberg state, zero vibrational energy band (Vi′ ) 0 for all vibrational modes i).18 Ions
observed are H+, CHm+ (m ) 0-3), iBr+ (i ) 79, 81), and
CHmiBr+ (m ) 0-3; i ) 79, 81). Except for C and Br atom
resonance wavelengths (see below) the strongest signal is
observed for CH3+. Mass signals for the CHm+ (m ) 0-3) ions
vary in intensity as CH3+ > CH2+ > CH+ > C+. Mass signals
Kvaran et al.
for iBr+, CHmiBr+, and H+ are very weak compared to those
for CH3+. Typically, CiBr+ (i ) 79 and 81) ion signals are found
to be the strongest among the CHmiBr+ ion signals. Relative
ion signals depend, however, to some extent, on the laser power.
One-dimensional (1D) REMPI spectra for individual ions are
derived by integrating mass signals as a function of two-photon
excitation wavenumber. Whereas relative intensities in different
ion 1D REMPI depend on the laser power, the structure of the
individual spectra is found to be largely independent of the ion.
This can be seen in Figure 1b for the 66 022 cm-1 system. Figure
1c shows the CH3+ 1D REMPI spectrum for the wavenumber
region 66 000-81 000 cm-1. It agrees well with the recently
published spectrum by Ridley et al.,18 showing characteristic
subspectra due to resonance transitions to Rydberg states, with
gradually rising background as the energy increases, most
probably due to an increasing contribution from transitions to
the ion-pair state.19
Bands due to transitions to the zero vibrational energy levels
of the [3/2]np;ω, [1/2]np;ω, [3/2]nd;ω, and [1/2]nd;ω Rydberg
states from the zero vibrational energy level of the ground state,
as assigned by Ridley et al.,18 are identified and marked in Figure
1c with solid line bars above the CH3+ 1D REMPI spectrum.
In addition,we have assigned bands due to transitions from the
ground electronic and vibrational state to vibrationally excited
levels of the [Ωc]nl;0 states. These are listed in Table 1 and
markedinFigure1cwithbrokenlinebarsforclear(Strong-Medium
intensity) bands. Less intense (Weak-Very Weak) bands, only
observable at enhanced laser power, are also listed in Table 1.
Some of these bands correspond to vibronic bands observed in
absorption spectra (albeit transition wavenumbers are offset by
about 20- 30 cm-1 (see Table 1)) assigned by Causley and
Russel.2 These assignments as well as those given by Ridley et
al.18 disagree with those given by Locht et al.5 Our assignment
of the vibrational bands was guided by the following.
(i) Generally the strongest spectral features previously
observed in absorption spectra2,4,5 match the strongest features
observed in our 1D (2+n) REMPI spectra. Since the potential
energy surfaces for the Rydberg states closely resemble those
for the ground states of CH3Br and CH3Br+,19 there is reason
to believe that the strongest spectral features are due to
transitions corresponding to unaltered vibrational energy, i.e.,
that ∆νi ) 0 transitions are the most Franck-Condon-factor
(FCF) favorable for all i. Furthermore, we expect transitions to
become less FCF favorable as vibrational quantum numbers for
the excited states deviate more from the original zero energy
level; i.e., the transition strength (intensities) will change as (Vi′
) 0) > (Vi′ ) 1) > (Vi′ ) 2), etc.
(ii) Frequencies of vibrational modes for Rydberg states are
expected to be close to those in the ground states CH3Br(X)
and CH3Br+(X).2,5 Hence, available experimental37 and calculated5,38 vibrational frequencies for CH3Br(X) and CH3Br+(X)
were useful in assigning vibrational bands. The Vi′ notation used
(Figure 1c, Table 1) assumes a1 symmetry (valid for the ground
state CH3Br X1A1) to be a good approximation for the Rydberg
states.2 Alternatively a′ symmetry notations (valid for the ground
state CH3Br+ X2A′) could be used, in which case V1(a1)
corresponds to V2(a′), V2(a1) to V4(a′), and V3(a1) to V6(a′).5 The
vibrational assignment is further detailed in Table 1.
(iii) We expect a close analogy in the spectroscopy of the
methyl halides (CH3X; X ) Cl, Br, I) and the corresponding
hydrogen halides (HX).18,19 Hence, the major Rydberg spectral
features will be due to transitions from the ground state to nle
Rydberg states (C3V notation; nlπ states in C∞V notation), i.e.,
due to transitions of electrons from lone pair e orbitals (C3V
2D-REMPI of CH3Br
J. Phys. Chem. A, Vol. 114, No. 37, 2010 9993
TABLE 1: Assignments and Transition Wavenumbers of
Bands Due to Transitions from Ground State CH3Br to
Vibrationally Excited Rydberg States
ν/cm-1
assignment
[Ωc]nl; ω, (V1, V2, V3)a
[3/2]np:
[3/2]5p;0,(0, 0,1)
[3/2]5p;0,(0, 1, 0)
[3/2]5p;0,(1, 0, 0)
[3/2]6p;0,(0, 0, 1)
[3/2]6p;0,(0, 1, 0)
[1/2]np:
[1/2]5p;0,(0, 0, 1)
[1/2]5p;0,(0, 1, 0)
[1/2]5p;0,(0, 2, 0)
[3/2]nd:
[3/2]4d;0,(0, 0, 1)
[3/2]4d;0,(0, 1, 0)
[3/2]4d;0,(1, 0, 0)
[3/2]5d;0,(0, 0, 1)
[1/2]nd:
[1/2]4d;0,(0, 0, 1)
[1/2]4d;0,(0, 1, 0)
[1/2]4d;0,(0, 2, 0)
this work
(intensity)c
ref 2
66 503 (M)
67 275 (M)
68 882 (M)
76 323 (W)
77 165 (M)
66 482
67 246
68 848
69 137 (W)
69 947 (M)
70 948 (VW)
69 105
69 932
73 507 (VW)
74 249 (M)
(75 905)b
78 890 (M)
(75 905)b
76 689 (M)
77 845 (M)
a
[Ωc]: total angular momentum quantum number for core ion. n:
principal quantum number for Rydberg electron. l: Rydberg electron
orbital (p, d). ω: total angular momentum quantum number for
Rydberg electron. (V1, V2, V3): vibrational quantum numbers referring
to vibrational modes. ν1 (symmetric stretch), ν2 (umbrella) and ν3
(C-Br stretch).5 b Spectral overlap c VW: very weak. W: weak. M:
medium.
Figure 1. (a) Mass spectra for the two-photon excitation wavenumber
66 022 cm-1 corresponding to transition to the [3/2]5p;0,(0,0,0) Rydberg
state (see Table 1); low resolution (below) and high resolution (above).
(b) M+ 1D REMPI spectra (M+ ) CHn+ (n ) 0-3), C79Cr+, 79Br+,
and H+) for two-photon transitions to the (3/2)5p;0,(0,0,0) Rydberg
state (see Table 1). (c) CH3+ 1D REMPI spectrum and assignment of
Rydberg states ([Ωc]nl; ω, (V1, V2, V3)) for the two-photon wavenumber
region 66 000-81 000 cm-1. Principal quantum numbers (n) of Rydberg
states are marked in bold. Total angular momentum quantum numbers
for Rydberg electrons (ω) are marked in italic. Vibrational quanta for
vibrational modes νi; i ) 1, 2, 3 (see text) of Rydberg states are marked
as V1, V2, and V3; unlabeled peaks correspond to transitions to the zero
vibrational energy levels, (V1, V2, V3) ) (0, 0, 0), whereas peaks labeled
Vi are due to transitions to vibrational states Vi ) 1 and Vj ) 0
(j * i).
notation; π orbital in C∞V notation) with dominant Br (for X )
Br) character to high energy lone pair orbitals (l). Rydberg
spectra due to transitions from bonding a1 orbitals (C3V notation;
σ orbital in C∞V notation) to high energy lone pair orbitals are
not expected to play a major role.18
C Atom REMPI; C/C* Formation Channels. The very
weak C+ REMPI signal, following excitations to Rydberg states
or the ion-pair state (see Figure 1a,b), largely shows the same
spectral structure as the much stronger CH3+ REMPI signals
(see Figures 1c and 2a) in the spectral region 66 000-80 600
cm-1 except for medium strong C atom REMPI lines, which
appear in the excitation region 69 500-77 500 cm-1 (see Figure
2a). The C+ 1D REMPI spectrum in the region 80 600-80 950
cm-1, on the other hand, is far stronger, showing overall intensity
comparable to the CH3+ REMPI. The structure, however, differs,
to some extent, from that of the CH3+ 1D REMPI spectrum, as
seen in Figure 2b. Observed C atom REMPI lines are listed in
Table 2 along with predicted wavenumbers derived from known
energy levels.37 Relative line intensities are indicated. Lines due
to resonance excitations of ground state C atoms (3PJ; J ) 0, 1,
2) and first excited state C*(1D2) atoms are observed. Only spin
conserved (∆S ) 0) transitions are detected. All the observed
C atom lines correspond to electron transfers of 2p electrons to
np (n > 2) orbitals, which satisfy ∆l ) 0, |∆L| e 2, and |∆J| e
2, as expected for two-photon resonance transitions.
Energetically, the C atom REMPI signal can be explained
by the formation of C and C* atoms by CH3Br** f H2 + C +
HBr (E0 ∼ 58 840 cm-1 from the ground state CH3Br)39,40 and/
or CH3Br** f H2 + C* + HBr (E0 ∼ 69 032 cm-1),39,40
followed by (2+1)REMPI of C/C* (see Figure 3a),
CH3Br + 2hν f CH3Br**(Ry,i-p)
(1a)
9994 J. Phys. Chem. A, Vol. 114, No. 37, 2010
Kvaran et al.
CH3Br**(Ry) f H2 + C/C* + HBr
(1b)
C/C* + 2hν f C**
(1c)
+
-
C** + hν f C + e
(1d)
Formation of 2H + C/C* + HBr, H2 + C/C* + H + Br, or 3H
+ Br + C/C* instead of (1b) is very unlikely on the basis of
the bond energies of H2 and HBr, 36 120 and 30 310 cm-1,
respectively.39 These would necessitate that (1a) is replaced by
a three- or four-photon processes, which puts the intermediate
already in the ionization continuum. It is unlikely that such a
highly energetic intermediate species does not autoionize and
that consecutive H, Br, H2, or HBr losses accompanied by
significant kinetic energy release leave it with enough internal
energy to form C atoms. An alternative H2 + C/C* + HBr
formation via initial excitation of dimers cannot be fully ruled
out. Since we operated the jet in conditions that limited cooling
(see Experimental Section) and no ion signals for dimers were
observed, we feel, however, that its involvement is not of major
importance. Even in the unlikely case that initial dimer excitation
contributes to the observed fragmentation channel, it is very
unlikely that this opens up new reaction channels, and the
nonfragmenting CH3Br could, thus, only act as a spectator,
possibly enhancing fragmentation, but not affecting the energetics of the process. The (1a)-(1d) mechanism gains further
support from (i) the observation of HBr REMPI signals, (ii)
the enhanced C+ REMPI signal above 80 600 cm-1, (iii) relative
intensities of C atom REMPI signals, (iv) power dependence
data, and (v) potential energy surface (PES) calculations. These
will now be discussed.
(i) The C atom REMPI lines at 75 204.6 cm-1 (C**(5p, 1D2)
rrC*(2p2, 1D2)) and 75 429.6 cm-1 (C**(5p, 1S0) rr C*(2p2,
1
D2)) follow excitations to the [1/2]4d;0,(0,0,0) Rydberg state
whereas the C atom REMPI lines at 77 023.3 cm-1 (C**(6p,
Figure 2. C+ REMPI. (a) C+ 1D REMPI spectra (bold) along with the CH3+ 1D REMPI spectrum (Figure 1c) (gray) for the two-photon wavenumber
region 69 500-77 500 cm-1. Insets show the spectral regions 69 640-69 740 and 71 300-71 400 cm-1. Peaks due to two-photon resonance transitions
from C(3PJ) (insets) and from C*(1D2) (top right) to C atom Rydberg states (C**) are labeled. See also Table 2. (b) C+ 1D REMPI spectra (bold;
above) along with the CH3+ 1D REMPI spectrum (Figure 1c) (gray; below) for the two-photon wavenumber region 80 500-81 000 cm-1. Assignment
of Rydberg states ([Ωc]nl;ω, (V1, V2, V3)) is shown (see caption for Figure 1c for further clarification). The energy threshold for two-photon ionization
of C*(1D2) (80 625.27 cm-1) is also shown.
J. Phys. Chem. A, Vol. 114, No. 37, 2010 9995
2D-REMPI of CH3Br
TABLE 2: Carbon Atomic Lines (cm-1) Due to (2+1) REMPI of C(2s22p2;3PJ) (a) and C*(2s22p2;1D2) (b), Following
Two-Photon Excitation of CH3Br vs Carbon Excited States (C**) (and Term Symbols) and Predicted Wavenumber Values
Derived from Energy Levels37 (Line Strengths Indicated)a
Table (a)
C(2s22p2; 3P0)
terms/2S′+1XJ′ (2s22p(2P)3p)
3
D1
D2
3
D3
3
P0
3
P1
3
P2
3
C(2s22p2; 3P1)
C(2s22p2; 3P2)
this work (intensitya)
NISTb
this work (intensitya)
NISTb
this work (intensitya)
NISTb
c
69 715.4 (W)
c
71 352.9 (W)
c
71 385.4 (VW)
69 689.48
69 710.66
69 744.03
71 352.51
71 364.90
71 385.38
69 675.3 (W)
69 697.7 (W)
69 733.1 (W)
c
71 348.9 (W)
71 369.1 (VW)
69 673.08
69 694.26
69 727.63
71 336.11
71 348.50
71 368.98
69 647.2 (W)
69 668.9 (M)
69 705.0 (M)
71 312.3 (VW)
71 324.3 (VW)
71 343.0 (W)
69 646.08
69 667.26
69 700.63
71 309.11
71 321.50
71 341.98
Table (b)
C(2s22p2; 1D2)
configuration; excited states
terms/2S′+1XJ′
2s22p(2P)4p
2s22p(2P)4p
2s22p(2P)5p
2s22p(2P)5p
2s22p(2P)6p
2s22p(2P)6p
a
1
D2
1
S0
1
D2
1
S0
1
D2
1
S0
this work (intensitya)
NISTb
71 577.0 (VW)
72 062.0 (VW)
75 204.6 (M)
75 429.6 (M)
77 023.3 (M)
77 150.8 (M)
71 577.16
72 059.08
75 207.18
75 432.55
77 025.63
77 148.41
M: medium. W: weak. VW: very weak. b Reference 37. c Not observed.
1
D2) rr C*(2p2, 1D2)) and 77 150.8 cm-1 (C**(6p, 1S0) rr
C*(2p2, 1D2)) follow transitions to the [3/2]6p;0,(0,1,0) state
(see Figures 1c and 2a and Tables 1 and 2b). Weak HBr REMPI
signals, due to the two-photon resonance transitions g3Σ- rr
X1Σ+(0,0) and F1∆2 rr X1Σ+(0,0),32 are also found to appear
near these atom resonances, following excitation to the same
Rydberg states as seen in Figure 4. Since these observations
are made under collision free conditions in a molecular beam,
formation of HBr (and H2) by secondary radical reactions can
be ruled out. Therefore, these spectra are due to (2+1)REMPI
of HBr(X1Σ+;V′′)0,J′′) most probably following steps (1a) and
(1b) for the corresponding CH3Br Rydberg states and C*(2p2,
1
D2) atom formation,
CH3Br + 2hν f CH3Br**(4d/6p,i-p)
(2a)
CH3Br**(4d/6p) f H2 + C*(2p2,1D2) + HBr(X)
(2b)
HBr(X) + 2hν f HBr**(g3Σ-,ν′ ) 0,J')/
HBr**(F1∆2,ν′ ) 0,J') (2c)
HBr** + hν f HBr+ + e-
(2d)
In addition to the rotational lines (J ) J′ ) J′′ ) 0 - 8; Q line)
observed by Gallagher and Gordon32 for the HBr, g3Σ- rr
X1Σ+(0,0) system, lines for J > 8 also are observed. This,
as well as preliminary simulation calculations of the HBr
(2+1)REMPI spectrum, suggests that HBr(X1Σ+;V′′ ) 0,J′′)
molecules formed by (2b) are rotationally hot.
(ii) The observed intensity enhancement in the C+ REMPI
signal in the region above 80 600 cm-1 (see Figure 2b) can be
explained as being due to switching from three-photon to twophoton ionization of C*(1D2) formed by step (2b), the threshold
for which is the ionization potential for C*(1D2) (80 625.27
cm-1).37 This strongly suggests that not only the C atom REMPI
signal but also the “nonresonant” REMPI C+ signal are due to
photoionization of C/C* atoms after their formation by photodissociation in this spectral region. Generally, the CH3+ REMPI
signal for excitation to ω ) 2 states is much weaker than the
corresponding signal for ω ) 0 states (see Figures 1c and 2b).
The opposite is found for the C+ REMPI signals in the region
80 600-81 000 cm-1. Although the formation mechanism for
CH3+, hence the CH3+ REMPI signal’s origin, is not certain,
this indicates that dissociation of ω ) 2 states, to form H2 +
C*(1D2) + HBr, is favored over that of dissociation of ω ) 0
states.
(iii) Whereas the C atom REMPI signal due to two-photon
resonance excitations of C*(1D2) to the 5p and 6p states are
medium strong (see Figure 2a and Table 2b), transitions to the
4p states are very weak (not shown in Figure 2a). Since there
is reason to believe that the transition probabilities for the lower
energy transitions to the 4p states are in fact larger than those
to the 5p and 6p states, this observation suggests that there is a
barrier on the potential energy surface for the transformations
of CH3Br**(Ry) to H2 + C*(1D2) + HBr (E ) 69 522 cm-1)
by step (1b) close to that of the excitation energies needed for
the C**(4p, 1D2/1S0) rr C*(1D2) transitions (71 577-72 062
cm-1), i.e., in the vicinity of 72 000 cm-1.
(iv) Slope values slightly larger than 3 were derived from
log-log plots for C atom REMPI signals vs laser power for
the medium strong atom lines at 69 668.9 cm-1 (C**(3p,3D2)
rr C(2p2, 3P2)) and 69 705.0 cm-1 (C**(3p,3D2) rr C(2p2,
3
P2)), respectively. A slope value of 5 is to be expected in the
low laser power limit for the overall (2r + 2r′ + 1i) REMPI
process, where 2r and 2r′ refer to the two-photon resonance steps
(1a) and (1c), respectively, and 1i refers to the one-photon
ionization step (1d). A slope value higher than 5 could indicate
a three-photon initial step, instead of (2a), and rule out the
proposed mechanism. The observed slope value, slightly higher
than 3, could indicate a near saturation effect in the Rydberg
excitation step (1a), difficult to avoid when looking for the
relatively weak atom signals. In fact, saturation of step (1a) may
be necessary for the presumably very low quantum efficiency
step (1b) to proceed to a measurable degree.
9996 J. Phys. Chem. A, Vol. 114, No. 37, 2010
Kvaran et al.
Figure 4. HBr+ 1D (2r+1i) REMPI spectra (top insets) along with
the C+ 1D REMPI spectrum (Figure 4a) (gray). The HBr+ spectrum
for the spectral region 75 200-75 400 cm-1 (top, left) shows rotational
structure due to the two-photon resonance transition g3Σ- rr X1Σ+
(0,0).32 The HBr+ spectrum for the spectral region 76 980-77 015 cm-1
(top, right) shows rotational contour due to the two-photon resonance
transition F1D2 rr X1Σ+ (0,0).32 Rotational line positions for HBr,
determined by Callaghan and Gordon,32 are shown.
Figure 3. Schematic energy diagrams relevant to C+ (a) and Br+ (b)
REMPI data, showing calculated potential energies as functions of the
CH3-Br bond distance13,19 as well as relevant energy thresholds and
transitions. (a) Transitions involving (2r+1i) REMPI (see text) of
C*(1D2) (77 023.3 cm-1; C**(6p,1D2) rr C*) and C(3P2) (69 668.9
cm-1; C**(3p,3D2) rr C) following two-photon excitations of CH3Br
to the Rydberg/ion-pair manifold and photodissociation to form H2 +
C/C* + HBr (broken arrows) are shown as bold and narrow line arrows,
respectively. Calculated thresholds (see text) for transformation of
methyl bromide in the lowest energy singlet state (CH3Br (S0)), via
CHBr + H2 formation, to H2 + C*(1D) + HBr are shown as solid line
energy levels joined by unbroken lines. Calculated thresholds and the
energy barrier (see text) for transformation of methyl bromide in the
lowest energy triplet state (CH3Br (T0)), via CHBr + H2 formation, to
H2 + C (3P) + HBr are shown as broken line energy levels joined by
broken lines. The excitation region for carbon atomic line detection is
also indicated. (b) Transitions involving (2r+1i) REMPI (see text) of
Br(2P3/2) (79 866.8 cm-1; Br**(2P1/2) rr Br) and Br*(2P1/2) (70 987.5
cm-1; Br**(4P5/2) rr Br*) following two-photon excitations of CH3Br
to the Rydberg/ion-pair manifold and photodissociation to form CH3
+ Br/Br* are shown as bold and narrow line arrows, respectively. The
excitation region for bromine atomic line detection is also indicated.
(v) For the proposed mechanism (1a)-(1d) to be feasible,
the overall barrier to the CH3Br f H2 + C/C* + HBr reaction
has to be smaller than the initial two-photon excitation energy
for CH3Br in step (1a). By analogy to our analysis for
photodissociation of acetylene (C2H2) to form C2 + H2,35 we
searched for the lowest energy thresholds for this dissociation
by calculating potential energy surfaces (PES) for transformations of the lowest energy singlet and triplet states of methyl
bromide (CH3Br (S0) and CH3Br (T0)) to H2 + C*(1D2) + HBr
and H2 + C(3P) + HBr, respectively. The potential energy
surfaces for the singlet and triplet states were calculated with
Gaussian0341 at the B3LYP/6-311++G(d,p) level of theory.
First, simultaneous H2 and HBr loss was studied by carrying
out a 2D potential energy surface scan, in which an H2 and a
HBr molecule were allowed to approach the carbon core in
constrained geometry optimizations. The simultaneous H2 +
HBr loss appears to be monotonously uphill in energy and,
therefore, not particularly likely. Second, when HBr was allowed
to approach C by constraining the C-Br bond length, the H
atom in HBr jumped over to C at a large distance. The time
inverse process of a Br atom leaving the core and the H
following it with a ca. 3 Å delay is extremely unlikely.
Therefore, it is suggested that (1b) takes place in two steps, the
first being the ejection of an H2 molecule. This process is found
to take place without a reverse barrier on the ground singlet
surface. The second step, the loss of HBr from HCBr is
energetically very similar to Br atom loss and takes place
practically without a reverse barrier on the ground singlet and
triplet surfaces. Thus, we conclude that the proposed mechanism
(1a)-(1d) is energetically feasible, as shown schematically in
Figure 3a.
Br Atom REMPI; Br/Br* Formation Channels. The weak
Br+ REMPI signals, following excitations to Rydberg states or
the ion-pair state (see Figure 1a,b), show the same overall
spectral structure as the stronger CH3+ REMPI signals (Figure
1c) except for strong Br atom REMPI lines that appear in the
excitation region 70 950-79 900 cm-1 (see Figure 5). Lines
due to resonance excitations of both ground state spin-orbit
components, Br(2P3/2) and Br*(2P1/2), are observed. Both spin
conserved (∆S ) 0) and spin-flip (∆S ) 2) transitions are
identified. All observed Br atom lines correspond to electron
transfers of 4p electrons to 5p orbitals, which satisfy ∆l ) 0,
|∆L| e 2, and |∆J| e 2 as to be expected for two-photon
J. Phys. Chem. A, Vol. 114, No. 37, 2010 9997
2D-REMPI of CH3Br
Figure 5. Br+ 1D REMPI spectra (bold) along with the CH3+ 1D
REMPI spectrum (Figure 1c) (gray) for the two-photon wavenumber
region 74 000-80 000 cm-1. Peaks due to two-photon resonance
transitions from Br(4p5;2P3/2) (top) and Br(4p5;2P1/2) (below) to
Br**((3PJ)c;5p), where (3PJ)c is the ion core term, are labeled. The
strongest atomic lines at 75 696.4 cm-1 (4D5/2 rr 2P3/2), 76 742.4 cm-1
(4D3/2 rr 2P3/2), and 78 079.6 cm-1 (2S1/2 rr 2P3/2) have been scaled
down by factors 2, 4, and 2, respectively, as indicated.
resonance transitions.37,42 In addition to the lines shown in Figure
5, very weak lines are observed at 70 987.5 and 70 987.08 cm-1
due to the 4P5/2 rr 2P1/2 and 4P3/2 rr 2P1/2 transitions,
respectively.37
The Br atom REMPI signal may be due to resonance
excitations of Br and Br* atoms formed by predissociation of
excited Rydberg states after two-photon excitation of CH3Br to
Rydberg states or the ion-pair state (CH3Br**(Ry,i-p)) (see
Figure 3b), i.e.
CH3Br + 2hν f CH3Br**(Ry,i-p)
(3a)
CH3Br**(Ry) f CH3 + Br/Br*
(3b)
Br/Br* + 2hν f Br**
(3c)
Br** + hν f Br+ + e-
(3d)
The ion-pair state is known to couple strongly to Rydberg states
of the same symmetry,43 and by analogy to the hydrogen halides
(HX), coupling beyond symmetry restrictions could also occur.
Couplings between singlet and triplet ∆-Rydberg states (Ω )
2, 1) as well as a 3Σ+(Ω)1) Rydberg state and the ion-pair
state V 1Σ+(Ω)0) have been observed in HCl.25–27,34,36 Predissociation, which occurs by crossing from Rydberg states to
repulsive valence states may involve a gateway Rydberg state
(i.e., a Rydberg-Rydberg interaction) by analogy to the
hydrogen halide systems.25,44 Alternatively, Br and Br* atoms
may be formed by dissociation of CH3Br** to form CH + H2
+ Br/Br* and/or CH2 + H + Br/Br* fragments instead of
channel (1b) (see Figure 3b).
The above mechanism (3a)-(3d) further gains support from
power dependence experimental data. Figure 6 shows the
log-log plot for the 79Br atom REMPI signal of the strong
78 680.0 cm-1 atom line (2D3/2 rr 2P3/2 transition) as a function
of laser power. The observed curvature of the plot, as laser
power increases, indicates a saturation effect.45 Slope evaluations
reveal the number of photons needed to create 79Br+ ions for
low laser power to be 5. This value fits the total number of
Figure 6. Power dependence of the 79Br+ ion signal at 78 680.0 cm-1
due to the two-photon bromine atomic resonance transition 2D3/2 rr
2
P3/2. Log-log plot of the relative 79Br+ ion intensity (Irel(79Br+)) as a
rel 79
+
rel
function of relative laser power (Prel
laser), i.e., log(I ( Br )) vs log (Plaser)
(circles joined by straight lines). Lines for slopes 5 and 3 are inserted.
photons in the overall (2r + 2r′ + 1i) REMPI process. A slope
value derived for higher power (ca. 3; see Figure 6) could be
due to saturation in the CH3Br**(Ry,i-p) formation step (3a),
in which case the ion signal will increase proportionally to the
laser power cubed (2r′ + 1i). Further “leveling off” in the
log-log plot as power increases could indicate additional
saturation in the Br atom resonance step (3c). A slope value
close to 5 was also derived in the low laser power limit for the
79
Br atom REMPI signal at 74 389.6 cm-1 (2S1/2 rr 2P1/2
transition).
Conclusions
2D REMPI spectra for CH3Br were recorded for the twophoton resonance excitation region 66 000-81 000 cm-1 by
recording ion TOF spectra as a function of the laser frequency.
Most spectral features could be assigned on the basis of previous
absorption2,4,5 and REMPI18 spectra as well as ab initio
calculations.5,19 These, however, disagree with assignments given
by Locht et al.5 The major spectral structure is due to twophoton electron transitions of lone pair electrons to np and nd
orbitals localized on the Br atom to produce Rydberg states
converging to either of the two (Ωc ) 3/2, 1/2) spin-orbit states
of the molecular ion for total electronic angular momentum
quantum numbers (ω) 0 or 2. In addition to previously assigned
bands in REMPI due to transitions involving no vibrational
excitation, i.e., 0-0 transitions,18 transitions involving one or
two quanta in a single vibrational mode only (∆νi ) 1, 2; ∆νj
) 0, j * i) were also observed. An observed rise in background
REMPI signal with increasing energy is attributed to a gradually
increasing contribution from transitions to the ion-pair state, as
was previously predicted.19
Medium strong carbon (2+1) REMPI signals are observed
in the 69 500-77 500 cm-1 region due to transitions from
ground triplet state C(3P) atoms and the first excited singlet state
C*(1D2) atoms. Most probably, these are due to resonance
excitations after dissociation of CH3Br** Rydberg states,
initially created by two-photon excitation, to form H2 + C/C*
+ HBr fragments. HBr REMPI signals, enhanced intensities of
C+ REMPI signals above 80 600 cm-1, power dependence data,
energy considerations, and potential energy surface calculations
support this mechanism. An increased relative intensity of the
C atom 5p and 6p REMPI signal compared with the 4p signal
9998 J. Phys. Chem. A, Vol. 114, No. 37, 2010
suggests that there is a barrier along the photodissociation
pathway. To our knowledge this is the first indication of a
photodissociative channel in a small molecule, in which four
bonds are broken and two bonds are formed.
The strong bromine (2+1) REMPI signals in the 70 950-79 900
cm-1 region and its power dependence behavior suggest that
Br(2P3/2) and Br*(2P1/2) atoms are formed by predissociation of
Rydberg states after initial two-photon excitation. Predissociation
to form CH3 + Br/Br* may give rise to this signal.
Acknowledgment. The financial support of the University
Research Fund, University of Iceland, and the Icelandic Science
Foundation is gratefully acknowledged. We thank Helgi Rafn
Hródmarsson for useful help with the project.
References and Notes
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JP104128J
Paper III
Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional
(2+n) REMPI of HCl: State interactions and photorupture channels via
low energy triplet Rydberg states. Journal of Chemical Physics, 131,
044324, 2009.
71
THE JOURNAL OF CHEMICAL PHYSICS 131, 044324 2009
Two-dimensional „2 + n… resonance enhanced multiphoton ionization of HCl:
State interactions and photorupture channels via low-energy triplet
Rydberg states
Ágúst Kvaran,a Kristján Matthiasson, and Huasheng Wang
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
Received 7 May 2009; accepted 25 June 2009; published online 29 July 2009
Mass spectra were recorded for 2 + n resonance enhanced multiphoton ionization REMPI of HCl
as a function of resonance excitation energy in the 81 710– 82 870 cm−1 region to obtain
two-dimensional REMPI data. Small but significant fragmentations and H+, Cl+, as well as
HCl+ formations are found to occur after resonance excitations to the triplet Rydberg states
f 32v = 0, f 31v = 0, and g 3+1v = 0. Whereas insignificant rotational line shifts could be
observed, alterations in relative ion signal intensities, due to perturbations, clearly could be seen,
making such data ideal for detecting and analyzing weak state interactions. Model analysis of
relative ion signal intensities, taking account of the major ion formation channels following
excitations to Rydberg states, its near-resonance interactions with ion-pair states as well as
dissociations and/or photodissociations were performed. These allowed verification of the existence
of all these major channels as well as quantifications of the relative weights of the channels and
estimates of state interaction strengths. The proposed mechanisms were supported by ion signal
power dependence studies. © 2009 American Institute of Physics. DOI: 10.1063/1.3180824
I. INTRODUCTION
Since the original work by Price1 on hydrogen halides, a
wealth of spectroscopic data on HCl has been derived from
absorption spectroscopy,2–5 fluorescence studies,5 as well as
resonance enhanced multiphoton ionization REMPI
experiments.6–15 Relatively intense single- and multiphoton
absorptions in conjunction with electron excitations as well
as rich band structured spectra make the molecule ideal for
fundamental studies. A large number of Rydberg states, several low-lying repulsive states as well as the V 1+ ion-pair
state have been identified. A number of spin-forbidden
transitions have been observed, indicating that spin-orbit
coupling is important in excited states of the molecule.
Perturbations due to state mixing are widely seen both
in absorption3–5 and REMPI spectra.7,8,10–12,15 The perturbations appear either as line shifts4,7,8,11,12,15 or as intensity
and/or bandwidth alterations.4,7,8,10–12,15 Pronounced ion-pair
to Rydberg state mixings are both observed
experimentally3,4,8,11,12,15,16 and predicted from theory.16,17
Interactions between the V 1+ ion-pair state and the E 1+
state are found to be particularly strong and to exhibit nontrivial rotational, vibrational, and electron spectroscopy. Perturbations due to Rydberg–Rydberg mixings have also been
predicted and identified.4,10 Both homogeneous = 0
Refs. 11, 12, 16, and 17 and heterogeneous 0 Refs.
12, 15, and 16 couplings have been reported. Such quantitative data on molecule-photon interactions are of interest in
understanding stratospheric photochemistry as well as being
relevant to the photochemistry of planetary atmospheres and
the interstellar medium.5
Photorupture studies of HCl have revealed a large
variety of photodissociation and photoionization processes.
In a detailed two-photon REMPI study, Green et al.7 reported
HCl+, Cl+, and H+ ion formations for excitations via
large number of = 0 Rydberg states as well as via the
V 1+ = 0 ion-pair state, whereas excitations via other
Rydberg states were mostly found to yield HCl+ ions. More
detailed investigations of excitations via various Rydberg
states and the V 1+ ion-pair state using photofragment imaging and/or mass-resolved REMPI techniques have revealed several ionization channels depending on the nature
of the resonance excited state.18–22 Results are largely based
on analysis of excitations via the E 1+ Rydberg state and
the V 1+ ion-pair state, which couple strongly to produce
the mixed adiabatic B 1+ state with two minima. Also,
analysis of excitations via the F 12v = 1 Rydberg state
and the V 1+v = 14 state has shown the characteristic effects of near-resonance interactions on photoionization
channels.22 Analysis of excitations via triplet states, however,
has not revealed fragmentations or shown the effects of coupling with the ion-pair state.7,20 These studies reveal characteristic ionization channels that have been summarized in
terms of excitations via 1 resonance noncoupled diabatic
Rydberg state excitations and 2 resonance noncoupled ionpair excitations.22 The major channels are as follows:
1
a
Author to whom correspondence should be addressed, Telephone: 354525-4694 and 354-525-4800. Fax: 354-552-8911. Electronic mail:
[email protected]. URL: http://www.hi.is/~agust/.
0021-9606/2009/1314/044324/9/$25.00
2
131, 044324-1
An ionization via a noncoupled Rydberg state is found
to involve i one-photon ionization of the Rydberg
states to form the molecular ion HCl+, followed by ii
a second one-photon excitation to a repulsive ion state
2 2 and dissociation to form H+ see Fig. 1. HCl+
could be formed partly by direct ionization and partly
by autoionization.19
Several ionization channels, via the noncoupled ion© 2009 American Institute of Physics
Downloaded 30 Jul 2009 to 130.208.137.190. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
044324-2
J. Chem. Phys. 131, 044324 2009
Kvaran, Matthiasson, and Wang
3
(2+n)
HCl+*
(4)
f ∆2 , ν' = 0 , R
3
HCl+*
H+ + Cl
f ∆2 , ν' = 0 , Q
H+ + Cl
H+
Cl+
(v)
HCl**
(T)
HCl+
(3)
HCl+
f ∆2 , ν' = 0 , P
(vi)
HCl**
1 Σ+
H+ Cl*
HCl**[A]1Σ+
H+Cl*
(i)
7
H+ + Cl-
H* +Cl
3
f ∆2 , ν' = 0 , S
2 7
2
1
V Σ , ν' = 8 , Q
7
6
6
2
4
(2)
HCl*
(Ry, v´,J´)
H+Cl(V1Σ+, v´,J´)
W12
H Cl
37
+
37
+
0
1
V Σ , ν' = 8 , O V 1 Σ , ν' = 8 , S
0
1
5
2
Cl
35 +
H Cl
35 +
Cl
+
H
(2)
(1)
(a)
6
2
3
f ∆2 , ν' = 0 , O
(vii)
(iii)
6
2
3
(iv)
(ii)
81800
(a)
(2+n)
81900
82000
-1
2hν [cm ]
82100
82200
(2+n)
HCl+*
H+ Cl+
(5)
Cl+
3
f ∆ 2 , ν' = 0 , Q
H+ +Cl
(4)
HCl+
(3)
2
7
(ii)
(ix)
(4)
HCl**
(viii)
HCl*
(RyG, v´,J´)
(3)
H37Cl+
H + Cl(J =1/2,3/2)
35Cl+(x10)
H+(x10)
(SO)
HCl*
3 Σ+
(3)
H35Cl+
(i)
SO
(b)
H+ Cl*
(2)
HCl*
(Ry, v´,J´)
H37Cl+
(1)
H35Cl+
3
x10
J´=2
FIG. 1. Ionization mechanisms. Schematics a and b showing possible
ionization channels following excitations and/or state transfer 1 to a diabatic Rydberg state channels i, ii, and ix, 2 to a hypothetical diabatic
V 1+ ion-pair state channels iii–vii, and 3 to neutral fragments
H + Cl 2 P1/2,3/2 via predissociation of a gateway Rydberg state viii. The
arrows represent excitations relevant to 2 + n ; n = 1 – 3 REMPI. Fragments
and excited state species are indicated. The ions formed are highlighted with
circles. The total number of photons is indicated.
pair state, have been proposed,18–21 involving iii onephoton autoionization via a repulsive superexcited state
that correlates with H + Cl to form HCl+ largely in high
vibrational v+ levels,19 followed by iv a second onephoton excitation to a repulsive ion state 2 2 and
dissociation analogous to ii, v one-photon excitation to repulsive triplet superexcited states,20,21 forming
H and ClCl = Cl4s , 4p , 3d, followed by onephoton ionization of Cl to form Cl+, vi one-photon
excitation to a repulsive superexcited state HCl, 1+,
forming Hn = 2 and Cl, followed by one-photon ionization of Hn = 2 to form H+, and vii one-photon
excitation to a bound superexcited state, which acts as a
gateway state to dissociation into the ion-pair
H+ + Cl−.18 More channels have been proposed18,20 via
the “noncoupled” ion-pair state but these are believed
to be of minor importance.
Thus, based on this overall ionization scheme H+ forma-
3
4
5
6
7
35Cl+
(b)
82015
82020
82025
-1
2hν [cm ]
82030
FIG. 2. a 1D 2 + n REMPI spectra for H+, 35Cl+, H 35Cl+, 37Cl+, and
H 37Cl+ derived from HCl with isotope ratios in natural abundance for the
two-photon excitation region of 81 710– 82 260 cm−1. Assignments for the
f 32 ← ← X 1+, 0,0, O , P , Q , R , S line and V 1+ ← ← X 1+, 8,0,
O , Q , S line transitions are shown. b 2D 2 + n REMPI contour below for
chlorine-containing ions and 1D 2 + n REMPI spectra above for H+,
35 +
Cl , H 37Cl+, and H 35Cl+ derived from HCl with isotope ratios in natural
abundance for the two-photon excitation region of 82 013– 82 033 cm−1.
Assignments for the f 32 ← ← X 1+, 0,0, Q line transitions are shown.
J = J-numbers are indicated in the figures.
tion clearly is indicative of both the ion-pair and the Rydberg
state contribution, whereas the Cl+ ions are characteristic indicators for the ion-pair state contribution. There are reasons
to believe that the HCl+ contribution to ion formation, via
excitation to the V state, is rather small.22 Therefore HCl+
formation is the main ion formation channel via Rydberg
state excitation channel i under low power conditions.
Therefore, working with relative normalized ion intensities
for Cl+ ICl+ / IHCl+ and for HCl+ IHCl+ / ICl+ as
indicators for the separate diabatic Rydberg and ion-pair
states, respectively, has been found to be useful.
In addition to the photorupture channels mentioned
above, further dissociation and/or photodissociation of reso-
Downloaded 30 Jul 2009 to 130.208.137.190. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
044324-3
J. Chem. Phys. 131, 044324 2009
2D REMPI of HCl
nance excited Rydberg states could occur. Thus dissociations
to form H + ClJ = 1 / 2 , 3 / 2 via predissociation of some
gateway states could be important, as predicted by Alexander
et al.23 In such cases, further photoionization of the
ClJ = 1 / 2 , 3 / 2 and H fragments could also occur see channel viii in Fig. 1b. Whereas the interactions between the
states involved could be of various kinds,23 spin-orbit
couplings most probably are dominant. Alternatively,
dissociations via photoexcitations to inner walls of bound
super-excited Rydberg states above dissociation limits
could form H + Cl and/or H + Cl see channel ix in Fig.
1b. We call channels viii and ix the “dissociation channels” hereafter.
In this paper, we use a two-dimensional 2D REMPI
approach, obtained by recording ion mass spectra as a
function of the laser frequency, to study the photorupture
dynamics of HCl for two-photon resonance excitations via
the triplet Rydberg states f 32v = 0, f 31v = 0 and
g 3+1v = 0 and the V 1+v = 8 , 9 ion-pair states. We
show, for the first time, that small but significant fragmentations and H+ and Cl+ formations occur after resonance excitations to the triplet states. Whereas insignificant line shifts
are seen, rotational quantum-level-dependent ion signal intensities due to perturbation effects are observed for all the
states. Thus, relative signal intensities are found to be more
sensitive measures of state interactions than line shifts. This
was proved to be a useful tool in assisting with state
assignment24 and could possibly be used for indirect characterization of hidden states. A model, based on the major photorupture channels mentioned above, is created and used to
simulate ion signal data for ionizations via excitations to the
Rydberg states. Thus, the observations are found to be consistent with a near-resonance couplings between the triplet
states and V 1+ states and b photodissociation via the dissociation channels. The importance of the dissociation channels is found to be Rydberg state dependent. The model further allows estimates of various interaction and weight
parameters relevant to the photorupture mechanism. The proposed mechanisms for resonance diabatic state excitations
are supported by ion signal power dependence studies.
II. EXPERIMENTAL
2D REMPI data for jet-cooled HCl gas were recorded.
Ions were directed into a time-of-flight tube and detected by
a microchannel plate MCP detector to record the ion yield
as a function of mass and laser radiation wavenumber.
The apparatus used is similar to that described
elsewhere.14,25 Tunable excitation radiation in the 241.2–
245.0 nm wavelength region was generated by excimer laserpumped dye laser systems, using a Lambda Physik COMPex
205 excimer laser and a Coherent ScanMatePro dye laser.
Dye C-480 was used and frequency doubling was obtained
with a Beta Barium Borate-2 BBO-2 crystal. The repetition
rate was typically 10 Hz. The bandwidth of the dye laser
beam was about 0.095 cm−1. The typical laser intensity used
was 0.1–0.3 mJ/pulse. The radiation was focused into an
ionization chamber between a repeller and an extractor plate.
We operated the jet in conditions that limited cooling in or-
1
F ∆ , ν´=0, O
a)
1
2
7
1
7 V Σ , ν´= 9, Q
6
8
5
1
4 V Σ , ν´= 9, O
4
2
3
F ∆ , ν´=0, P
2
3
1
2
1 0
1
F ∆ , ν´=0, Q
0
3
f ∆1 , ν´ = 0, S
3
f ∆1 , ν´ = 0, Q
3
2
3
f ∆1 , ν´ = 0, R
3
f ∆1 , ν´ = 0, P
2
2
4
2
5
4
6
7
8
6
1
37
H Cl
37
Cl
+
+
35
H Cl
35
H
(a)
82500
82600
-1
82700
Cl
+
+
+
82800
2hν / [cm ]
3
g Σ , (ν'=0) , Q
7 D 1Π , J'=1, R
5
3
1
35
H Cl
37
H Cl
82508
(b)
82512
82516
-1
2xhν [cm ]
82520
FIG. 3. a 1D 2 + n REMPI spectra for H+, 35Cl+, H 35Cl+, 37Cl+, and
H 37Cl+ derived from HCl with isotope ratios in natural abundance for the
two-photon excitation region of 82 450– 82 870 cm−1. Assignments for the
f 31 ← ← X 1+, 0,0, P , Q , R , S line and V 1+ ← ← X 1+, 9,0, O , Q
line and F 12 ← ← X 1+ 0,0, O , P , Q line transitions are shown. b 1D
2 + n REMPI spectra for H 35Cl+ and H 37Cl+ for the region of
82 508– 82 522 cm−1. Assignments for the g 3+1 ← ← X 1+, 0,0, Q
line and the D 11 ← ← X 1+, 0,0, R, J = 1 line transitions are shown.
J = J-numbers are indicated in the figures.
der not to lose the transitions from the high rotational levels.
Thus, an undiluted, pure HCl gas sample Merck-Schuchardt
OHG; purity 99.5% was used. It was pumped through a
500 m pulsed nozzle from a typical total backing pressure
of about 1.0–1.5 bars into the ionization chamber. The pressure in the ionization chamber was lower than 10−6 mbar
during experiments. The nozzle was kept open for about
200 s, and the laser beam was typically fired 500 s after
the nozzle was opened. Ions were extracted into a time-offlight tube and focused on a MCP detector, of which the
signal was fed into a LeCroy 9310A, 400 MHz storage oscilloscope, as a function of the flight time. The average signal levels were evaluated and recorded for a fixed number of
laser pulses typically 100 pulses to obtain the mass spectra.
Mass spectra were typically recorded in 0.05 or 0.1 cm−1
laser wavenumber steps to obtain 2D REMPI spectra.
REMPI spectra for certain ions as a function of excitation
wavenumber one-dimensional 1D REMPI were obtained
by integrating signal intensities for narrow time-of-flight
hence, mass ranges covering the particular ion mass. The
power dependence of the ion signal was determined by integrating the mass signals repeatedly and averaging for 1000
pulses, after bypassing a different number of quartz windows
to reduce power. Care was taken to prevent saturation effects
as well as power broadening by minimizing laser power. La-
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044324-4
J. Chem. Phys. 131, 044324 2009
Kvaran, Matthiasson, and Wang
TABLE I. Rotational lines of relevant transitions derived by Green et al. Ref. 9 marked “others” and us “ours” cm−1. The accuracy of “our” values is
about 1.0 cm−1.
f 32 ← ← X 1+0 , 0
O
P
Q
R
S
J
Others
Ours
Others
Ours
Others
Ours
Others
Ours
Others
Ours
2
3
4
5
6
7
81 871.3
81 871.8
81 832.4
81 793.5
81 756.2
81 719.8
81 954.5
81 936.8
81 919.0
81 900.9
81 883.1
81 865.0
81 956.4
81 938.8
81 921.6
81 902.3
81 883.4
81 864.9
82 017.2
82 019.8
82 022.9
82 025.6
82 017.2
82 019.7
82 022.5
82 025.4
82 028.0
82 030.2
82 059.3
82 082.7
82 106.0
82 129.8
82 059.3
82 082.4
82 106.3
82 131.1
82 154.7
82 080.0
82 124.1
82 168.4
82 212.7
82 256.8
82 079.9
82 125.1
82 169.2
82 212.9
82256.5
81 793.6
81 754.8
P
Q
f 31 ← ← X 1+0 , 0
J
Others
Ours
Others
Ours
1
2
3
4
5
6
7
8
82 481.4
82 460.0
82 478.9
82 458.1
82 523.2
82 521.0
R
Others
Ours
Others
Ours
82 564.8
82 584.7
82 605.0
82 563.8
82 585.8
82 605.7
82 625.9
82 646.2
82 585.6
82 626.4
82 666.9
82 707.3
82 748.0
82 788.1
82 585.8
82 626.1
82 665.4
82 704.8
82 745.0
82 786.0
82 645.4
O
J
Others
Ours
0
1
2
3
4
5
6
7
82 163.3
82 106.9
82 107.5
V 1+ ← ← X 1+8 , 0
Q
Others
Ours
82 225.7
82 211.3
82 182.0
82 140.3
82 225.7
82 211.7
82 182.6
82 140.7
82 080.3
82 007.8
81 923.6
81 826.8
S
S
O
Others
Ours
82 244.8
82 242.8
82 244.9
82 242.9
82 225.7
82 194.8
82 244.9
82 242.9
82 194.9
ser calibration was performed by recording an optogalvanic
spectrum, obtained from a built-in neon cell, simultaneously
with the recording of the REMPI spectra. The atomic reference lines, for absolute wavelength calibration 5 pm accuracy, were provided using an optical SPOCK Simulation
Program for Optical Circuit Knowledge function. Line positions were also compared to the strongest hydrogen chloride rotational lines reported by Green et al.9 The accuracy of
the calibration was found to be about 1.0 cm−1 on a twophoton wavenumber scale. Intensity drifts during the scan
were taken into account, and spectral intensities were corrected for accordingly.
III. RESULTS AND ANALYSIS
A. Two-dimensional REMPI and relative ion signals
Figure 2a shows 1D 2 + n REMPI spectra for H+,
Cl+, H 35Cl+, 37Cl+, and H 37Cl+ derived from HCl with isotope ratios in natural abundance for the two-photon excitation region of 81 710– 82 260 cm−1. Figure 2b shows the
corresponding 2D REMPI contour below and 1D REMPI
spectra above for the narrow spectral region of
35
Others
82 777.0
82 721.8
82 653.2
g 3+1 ← ← X 1+0 , 0
Q
Ours
82 520.8
82 519.7
82 518.5
82 517.2
82 515.3
82 512.8
82 509.4
82 504.4
V 1+ ← ← X 1+9 , 0
Q
Ours
Others
Ours
82 774.7
82 721.8
82 653.8
82 570.0
82 471.5
82 839.7
82 826.3
82 799.2
82 758.1
82 703.1
82 839.7
82 826.7
82 798.6
82 755.8
82 700.3
82 634.5
82 547.0
82 451.4
S
Others
82 862.0
82 862.6
82 013– 82 033 cm−1. Figure 3a shows the 2 + n REMPI
spectra for H+, 35Cl+, H 35Cl+, 37Cl+, and H 37Cl+ for the twophoton excitation region of 82 450– 82 870 cm−1. Figure
3b shows the expanded 2 + n REMPI spectra for H 35Cl+
and H 37Cl+ for the region of 82 508– 82 522 cm−1. By comparison with data reported by Green et al.,7 rotational peaks
due
to
the
transitions
f 32 ← ← X 1+0 , 0,
V 1+ ← ← X 1+8 , 0,
V 1 +
f 31 ← ← X 1+0 , 0,
← ← X 1+9 , 0, and F 12 ← ← X 1+0 , 0 for H 35Cl
have been identified and assigned. In addition, several more
rotational lines have been assigned to these electronic transitions see also Table I. The major structure in Fig. 3b is
due to the resonance transition g 3+1 ← ← X 1+.24 Other
peaks observed in this region are due to the transitions
d 30+ ← ← X 1+ and D 11 ← ← X 1+0 , 0.7
On a relative scale, significant ion signals for all ion
species are observed for the V 1+ ← ← X 1+8 , 0 and
1 +
V ← ← X 1+9 , 0 systems, whereas the parent ion signals dominate the REMPI for f 32 ← ← X 1+0 , 0,
f 31 ← ← X 1+0 , 0, and g 3+1 ← ← X 1+, in agreement with earlier observations.7,24 Weak but significant H+,
35 +
Cl , and 37Cl+, however, are also observed for the
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044324-5
J. Chem. Phys. 131, 044324 2009
2D REMPI of HCl
0.06
f 3∆2 , ν’=0
0.025
a)
Q
0.05
I( 35Cl+)/ I(H35Cl+)
I( 35Cl+)/ I(H35Cl+)
0.04
0.03
0.02
g 3Σ+1 , ν’=0
d)
0.02
Calc
0.015
0.01
Calc
Q
R
0.005
0.01
0
0
2
3
4
5
6
7
1
2
3
4
1.5
5
6
7
8
J'
J´
J´
J'
0.6
V 1Σ , ν’=8
b)
V 1Σ , ν’=9
e)
0.5
35Cl
35Cl
0.4
37Cl
I(HiCl+) / I(iCl+)
I(HiCl+) / I(iCl+)
1.0
0.5
37Cl
0.3
0.2
0.1
0.0
0
0
0.014
0.012
1
2
3
J'
J´
f 3∆1 , ν’=0
4
5
6
7
0
1
2
3
4
5
6
J´J'
c)
S
I( 35Cl+)/ I(H35Cl+)
Calc
0.01
R
0.008
0.006
0.004
0.002
0
2
3
4
5
6
7
8
J´J'
FIG. 4. Relative normalized ion signal intensities, a I 35Cl+ / IH 35Cl+ for f 32 ← ← X 1+, 0,0, derived from the following: i Q rotational lines white
columns, ii R lines black columns, and iii simulations of the data for the Q lines, marked as “calc.” gray columns; see text. b IH 35Cl+ / I 35Cl+
and IH 37Cl+ / I 37Cl+ for V 1+ ← ← X 1+, 8,0, derived from Q lines. Ratios for J = 4 could not be derived because of rotational line overlapping. c
I 35Cl+ / IH 35Cl+ for f 31 ← ← X 1+, 0,0, derived from the following: i S lines white columns, ii R lines black columns, and iii simulations of
the data for the S lines, marked as calc. gray columns; see text. d I 35Cl+ / IH 35Cl+ for g 3+1 ← ← X 1+, 0,0, derived from the following: i Q lines
white columns, ii simulations of the data for the Q lines, marked as calc. gray columns; see text. e IH 35Cl+ / I 35Cl+ and IH 37Cl+ / I 37Cl+ for
V 1+ ← ← X 1+, 9,0, derived from Q lines.
transitions to the triplet states. The observation for the
V 1+ ← ← X 1+, 8,0 and 9,0 systems is in agreement
with earlier observations7,22 and expectations.22 Relative
normalized ion signal intensities for the systems of concern
are shown in Fig. 4.
Weak but significant enhancement of the normalized
35 +
Cl signal intensity is observed for f 32 ← ← X 1+, 0,0,
Q line, J = 5 see Fig. 4a. This corresponds to the smallest
spacing between the rotational energy levels in the
f 32v = 0 and the V 1+v = 8 states for the same J = 5
value see Table II, suggesting a near-resonance interaction
between the two states.12,15,22 This effect does not show as
an enhanced normalized H 35Cl+ signal for the
V 1+ ← ← X 1+, 8,0 system see Fig. 4b, however, underlining the interaction weakness. No significant shifts of
rotational energy levels or irregularities in line spacing
could be seen for either of these two systems, further underlining the interaction weakness. Weak but significant enhancement of the normalized 35Cl+ signal intensity is observed for both systems f 31 ← ← X 1+, 0,0, S line and
g 3+1 ← ← X 1+0 , 0, Q line for J = 6. This also corresponds to the smallest spacing between the rotational energy
levels in the Rydberg states and the closest ion-pair state,
V 1+v = 9 for the same J = 6 value see Table II, also
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044324-6
J. Chem. Phys. 131, 044324 2009
Kvaran, Matthiasson, and Wang
TABLE II. EJ relevant to near-resonance interactions for f 32 ↔ V 1+, v = 8, f 31 ↔ V 1+, v = 9, and
g 3+1 ↔ V 1+, v = 9.
J
E = Ef 32 ; v = 0
− EV 1+ ; v = 8
cm−1
E = Ef 31 ; v = 0
− EV 1+ ; v = 9
cm−1
E = Eg 3+1 ; v = 0
− EV 1+ ; v = 9
cm−1
1
2
3
4
5
6
7
164.9
119.9
57.49
17.7
105.4
203.4
303.0
276.2
235.9
180.8
113.7
27.9
66.5
305.4
279.5
239.4
184.6
118.2
34.2
57.9
indicating near-resonance interactions. Close to constant,
nonzero “background values” are obtained for other J’s
which we believe correspond to the existence of the dissociation channels see below. Now an enhanced normalized
H 35Cl+ signal for the V 1+ ← ← X 1+9 , 0 system, J = 6,
is clearly observed, whereas no significant shifts of rotational
energy levels or irregularities in line spacing could be seen
for any of these systems. The overall trends in relative signal
strengths observed for the V 1+ ← ← X 1+8 , 0 and 9,0
systems Figs. 4b and 4e are due to nonresonance
interactions between these states and other singlet Rydberg
states. Thus, significant drops in the signal strengths observed for V 1+ ← ← X 1+8 , 0, 1 J 5 and for
V 1+ ← ← X 1+9 , 0, 0 J 5 could largely be due to
decreasing interactions with the singlet Rydberg state
E 1+v = 0 and D 1v = 0 in the former case and decreasing interactions with E 1+v = 0 in the latter
case.11,12,16,22 Analogous but less clear effects were also seen
for normalized H+ signal intensities.
Assuming a level-to-level interaction scheme holds for
Rydberg 1 to ion-pair 2 state interactions Fig. 1, weight
factors fractions for the state mixing can be expressed as
follows:
1 E2 − 4W122
,
2
2E
1
for E = E1 − E2, where E1 and E2 are the resulting level energies of the perturbed states 1 and 2 and W12 is the
matrix element of the perturbation function/interaction
strength.22,26 In the case of homogeneous = 0 interac-
ICl+
=
IHCl+
+
1
−
2
EJ2 − 4W12
2JJ + 1
2EJ
2
for constant W12
. W12 is related to the resulting level energies
and the zero-order level energies for the unperturbed state
0
0
E1 and E2; E0 = E01 − E02 by the following:
Ei = 21 E01 + E02 21 4W122 + E021/2 .
3
Assuming the mechanism, discussed before see Fig. 1;
channels i–ix, holds, we make the following assumptions: The Cl+ ion intensity observed ICl+ is proportional
to the fraction of HCl in the ion-pair state 2; c22 as well as
its fraction in the Rydberg state 1; c21,
ICl+ = 2c22 + 1c21 .
4
Similarly, the HCl+ intensity IHCl+ is assumed to be proportional to the same fractions,
5
For = 2 / 1, = 1 / 2, = 1 − 2 / 1, and c21 = 1 − c22, the
ratio of ICl+ over IHCl+ now can be expressed as
+ c221 − ICl+
=
.
IHCl+
1 − c22
6
There is reason to believe that the contribution to the HCl+
formation see Eq. 5 by excitation from the diabatic ionpair state is small;22 hence, the ratio of the proportionality
factor 2 to that for the HCl+ formation from the diabatic
Rydberg state, 1 i.e., 2 / 1, is negligible and 1. By
combining Eqs. 1, 2, and 6 and assuming = 1, the following expression is derived:
2JJ + 1
1 EJ2 − 4W12
−
1 − 2
2EJ
1−
JJ + 11/2 ,
W12 = W12
IHCl+ = 1c21 + 2c22 .
B. State interactions versus excitation mechanisms
c2i =
tion, W12 is independent of the total angular momentum
quantum number, J, whereas for heterogeneous 0
interactions W12 is expressed as follows:12,22,27
,
7
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044324-7
J. Chem. Phys. 131, 044324 2009
2D REMPI of HCl
TABLE III. Parameter values in the least square fit model for ion intensity
ratios ICl+ / IHCl+ as a function of J; see Eq. 7, related equations,
and discussion Sec. III B.
J near resonance Jres
Emax / cm−1 a,b
a–c
2
Wmax
c
12
1,min
c21,min a,c
W12max / cm−1 a,d
=1 / 2
=2 / 1
f 3 2; v = 0
f 3 1; v = 0
g 3+1
5
0.5
2
0.987
0.4
0
4.0
6
1.0
4
0.979
0.7
0.002
0.5
6
2.0
6
0.968
1.0
0.004
0.6
a
c
b
d
See Eq. 1.
See Eq. 2.
See text.
See Eq. 8.
for excitations via Rydberg 1 state. This expression allows
relative ion signal data, such as that shown in Figs. 4a, 4c,
and 4d, to be fitted for known E values see Table II
using the variables , , and W12
. These three parameters
now will be discussed in more detail.
=1 / 2 is a measure of the rate of formation of Cl+
via the diabatic Rydberg state the dissociation channels to
that of its formation from the diabatic ion-pair state. The
latter Cl+ formation process is one of the major characteristic ionization channels. Hence is a relative measure of the
importance of the dissociation channels.
=2 / 1 measures the relative rate of the two major/
characteristic ionization channels, i.e., for the Cl+ formation
for excitation from the diabatic ion-pair state 2 to the
HCl+ formation from the diabatic Rydberg state 1. Considering the fact that the Cl+ ion signals via excitations to the
ion-pair states and the HCl+ ion signals via excitations to the
Rydberg states are comparable or of the same order of magnitude see Figs. 2 and 3 we feel that should be somewhat
close to unity and certainly in the range of 10−1 10.
From Eq. 3, W12 can be expressed in terms of E and
the difference, E − E0 =E, as
W12 =
1
2
E2 − E − E2 .
8
For strong enough near-resonance interactions to show the
clear shifts of the rotational peaks, hence, the clear shifts of
rotational levels E and W12 can be evaluated.12,15 Since
the interactions here are too weak to show as line/level shifts
see discussion above, only the upper limits for E i.e.,
Emax based on variations in the line/level spacing can
be estimated. From these, the upper limit values for W12 for
the near-resonance rotational levels Jres
Wmax
and the
12 Jres
W12
parameters W12
max can be evaluated from Eqs. 8 and
2. These are listed in Table III for the three Rydberg states
of concern along with corresponding weight fraction factors, c21, which represent the minimum values c21,min derived
from Eq. 1. Low Wmax
max and high i.e., close to
12 W12
unity c21,min values are indicative of small, yet measurable,
interaction strengths. By using W12
= W12
max and performing a
least square fit of the expression on the right side of Eq. 7
35 +
35 +
to the data for I Cl / IH Cl shown in Figs. 4a, 4c,
and 4d, the and values listed in Table III were derived.
The corresponding calculated fitted ion ratios are shown in
the same figures gray columns.
Reasonably good overall fits of calculated to experimental ion ratios I 35Cl+ / IH 35Cl+ versus J are obtained for
all the Rydberg resonance systems analyzed see Figs. 4a,
4c, and 4d. Thus, clear main peaks, corresponding to the
resonance interactions, are reproduced in all cases. Slight,
but significant, enhancements of the ratios closest to the
resonance peaks also are reproduced qualitatively, and in the
case of the systems f 31 ← ← X 1+, 0,0, S lines and
g 3+1 ← ← X 1+, 0,0, Q lines, close to constant, nonzero background values are obtained for other J’s corresponding to the existence of the dissociation channels. All in
all, this supports the validity of the model as described above
and based on the major ionization channels for Cl+ and HCl+
formations shown in Fig. 1. Whereas, negligible contribution
to the Cl+ ion formation is found to be from the dissociation
channels for resonance excitation to f 32 = 0; Table III,
the increasing weight of its contribution is found for the
other triplet Rydberg states as f 31 g 3+1 = 0.002
and 0.004, respectively. This fits with the prediction given
by Alexander et al.,23 who showed no spin-orbit coupling
between the f 32 state and the nearby Rydberg state, which
could act as a gateway for further predissociation via spinorbit coupling with a repulsive t 3+ state, whereas the
Rydberg states C , D 1 and b , d 31 all could act as such
both for f 31 and g 3+1. In addition, the nearby g 3−1
Rydberg state could also act as a gateway state for g 3+1
toward predissociation, which might explain the still greater
importance of that mechanism for g 3+1.
The small but reproducible enhancement in the
I 35Cl+ / IH 35Cl+ ratio observed for the g 3+1
← ← X 1+, 0,0 system, J = 3, could not be explained as
being due to near-resonance interaction between the g 3+1
state and any neighbor Rydberg or ion-pair state. A possible
explanation is the following. Predissociation on repulsive potential energy surfaces for t 3+ states, via gateway Rydberg
states C , D 1, b , d 31, and g 3−1, will produce
H + Cl3p , 2 P3/2 and H + Cl3p , 2 P1/2 followed by excitations to form Cl+ + e−. Resonance excitation for the transitions g 3+1 ← ← X 1+, 0,0, Q lines i.e., two-photon
excitations in the region of 82 508– 82 522 cm−1 happens
to be near resonance with the two-photon transition
Cl4p , 4 P1/2 ← ← Cl3p , 2 P1/2 82 482.58 cm−1,28 which,
although spin forbidden, is allowed in terms of the orbital
angular momentum quantum numbers, ll = 0 and
LL = 0, as well as in terms of the total angular momentum
quantum number JJ = 0 with relatively strong transition
probability. Therefore, J-dependent Cl+ ion formation over
HCl+ formation following dissociation by the dissociation
channel viii Fig. 1b, as seen near J = 3 Fig. 4d,
could be due to the effects of near-resonance excitations
between surfaces correlating with H + Cl4p , 4 P1/2 and
H + Cl3p , 2 P1/2 during the dissociation process.
In addition to the ion-ratio values for the
f 32 ← ← X 1+, 0,0, Q lines and the f 31 ← ← X 1+,
0,0, S lines, mentioned above, values derived for the same
systems but for R lines were derived see Figs. 4a and
4c. These are consistently found to be lower. In particular,
this is the case for the resonance peaks J = 5 for f 32
← ← X 1+, 0,0 Fig. 4a and J = 6 for f 31
Downloaded 30 Jul 2009 to 130.208.137.190. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
044324-8
J. Chem. Phys. 131, 044324 2009
Kvaran, Matthiasson, and Wang
/ 01234
"*
-
!(
,
(!
)
!(
&
(!
"*
(# !# ,
(# )
!# &
(# '
.
' !(
% (+!
! Σ!
#' ∆%
,# !
)# (
&# !
( %)
$ %& %'
$ %& %'
!# &
!ν
ν "#$%& '"'(%& )
∆" 5 (%#( #"# #% + $ %( %& %) %'
! 6! + ( 6 (
'# (
%# !
#(
"# !
Σ!
" **
* +& (%$%, + '%"+#$, "'(%& )
∆" *5 "
! 6! + ( 6 (
FIG. 5. Schematic energy levels marked with parities and relevant J
quantum numbers and selected two-photon transitions J = 4 for the
f 32 ← ← X 1+ and V 1+ ← ← X 1+ electronic transitions and the P , R
and O , Q , S rotational transitions. Selection rules relevant to two-photon
transitions and state interactions are indicated at the bottom right corner of
the figure. According to the selection rules, only the fA state component
of the f 32 state is accessed by the P and R rotational transitions whereas
the eA state components of the excited states are accessed by the O, Q,
and S transitions. Based on the selection rules for state interactions, only
crossing between eA states components can occur.
← ← X 1+, 0,0 Fig. 4c. This can be explained with
reference to Fig. 5. Figure 5 shows examples of observable
“allowed” two-photon resonance transitions from the
ground state X 1+, J = 4 used as a particular example to a
Rydberg state f 32; J = 3P, 5R and J = 2O, 4Q,
6S as well as to the ion-pair state V 1+; J = 2O, 4Q,
6S. Parities of levels states are indicated as . Observed
transitions are determined by the two-photon absorption selection rules,13,29
+ ↔+
or
− ↔−,
J = 0, 1, 2.
Thus, the eA component of the Rydberg state is accessed
by the O, Q, and S lines whereas the fA component is
accessed by the P and R lines.7 Notice that the ground and
the ion-pair states consist only of eA state components.
State interactions between the Rydberg state f 32; the same
holds for f 31 and the ion-pair state V 1+ are determined
by the selection rules,26
+ ↔+
or
− ↔−,
J = 0.
Therefore, strictly, only interactions between the eA states
accessed by the O, Q, and S lines are allowed. Thus, if Cl+
formation, following resonance excitation to a Rydberg state,
was mainly due to interaction with the ion-pair state but was
negligible due to the dissociation channels as is the case for
excitation to the f 32 state see above, one might indeed
expect a large drop in the Cl+ ion intensities for the P and R
lines compared to that for the O, Q, and S lines. The fact that
the I 35Cl+ / IH 35Cl+ ratios for the R lines are nonzero,
however, and actually peak for J = 5, analogous to that
found for the Q lines, suggests some violation of the parity
selection rule for the state interaction. The clear drop in the
ratio value for f 31 ← ← X 1+, 0,0, J = 6 by going from
the S line to the R line shows an analogous effect. However,
the ratios both for J = 6 and 2, R lines are larger than
that observed for the dissociation channels contributions
J = 3 – 5, according to the S lines, suggesting that the relative enhancement is due to some detailed difference in that
mechanism depending on whether the transfer is from the
eA or the fA Rydberg states components.
C. Laser power dependence versus excitation
mechanisms
Slope evaluations of log-log plots for the H+ and HiCl+
i = 35 and/or 37 ion intensities as a function of laser
power,22 derived for various rotational lines, revealed the
number of photons needed to create ions 4 and 3, respectively, in the cases of resonance excitations to all systems of
concern f 32, v = 0; f 31, v = 0; g 3+1, v = 0; V 1+,
v = 8 and 9. This is what is to be expected in cases of the
dominant ion product channels discussed earlier and shown
in Fig. 1,22 which further supports the proposed mechanisms.
Analogous analysis of the Cl+ ion intensities reveals less
consistent results with slope values ranging between 3 and 4.
Thus, the slope values for log-log plots of iCl+ i = 35 and/or
37 versus laser power for resonance excitations to the
V 1+, v = 8 and 9 states, various rotational levels, are found
to be close to or slightly larger than 3, whereas the corresponding slope values for the f 31, v = 0 state are closer to
4. Judging from the ionization mechanism see Fig. 1, four
photons or more are what might be needed to create Cl+.
Analogous observations of fractional slope values have been
seen before for other systems.22,30 This could be due to saturation effects in one or more excitation steps resulting in
values lower than the nominal number of photons. Such effects would be particularly important for channel viii, in
which case large laser fluence is required to perform as many
as five photon excitations to create Cl+ see Fig. 1b. Resonance or near-resonance multiphoton excitations of Cl
and/or H + ClJ = 1 / 2 , 3 / 2, involved, as discussed before,
may complicate things still more.
IV. CONCLUSIONS
2D REMPI data for HCl, obtained by recording ion mass
spectra as a function of the laser frequency, were recorded
for the two-photon resonance excitation regions of
81 710– 82 260 and 82 450– 82 870 cm−1. The observed
spectra cover the rotational structures due to two-photon
resonance transitions to the triplet excited states
f 32v = 0, f 31 v = 0, g 3+1v = 0 and to the ion-
Downloaded 30 Jul 2009 to 130.208.137.190. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
044324-9
pair states, V 1+v = 8 , 9 among others. For the first time,
small but significant Cl+ and H+ ion formations could be
observed for the triplet states. Relative normalized ion signals, suitable for identifying interactions between Rydberg
states and ion-pair states,22,24 showed that near-resonance interactions occur between all the triplet states and the
V 1+v = 8 , 9 states. This could not be seen or quantified
by a more standard way of analyzing line shifts12,15,26,27 due
to the interaction weakness, showing that the relative ion
intensities are significantly more sensitive measures of perturbation effects. A model, which takes into account the major ion formation channels following excitations to Rydberg
states, its near-resonance interactions with ion-pair states as
well as dissociation or photodissociation processes dissociation channels, was created and used to analyze the data of
the ion signals as a function of rotational quantum numbers.
Qualitative comparison of the model calculations and experimental data verified the existence of the major channels.
Least-square simulation analysis allowed quantifications of
relative weights of the channels as well as the upper limits of
state interaction strengths. The varying weight of the dissociation channels is found to be consistent with the increasing
number of spin-orbit coupling states involved, favoring
channel viii Fig. 1.23 Power dependence studies of the H+
and HiCl+ i = 35 and/or 37 ion intensities are found to support the major photorupture mechanisms proposed. Most
probably, due to partial saturation effects in the excitation
process, corresponding measurements of Cl+ ion signals are
not as easily interpretable, in agreement with earlier
observations.22,30
ACKNOWLEDGMENTS
The financial support of the University Research Fund,
University of Iceland, and the Icelandic Science Foundation
is gratefully acknowledged. Á.K. thanks Professor Jan Petter
Hansen for his support during his stay at the physics department, University of Bergen. We also thank Þórey Anna
Grétarsdóttir and Arnar Hafliðason for useful help with the
project.
1
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J. Chem. Phys. 131, 044324 2009
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1991.
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D. S. Green, G. A. Bickel, and S. C. Wallace, J. Mol. Spectrosc. 150, 354
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C. Romanescu, S. Manzhos, D. Boldovsky, J. Clarke, and H. Loock, J.
Chem. Phys. 120, 767 2004.
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A. I. Chichinin, C. Maul, and K. H. Gericke, J. Chem. Phys. 124, 224324
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Vasyutinskii, and K. H. Gericke, J. Chem. Phys. 125, 034310 2006.
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Á. Kvaran, K. Matthíasson, H. Wang, A. Bodi, and E. Jonsson, J. Chem.
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231, 331 1998.
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K. Matthíasson, H. Wang, and Á. Kvaran, J. Mol. Spectrosc. 255, 1
2009.
25
Á. Kvaran, K. Matthíasson, and H. Wang, Physical Chemistry; An Indian
Journal. 1, 11 2006; Á. Kvaran, Ó. F. Sigurbjörnsson, and H. Wang, J.
Mol. Struct. 790, 27 2006.
26
G. Herzberg, Molecular Spectra and Molecular Structure; I. Spectra of
Diatomic Molecules, 2nd ed. Van Nostrand Reinhold, New York, 1950.
27
H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Diatomic Molecules Academic, London, 1986.
28
Y. Ralchenko, A. Kramida, J. Reader, and N. A. Team, National Institute
of Standards and Technology, Gaithersburg, MD, 2008.
29
R. G. Bray and R. M. Hochstrasser, Mol. Phys. 31, 1199 1976; J. B.
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5
6
Downloaded 30 Jul 2009 to 130.208.137.190. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
Paper IV
4Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two
Dimensional (2+n) REMPI of HCl: Observation of a new electronic
state, Journal of Molecular Spectroscopy, available online, 2009.
83
Journal of Molecular Spectroscopy 255 (2009) 1–5
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy
journal homepage: www.elsevier.com/locate/jms
Two-dimensional (2 + n) REMPI of HCl: Observation and characterisation
of a new Rydberg state
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran *
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
a r t i c l e
i n f o
Article history:
Received 17 December 2008
In revised form 2 February 2009
Available online 21 February 2009
Keywords:
REMPI
Rydberg states
Photoionisation
Photodissociation
Multiphoton absorption
a b s t r a c t
Two-dimensional REMPI data, obtained by recording ion mass spectra for HCl as a function of two-photon
wavenumber, revealed a previously unobserved (2 + n) REMPI spectra for H35Cl and H37Cl with band origin for H35Cl at 82 521.2 cm�1. Analysis of the data, involving simulation calculations, relative ion-yield
determinations laser-power-dependence measurements and comparison with earlier experimental and
theoretical work allowed the upper state to be assigned as the g3R+(1), v0 = 0 Rydberg state with
B00 = 10.26 cm�1 for H35Cl.
2009 Elsevier Inc. All rights reserved.
1. Introduction
Hydrogen chloride is one of the most studied molecules in the
fields of spectroscopy, for a number of reasons. Quantitative data
on molecule-photon interactions are of interest in understanding
stratospheric photochemistry as well as being relevant to the photochemistry of planetary atmospheres and the interstellar medium
[1]. Furthermore, relatively intense single- and multi-photon
absorption in conjunction with electron excitations, as well as rich
band-structured spectra, make the molecule ideal for fundamental
studies in these fields.
Green et al. reported a comprehensive (2 + 1) REMPI study of the
HCl molecule [2–5]. In their papers more than 50 new states are reported and combined with previous work by others. Furthermore,
Tilford et al. reported 3P states [6] and Ginter and Ginter have reported a 1R� state [7] using single photon excitations. More recently
our group reported observations of U states using (3 + 1) REMPI
[8,9].
Despite numerous experimental studies on the photochemistry
and photophysics of the electronically excited states of HCl, only a
limited number of theoretical studies have been performed on the
excited states [10–16]. Of particular interest to our work presented
in this paper are ab initio CI (configuration interaction) calculations
carried out by Li et al. [14] and semi-empirical studies performed
by Liyanage et al. [15] concerning energy levels of 3R+ states of
* Corresponding author. Fax: +354 552 8911.
E-mail addresses: [email protected], [email protected] (Á. Kvaran).
URL: http://www.hi.is/~agust/ (Á. Kvaran).
0022-2852/$ - see front matter 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.jms.2009.02.002
HCl. Additionally, Greening has calculated the energy difference
for 3R� and 3R+ states, using Recknagel parameters [16].
No 3R+ states have been detected experimentally, despite being
theoretically predicted (10–11). In this paper we present a previously unreported spectrum which we believe to be due to transitions to a 3R+(1) state of HCl.
2. Experimental and method of analysis
Resonance enhanced multi-photon ionisation (REMPI) of jetcooled HCl gas was performed. Ions were directed into a time-offlight tube and detected by a MCP detector to record the ion-yield
as a function of mass and laser radiation wavenumber, i.e. to obtain
two-dimensional REMPI data.
The apparatus used is similar to that described elsewhere
[8,13,17,18]. Tunable excitation radiation was generated by an
Excimer laser-pumped dye laser system, using a Lambda Physik
COMPex 205 Excimer laser with a Coherent ScanMatePro dye laser.
The C-480 dye was used and frequency doubling was performed
with a BBO-2 crystal. The repetition rate was typically 10 Hz. The
bandwidth of the dye laser beam was about 0.095 cm�1. Typical laser intensity used was about 0.1–0.3 mJ/pulse. The radiation was
focused into an ionisation chamber between a repeller and an
extractor plate. Undiluted pure HCl gas sample (Merck–Schuchardt
OHG; purity >99.5%) was pumped through a 500 lm pulsed nozzle
from a typical total backing pressure of about 1.0–1.5 bars into the
ionisation chamber. The pressure in the ionisation chamber was
lower than 10�6 mbar during experiments. The nozzle was kept
open for about 200 ls and the laser beam was typically fired
2
K. Matthíasson et al. / Journal of Molecular Spectroscopy 255 (2009) 1–5
a
Experimental
3
3
f Δ1 ; S
f Δ1 ; O
3
1
f Δ1 ; R
3
D Π ; R-line ; J'=1
f Δ1 ; Q
3
f Δ1 ; P
1
D Π1 ; S
1
D Π1 ; P
1
1
D Π1 ; Q D Π1 ; R
3
J'=1
Experimental
New state ; Q
5
Calculated
7
*
*
82400
82500
Calculated
b
82600
*
*
82700
82508
82512
2xhν [cm ]
82516
82520
2xhν [cm-1]
-1
Fig. 2. Simulation of the H35Cl spectrum in Fig. 1b obtained by assuming twophoton resonance transitions from the ground state (X1R+(v00 = 0)) to a K = 0 upper
state (Hunds case (b)), Q-branch lines. J0 = J00 numbers are indicated.
35
H Cl
Table 2
Spectroscopic constants for HCl derived from the simulation of the new spectral band.
37
H35Cl
H37Cl
H Cl
82508
82512
82516
-1
2xhν [cm ]
82520
Fig. 1. (a) (2 + n) REMPI spectrum of HCl derived by recording H35Cl+. Overall
simulation of the new band (see b) is shown at bottom, obtained for two-photon
resonance transitions from the ground state (X1R+(v00 = 0) to a K = 0 upper state.
The calculated spectrum shows relatively strong Q-branch lines, whereas S- and Obranch lines are weak and not detectable in the experimental spectrum. Peaks due
to transitions to the Rydberg states f3D1 and D1P1 have been assigned [2]. Peaks
marked with asterisks are due to transitions to the V1R+, v0 = 9 ion-pair state [2]. (b)
(2 + 1) REMPI spectra of the new system derived by recording the H35Cl+ and H37Cl+
ions.
B0 [cm�1]
D0 [cm�1]
m00 [cm�1]
10.26 ± 0,02
10.27 ± 0,02
0.0010 ± 0,0003
0.0009 ± 0,0003
82 521.2 ± 0.5
82 521.0 ± 0.5
the REMPI spectra. Line positions were also compared with hydrogen chloride rotational lines reported by Green et al. [2–4]. Care
was taken to prevent saturation effects as well as power broadening by minimising laser power.
a
J’
8
6
4
500 ls after opening the nozzle. Ions were extracted into a timeof-flight tube and focused onto a MCP detector, of which the signal
was fed into a LeCroy 9310A, 400 MHz storage oscilloscope as a
function of flight time. Average signal levels were evaluated and
recorded for a fixed number of laser pulses to obtain the mass
spectra. Mass spectra were typically recorded in 0.05 or 0.1 cm�1
laser wavenumber steps. Spectral points were generally obtained
by averaging over 100 pulses. The power dependence of the ion
signal was determined by integrating the mass signals repeatedly
and averaging over a large number of pulses. Laser calibration
was performed by recording an optogalvanic spectrum, obtained
from a built-in Neon cell, simultaneously with the recording of
2
H+
H35/37Cl+
b
35
35
Cl
Table 1
Peak positions for the new band (Q branches) for H35Cl and H37Cl (cm�1).
J0
H35Cl
H37Cl
1
2
3
4
5
6
7
8
82 520.8 ± 0.5
82 519.7 ± 0.5
82 518.5 ± 0.5
82 517.2 ± 0.5
82 515.3 ± 0.5
82 512.8 ± 0.5
82 509.4 ± 0.5
82 504.4 ± 0.8
82 520.6 ± 0.5
82 519.6 ± 0.5
82 518.4 ± 0.5
82 517.2 ± 0.5
82 515.2 ± 0.5
82 512.8 ± 0.5
82 509.8 ± 0.5
+
H Cl
32
34
37
H Cl
+
36
38
+
40
42
Mw [amu]
Fig. 3. Mass spectra for Q lines in the new spectral system (excitation region
82 508–82 522 cm�1). (a) For rotational lines corresponding to J0 = J00 = 1–8. (b) For
rotational line corresponding to J0 = J00 = 6.
3
K. Matthíasson et al. / Journal of Molecular Spectroscopy 255 (2009) 1–5
0.025
Cl +/ HCl + Ratio.
0.02
0.015
0.01
0.005
0
1
2
3
4
5
6
7
8
J'
Fig. 4. 35Cl+ over H35Cl+ ion signal ratios (I(35Cl+)/I(H35Cl+)) for the Q-branch
rotational lines in the new spectral system corresponding to J0 = J00 = 1–8.
Spectra were simulated by comparison of experimental REMPI
spectra and calculated spectra for two-photon absorption, as has
previously been described [13,19–21]. The method is based on
evaluations of rotational line positions derived from rotational
constants and line intensities obtained from relevant Hönl–London
factors [22] which are characteristic for electron angular momentum quantum numbers of states involved.
to K = 1 or 2 states (or to X = 1 or X = 2 states in Hunds case (c))
could be ruled out due to structural differences in the Q-branch,
and to nonobservable P- and R-branch lines. Spectroscopic constants derived from simulations of the H35Cl and H37Cl spectra
are listed in Table 2. The rotational constants B0 , being close to
those for the ground states of the neutral and ion species,
X1R+) = 10.439826 cm�1
and
Bv þ ¼0 (H35Cl+,
(Bv00 = 0(H35Cl,
X2P) = 9.79303 cm�1 [23]), are typical values observed for unperturbed or only slightly perturbed Rydberg states [2]. The small isotope shift observed for the two isotopomers suggests that the
spectra correspond to transitions to v0 = 0.
Fig. 3 shows mass spectra derived from the excitations via the
J0 = 0–8 levels in the new system. Strong signals are found for
HCl+, whereas weak H+ signals are observed. Expansion of the mass
spectra in the region of the chlorine containing ions revealed very
weak 35Cl+ ion signals for the maximum at J0 = 6 (see Fig. 3b). A plot
of 35Cl+ ion signals over H35Cl+ ion signals (i.e. ‘‘normalised 35Cl+
ion signals” [13]) as a function of J0 shows a ratio for J0 = 6 which
contrasts sharply with those observed for J0 = 1–5, 7–8 (Fig. 4). This
observation is typical for a transition to a Rydberg state which only
couples very weakly to the V1R+ (X = 0) ion-pair state such as to
X > 0 singlet states [13] or to triplet states [24,25] showing enhanced Cl+ ion signal for near-resonance interactions between a
Rydberg state level and an ion-pair level [13]. This is consistent
with the energies derived for J0 levels for the new state and the
V1R+(v0 = 9) where the energy-gap is found to be smallest for
J0 = 6, DJ0 = 0 (see Fig. 5 and Table 3). Furthermore, power-dependence measurements for the H35Cl+ and H+ ion signals revealed
these to behave proportionally with laser power cubed and laser
3. Results and analysis
Fig. 1a shows a (2 + n) REMPI spectrum in the region of 82 370–
82 710 cm�1 obtained by recording H35Cl+ ions as a function of
excitation wavenumber. Rotational peaks due to two-photon resonance transitions to the V1R+ (v0 = 9), D1P (v0 = 0) and f3D1 (v0 = 0)
states were identified, whereas a rotationally-structured spectrum,
not previously reported, was observed in the spectral region of
82 508–82 522 cm�1 (Fig. 1a and b). Peak positions are listed in
Table 1.
The new structure could be simulated by assuming two-photon
resonance absorption for Q-branch transitions to a K = 0 state in
Hunds case (b) approximation (see Fig. 2). Two-photon transitions
Table 3
Energies for the new state and for V1R+, v0 = 9 and energy differences, DE for DJ0 = 0
(cm�1).
J0
New state
V1R (v0 = 9) [4]
DE
1
2
3
4
5
6
7
8
82 541.7 ± 0.5
82 582.3 ± 0.5
82 643.7 ± 0.5
82 725.7 ± 0.5
82 827.9 ± 0.5
82 950.2 ± 0.5
83 092.2 ± 0.5
83 253.1 ± 0.8
82 847.17
82 861.81
82 883.27
82 911.64
82 946.14
82 986.73
83 029.23
�305.5
�279.5
�239.6
�185.9
�118.2
�36.5
63.0
3
83.4x10
83.2
-1
2 xh ν [cm ]
J’=7
83.0
J’=6
J’=0
82.8
1 +
V Σ (v'=9)
82.6
3
82.4
+
New state / g Σ1
J’=1
Fig. 5. Rotational energy levels derived from REMPI spectra for the new state (g3R+(1)) (left) and the V1R+(v0 = 9) state (right). The strongest near-resonance interactions
between the rotational states closest in energy with equal J0 values for J0 = 6 and 7 are indicated with arrows. Interaction strength for J0 = 6 >Interaction strength for J0 = 7.
4
K. Matthíasson et al. / Journal of Molecular Spectroscopy 255 (2009) 1–5
a
K J
6
6 7
5
5
4
5
6
4
+
+
+
4
5
3
-
+
-
(b)
3
3 4
2
2
3
1
2
0 1
-
4
-
3
3Σ -
(0+)
b
5
+
-
4
+
3
+
-
2
+
+
+
+
-
5
+
4
5
-
1
3
1
+
0
J
+
+
+
+
5
6
4
-
4
5
3
+
+
+
+
3
3 4
2
-
2
3
1
+
+
+
1
1 2
0
-
0 1
+
+
2
-
1
2
+
0
X1Σ+ (0+)
6
(c)
-
4
+
3
-
2
+
1
-
0
(0-)
+
-
5
+
4
+
-
3
+
2
+
-
1
5
(1)
3Σ+
J
J
7
-
(b)
2
-
K J
6
6 7
5
4
5
(1)
-
+
+
+-
6
(c)
+
+
+
1
1 2
0
7
-
-
J
J
J
-
5
+
4
-
3
+
2
-
1
+
0
X1Σ+ (0+)
Fig. 6. Schematic energy levels marked with parities (+/�) and relevant quantum numbers (J, K) as well as selected two-photon transitions, (a) for 3R� (Hunds case (b); left),
3 � +
R (0 ) and 3R�(1) (Hunds case (c); middle) and the ground state (X1R+; right). Transitions shown as arrows refer to allowed two-photon transitions for a particular J00 (J00 = 3)
based on Hunds case (b) approximation. (b) For 3R+ (Hunds case (b); left), 3R+(0�) and 3R+(1) (Hunds case (c); middle) and the ground state (X1R+; right). Solid arrows are
allowed two-photon transitions for a particular J00 (J00 = 3) based on Hunds case (b) approximation, whereas dashed arrows are forbidden transitions.
power to the fourth, respectively, as expected for a near-diabatic
Rydberg state [13]. These observations further support the energetics for the new state and rule out an X = 0 assignment. Therefore the new, K = 0, state must be a triplet state, i.e. a 3R state.
Four low-lying 3R Rydberg states, with the configuration
r2p3[2P]4pp, are expected to be found in this energy region, the
g3R�(0+), g3R�(1), g3R+(0�) and g3R+(1) states, assuming these to
belong to Hunds cases intermediate between (b) and (c) [26].
Whereas the g3R�(0+) and g3R�(1) states have been observed
(m0 = 83 087.7 cm�1 and m0 = 83 263.6 cm�1, respectively) both in
absorption [7] and in (2 + 1) REMPI [2,3], the g3R+(0+) and
g3R+(1) have not. Fig. 6a and b shows schematic energy level structures for the 3R� (Fig. 6a) and 3R+ (Fig. 6b) states in the Hunds
cases (b) and (c) representations and energy levels for the ground
state (X1R+). Parities of levels are indicated as + and �. Strong sigX1R+ trannals are observed in (2 + n) REMPI for the g3R�(0+)
sitions whereas weak(er) signals are observed for the g3R�(1)
X1R+ transitions corresponding to DJ = �1 (O lines), DJ = 0 (Q) and
DJ = +1 (R) only. This is indicated by broad and narrow double arrows for transitions from one selected ground state level (J00 = 3) in
Fig. 6a. Due to the two-photon excitation selection rules in terms of
the parities
þ$þ
or
�$�
new excited state of concern is the 3R+(1) state, which by comparX1R+ REMPI spectrum and by assuming
ison with the g3R�(1)
Hunds case (b) dominance will show negligible or no P and R lines.
Based on united-atom guideline-calculations made by Greening
in 1975 [16], where HCl was replaced by the argon atom, the two
3 +
g R states were predicted to be close in energy and lower than the
g3R�(0+) state by about 2000 cm�1 (i.e. m0 � 81 000 cm�1). Ab initio
multireference single- and double-excitation configuration interaction (MRD-CI) calculations, which, based on calculations for
known states, could be in error by several hundreds of wavenumbers [11,14], predict the g3R+ states to be located at about
81 300 cm�1 relative to the ground state [14]. The semi-empirical
effective Hamiltonian method, which allowed deperturbation of
several Rydberg states as well as the V1R+ ion-pair state of HCl,
predicts the origin of the 3R+ state to lie near the origin of the
zero-order d3P state (m0 = 81 932.5 cm�1), i.e. at an energy of about
81 860 cm�1 [15]. Taking into account the expected uncertainties
and the discrepancies in the theoretically-based predictions (see
Table 4), as well as allowing for possible deviation of the energies
of the g3R�(1) and g3R+(0�) states from zero-order 3R+ state due to
interactions and perturbations, we feel that m0 = 82 521.2 cm�1 for
the 3R+(1) state is a truthful value.
and in terms of J
Table 4
Calculated and measured excitation energies for the 3R+ state (cm�1).
DJ ¼ 0; �2
Ref.
Greening [16]
Li et al. [14]
Liyanage et al. [15]
E(3R+)
E(g3R+(1))
�81 000
81 305
81 860 ± 50
no transitions are to be expected for g3R+(0�)
X1R+. The latter
is indicated in Fig. 6b by dashed arrows. Hence we believe that the
This work
82521.2 ± 0.5
K. Matthíasson et al. / Journal of Molecular Spectroscopy 255 (2009) 1–5
Ab initio MRD-CI calculations [11,14] predict pronounced Rydberg-valence mixing in the 3R+ manifolds. Therefore large predissociation linewidths have been predicted for the v0 = 0 and 1
vibrational levels of the lowest bound 3R+ state, whereas these
are expected to decrease as v0 increases. This has been taken to
be consistent with the fact that the corresponding state has not
been identified by spectroscopic means. Our simulation calculations (Fig. 2), on the other hand, reveal rather sharp lines
(C � 0.6 cm�1), hence lifetimes s > 8.8 ps for the new state. A theoretical underestimation of the state energy as discussed above
could, however, affect locations of the curve crossings, hence the
lifetime estimates. Lack of earlier observation of the g3R+(1) could
therefore simply be due to relatively low transition strength (see
Fig. 1a). Mixing of states via spin-orbit interactions is considered
largely responsible for the detection of the band systems for the
spin-forbidden singlet to triplet transitions [3]. Thus the excitation
X1R+ will probably mainly borrow transition strength
g3R+(1)
from the D1P(1) spin-orbit interaction with 3R+(1), the D1P(1),
v0 = 0 state being very close in energy (see Figs. 1 and 2; m0
D1P(1), v0 = 0) = 82 489 cm�1 for H35Cl [2]).
4. Conclusions
A previously unobserved (2 + n) REMPI spectrum of HCl in the
two-photon resonance excitation region 82 508–82 522 cm�1 was
recorded and analysed. Spectra simulations allowed peak assignments
and
determinations
of
band
origins
(m0(H35Cl) = 82 521.2 cm�1), as well as rotational constants for
the upper state. The simulation calculations, along with ion-yield
analysis of mass resolved spectra, and laser-power-dependence
measurements for ion signals, revealed this spectral structure to
be due to a two-photon resonance excitation from the ground state
(X1R+(v00 = 0)) to a 3R(v0 = 0) Rydberg state. Based on previous
experimental observations of spectra due to resonance transitions
to the g3R�(0+) and g3R�(1) states, theoretical predictions of ener-
5
gies of g3R+ states (g3R+(0�) and g3R+(1)) and two-photon excitation selection rules, the new excited state is assigned as the lowest
energy g3R+(1), r2p3[2P]4pp, v0 = 0 Rydberg state.
Acknowledgments
The financial support of the University Research Fund, University of Iceland and the Icelandic Science Foundation is gratefully
acknowledged.
References
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[3]
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D.S. Green, S.C. Wallace, J. Chem. Phys. 96 (8) (1992) 5857–5877.
S.G. Tilford, M.L. Ginter, J.T. Vanderslice, J. Mol. Spectrosc. 33 (1970) 505–519.
D.S. Ginter, M.L. Ginter, J. Mol. Spectrosc. 90 (1981) 177–196.
Á. Kvaran, H. Wang, Molec. Phys. 100 (22) (2002) 3513–3519.
Á. Kvaran, H. Wang, J. Mol. Spectrosc. 228 (1) (2004) 143–151.
D.M. Hirst, M.F. Guest, Mol. Phys. 41 (6) (1980) 1483–1491.
M. Bettendorff, S.D. Peyerimhoff, R.J. Buenker, Chem. Phys. 66 (1982) 261–279.
J. Pitarch-Ruiz et al., J. Phys. Chem. A 112 (14) (2008) 3275–3280.
Á. Kvaran et al., J. Chem. Phys. 129 (17) (2008) 164313.
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F.R. Greening, Chem. Phys. Lett. 34 (3) (1975) 581–584.
Á. Kvaran, K. Matthíasson, H. Wang, Phys. Chem: Indian J. 1 (1) (2006) 11–25.
Á. Kvaran, Ó.F. Sigurbjörnsson, H. Wang, J. Mol. Struct. 790 (2006) 27–30.
Á. Kvaran, Á. Logadóttir, H. Wang, J. Chem. Phys. 109 (14) (1998) 5856–5867.
Á. Kvaran, H. Wang, Á. Logadóttir, J. Chem. Phys. 112 (24) (2000) 10811–
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Paper V
Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi,
Erlendur Jónsson, Two dimensional (2+n) resonance enhanced
multiphoton ionisation of HCl: Photorupture channels via the F-1
Delta(2) Rydberg state and ab initio spectra, Journal of Chemical
Physics, 129(16), 164313, 2008.
91
THE JOURNAL OF CHEMICAL PHYSICS 129, 164313 2008
Two-dimensional „2 + n… resonance enhanced multiphoton ionization
of HCl: Photorupture channels via the F 12 Rydberg state
and ab initio spectra
Ágúst Kvaran,a Huasheng Wang, Kristján Matthiasson, Andras Bodi, and
Erlendur Jónsson
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
Received 17 June 2008; accepted 15 September 2008; published online 27 October 2008
Mass spectra were recorded for 2 + n resonance enhanced multiphoton ionization REMPI of HCl
as a function of resonance excitation energy in the 82 600– 88 100 cm−1 region to obtain
two-dimensional REMPI data. Analysis of ion-mass signal intensities for excitations via the
F 12v = 0 – 2 and the V 1+v states as a function of rotational quantum numbers in the
intermediate states either revealed near-resonance interactions or no significant coupling between
the F 12 and the V 1+ states, depending on quantum levels. Ion-signal intensities and power
dependence measurements allowed us to propose photoionization mechanisms in terms of
intermediate state involvement. Based on relative ion-signal intensities and rotational line positions
we quantified the contributions of Rydberg and valence intermediate states to the photoionization
product formation and evaluated coupling strengths for state mixing. Time-dependent density
functional theory TD-DFT, equation-of-motion coupled cluster EOM-CC, and completely
renormalized EOM-CC calculations with various basis sets were performed to derive singlet state
potential energy curves, relevant spectroscopic parameters, and to calculate spectra. Experimentally
observed spectra and older calculations are compared with the reported ab initio results. © 2008
American Institute of Physics. DOI: 10.1063/1.2996294
INTRODUCTION
Hydrogen chloride is one of the most studied molecules
in the fields of spectroscopy1–17 and photoruptures i.e., photodissociation and photoionization18–23 for a number of reasons. Quantitative data on molecule-photon interactions are
of interest in understanding stratospheric photochemistry as
well as being relevant to the photochemistry of planetary
atmospheres and the interstellar medium.4 Furthermore, relatively intense single- and multiphoton absorption in conjunction with electron excitations as well as rich band structured
spectra make the molecule ideal for fundamental studies in
these fields. Last but not least, detailed studies of resonance
enhanced multiphoton ionization REMPI spectra of small
molecules such as HCl are of importance in order to determine relative populations of quantum states in conjunction
with frequent use of REMPI detection of product molecules
in reaction dynamics.11,24
Since the original work by Price in 1938 on the hydrogen halides,25 a wealth of spectroscopic data on HCl
has been derived from high resolution absorption
spectroscopy,1–4 fluorescence studies,4 and from REMPI
experiments.5–17 A large number of Rydberg states have been
identified, as well as the V 1+ ion pair state. A number of
spin-forbidden transitions are observed, indicating that spinorbit coupling is important in excited states of the molecule.
a
Author to whom correspondence should be addressed. Tels.: 354-5254694 and 354-525-4800. FAX: 354-552-8911. Electronic mail:
[email protected]. URL: http://www.hi.is/agust/.
0021-9606/2008/12916/164313/11/$23.00
Perturbations due to state mixing are widely seen both in
absorption2–4 and REMPI spectra.6,7,9,11,13,14,17 The perturbations appear either as line shifts3,6,7,9,13,14,17 or as intensity
and/or bandwidth alterations.3,6,7,9,11,13,14,17 Pronounced ion
pair to Rydberg state mixings are both observed
experimentally2,3,7,9,13,14,17,26 and predicted from theory.26,27
Interactions between the V 1+ ion-pair state and the E 1+
state are found to be particularly strong and to exhibit nontrivial rotational, vibrational, and electron spectroscopies.
Perturbations due to Rydberg-Rydberg mixings have also
been predicted and identified.3,11 Whereas most observed
perturbation effects are believed to be homogeneous in nature = 0,13,14,26,27 heterogeneous 0 couplings
have also been reported.14,17,26
Despite numerous experimental studies on the photochemistry and photophysics of the electronically excited
states of HCl, only a limited number of theoretical studies
have been performed on the excited states. The first ab initio
calculations reported on the excited states of HCl, by Hirst
and Guest only dealt with the valence states, emphasising
vertical electronic transitions.28 The pioneering work by Bettendorff et al.,27 based on configuration interaction calculations and on the use of large atomic orbital basis sets, has
served well for identifying and assigning electronically excited states, but is less useful for detailed quantitative comparison. More recently, Pradhan et al. have performed
ab initio calculations on the ground and excited states of the
HCl+ ion.29 Since the state-of-the-art work of Bettendorff
et al. in 1982, a number of standard methods have been
developed to handle excited states of molecules. Equation-
129, 164313-1
© 2008 American Institute of Physics
Downloaded 27 Oct 2008 to 130.208.167.39. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
164313-2
Kvaran et al.
of-motion coupled cluster EOM-CC theory30 has been
shown to reproduce experimental excitation energies very
well in certain cases.31 Recently, Pitarch-Ruiz et al. published calculations on vertical excitation energies to various
Rydberg states of hydrogen chloride using a coupled-cluster
approach.32 We feel that it would also be of interest to apply
such methods to study the potential energy curves relevant to
electronic excitations and photorupture processes in HCl.
Photorupture studies of HCl have revealed a large variety of photodissociation and photoionization processes.
Thus, photodissociation processes yielding excited states of
both hydrogen and chlorine atoms have been observed.33,34
Competition between autoionization and predissociation processes via a superexcited state has been identified and
analyzed.34 Superexcited states have been found to dissociate
into electronically excited atomic fragments as well as to the
H+ + X− ion pair.18 In a detailed two-photon REMPI study,
Green et al. reported HCl+, Cl+, and H+ ion formations for
excitations via large number of = 0 Rydberg states as well
as via the V 1+ = 0 ion-pair state, whereas excitations
via other Rydberg states are mostly found to yield HCl+
ions.6 More detailed investigations of excitations via various
Rydberg states and the V 1+ ion-pair state by use of photofragment imaging and mass-resolved REMPI techniques
have revealed several ionization channels depending on the
nature of the resonance excited state.19–22 Results are mostly
based on analysis of excitations via the E 1+ Rydberg state
and the V 1+ ion-pair state, which couple strongly to produce the mixed adiabatic B 1+ state with two minima, but
to a lesser extent on analysis of excitations via triplet states,
which show no coupling with the ion-pair state. These studies reveal characteristic ionization channels which can be
summarized with reference to Fig. 1 as follows. For clarity
we will distinguish between 1 resonance noncoupled diabatic Rydberg state excitations and 2 resonance noncoupled diabatic ion-pair excitations see Fig. 1b. The
former could correspond to transitions via triplet Rydberg
states which have not been found to couple to the ion-pair
state, whereas the latter is an imaginary case of a “noncoupling” V 1+ state. Notice that in the case of a transition to a
Rydberg state which couples to the V 1+ state, as well as to
the V 1+ state itself which does mix with a number of
Rydberg states, both groups of excitation channels 1 and 2
will be involved. This is because it involves excitations to
the adiabatic states which are obtained by a combination of
the diabatic noncoupling states. Therefore those excitations
will show characteristics according to the mixing of the diabatic components.
1
2
An ionization via a noncoupled diabatic Rydberg state
is found to involve i one-photon ionization of the
Rydberg states to form the molecular ion HCl+, followed by ii a second one-photon excitation to a repulsive ion state 22 and dissociation see Figs. 1a
and 1b to form H+. HCl+ could be formed partly by
direct ionization and partly by autoionization.19
Several ionization channels, via the noncoupled diabatic ion-pair state, have been proposed,19–22 involving
iii one-photon autoionization via a repulsive superex-
J. Chem. Phys. 129, 164313 2008
FIG. 1. HCl energetics. a Potential energy curves, asymptotic energies
right, and vibrational levels in the Rydberg states F 12 and E 1+v
= 0 – 2 and in the V 1+ ion-pair state v = 10, 14, and 18. The potential
curves for the F and V states are Morse potentials solid curves derived
from experimental data in Refs. 6 and 14 F 12 and 6 and 52 V 1+.
Other potential curves dotted curves are based on theoretical calculations
in Ref. 27 E state and 29 ion states and superexcited state HCl**. The
arrows represent excitations relevant to 2 + n; n = 1 , 2 REMPI via the
F 12v = 1 left and the V 1+v = 14 states. b Schematic diagram
showing major ionization channels following excitations 1 to diabatic Rydberg states left of vertical broken line; channels i and ii and 2 to a
hypothetical diabatic V 1+ ion-pair state right of vertical broken line; channels iii and vii. The arrows represent excitations relevant to 2 + n; n
= 1 , 2 REMPI. Fragment and excited state species are indicated. Ions
formed are highlighted with circles. Main ion formations HCl+, H+, and
Cl+ are indicated with bold circles. Total number of photons is indicated to
the left. See text for further clarification.
cited state which correlates with H + Cl* to form HCl+
largely in high vibrational v+ levels,19 followed by
iv a second one-photon excitation to a repulsive ion
state 22 and dissociation analogous to ii, v onephoton excitation to repulsive triplet superexcited
states,20,21 forming H and Cl* Cl* = Cl*4s , 4p , 3d,
followed by one-photon ionization of Cl* to form Cl+,
vi one-photon excitation to a repulsive superexcited
state HCl* , 1+, forming H*n = 2 and Cl 2P1/2, followed by one-photon ionization of H*n = 2 to form
H+, and vii one-photon excitation to a bound superexcited state A 2+ 1+, which acts as a gateway
state to dissociation into the ion-pair H+ + Cl−.22 The
last channel was found to be V 1+-vibrational-state selected. More channels have been proposed20,22 via the
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164313-3
J. Chem. Phys. 129, 164313 2008
2D REMPI of HCl
noncoupled ion-pair state, but these are believed to be
of minor importance.
Thus, based on this overall ionization scheme, Cl+ and
Cl− are characteristic indicators for the ion-pair state contribution. H+ formation clearly is both indicative of the ion pair
and the Rydberg state contribution. However, its major formation pathway is found to be the fragmentation channel vi
indicative of excitation to the ion-pair state. HCl+ formation
is the main ion formation channel via Rydberg state excitation channel i under low power conditions. There are reasons to believe that the HCl+ contribution to ion formation,
via excitation to the V state, is rather small. For example, de
Beer et al. have shown that the main source of photoelectrons arising from excitation of the v = 9 level of the V state is
the photoionization of the excited hydrogen and chlorine
atoms10 and Green and Wallace have observed a large contribution of the photofragmentation channels upon excitation
of the E and V states.9 Furthermore, Chichinin et al. found
rather limited contribution of HCl+ in high v+ levels for excitations via the V state, v = 12. Hence we believe that the
HCl+ formation is mainly an indicator for the Rydberg state
contribution.
In this paper, we use a two-dimensional 2D REMPI
approach, obtained by recording ion-mass spectra as a function of the laser frequency, to study the photorupture dynamics of HCl for two-photon resonance excitations via the
F 12 Rydberg state and the V 1+ ion-pair state. Quantum
level dependent ion-signal intensities, consistent with nearresonance couplings, are observed for H 35Cl and H 37Cl.
Coupling strengths W12 can be derived from signal intensity
and line shift analysis. Proposed mechanisms for resonance
diabatic Rydberg state excitations are supported by ionsignal power dependence studies. Furthermore, we calculated potential energy curves relevant to the abovementioned processes by various ab initio methods and
performed comparisons with experimental data and calculations by others. We carried the theoretical treatment a step
further and evaluated v-dependent rotational constants and
calculated the corresponding “ab initio REMPI spectra” for
comparison with the experimental data.
EXPERIMENTAL
REMPI of jet cooled HCl gas was performed. Ions were
directed into a time-of-flight tube and detected by a microchannel plate MCP detector to record the ion yield as a
function of mass and laser radiation wavenumber to obtain
2D REMPI data.
The apparatus used is similar to that described
elsewhere.16,35 Tunable excitation radiation in the
227– 242 nm wavelength region was generated by excimer
laser-pumped dye laser systems, using a Lambda Physik
COMPex 205 excimer laser, either with a Lumonics Hyperdye 300 or a Coherent ScanMatePro dye laser. Relevant dyes
were used and frequency doubling obtained with BBO-B or
BBO-2 crystals. The repetition rate was typically 5 or 10 Hz.
The bandwidths of the dye laser beam were about 0.05 cm−1
for Lumonics Hyperdye 300 and about 0.095 cm−1 for
Coherent ScanMatePro. Typical laser intensity used was
0.2 mJ/ pulse. The radiation was focused into an ionization
chamber between a repeller and an extractor plate. We operated the jet in conditions that limited cooling in order not to
lose transitions from high rotational levels. Thus, an undiluted, pure HCl gas sample Merck-Schuchardt OHG; purity
99.5% was used. It was pumped through a 500 m pulsed
nozzle from a typical total backing pressure of about
1.0– 1.5 bars into the ionization chamber. The pressure in the
ionization chamber was lower than 10−6 mbar during experiments. The nozzle was kept open for about 200 s and the
laser beam was typically fired 500 s after opening the
nozzle. Ions were extracted into a time-of-flight tube and
focused onto a MCP detector, of which the signal was fed
into a LeCroy 9310A, 400 MHz storage oscilloscope as a
function of flight time. Average signal levels were evaluated
and recorded for a fixed number of laser pulses to obtain the
mass spectra. Mass spectra were typically recorded in 0.05 or
0.1 cm−1 laser wavenumber steps. Spectral points were generally obtained by averaging over 100 pulses. The power
dependence of the ion signal was determined by integrating
the mass signals repeatedly and averaging over approximately 1000 pulses, after bypassing different numbers of
quartz windows to reduce power. Care was taken to prevent
saturation effects as well as power broadening by minimizing
laser power. Wavelength calibration was achieved by recording iodine atomic lines36 and by the strongest hydrogen chloride rotational lines reported by Green et al.8 The accuracy of
the calibration was found to be about 1.0 cm−1 on a twophoton wavenumber scale. Intensity drifts during the scan
were taken into account, and spectral intensities were corrected for accordingly.
RESULTS AND ANALYSIS
2D REMPI
Figures 2a and 2b show 2D REMPI data for HCl
H 35Cl: H 37Cl 3 : 1 in the two-photon excitation region of
85 300– 85 700 cm−1. Contour plots are shown below, and
REMPI spectra for different ion masses, as well as for total
mass signals are shown above. The REMPI spectra for individual ions were obtained by integrating signal intensities for
narrow time-of-flight hence mass ranges such as that
marked by the squared area in the lower part of Fig. 2b for
H 35Cl+. Figure 2b shows the Q branch rotational lines for
J = 2 – 9, F 12v = 1 ← ← X 1+v = 0 and for J = 8,
V 1+v = 14 ← ← X 1+v = 0 in the 85 320– 85 365 cm−1
excitation energy region. Rotational transitions due to
the F 12v = 1 ← ← X 1+v = 0 and V 1+v = 14
← ← X 1+v = 0 transitions have been identified and assigned. H+ signals are observed for all resonance transitions
involved. H 35Cl+ and H 37Cl+ ions are detected for all transitions within H 35Cl and H 37Cl, respectively, whereas 35Cl+
and 37Cl+ ions are observed for all V ← ← X transitions but
only for transitions to J = 8 in F 12v = 1 within H 35Cl
and H 37Cl, respectively see Fig. 2b. This observation for
the V ← ← X resonance transitions is in agreement with expectations, since the V state couples to a number of Rydberg
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164313-4
Kvaran et al.
J. Chem. Phys. 129, 164313 2008
FIG. 2. 2D REMPI contours below and REMPI spectra above for H+, 35Cl+, H 35Cl+, 37Cl+, and H 37Cl+ derived from HCl with isotope ratios in natural
abundance. J = J in the figures. a Excitation region of 85 300– 85 700 cm−1. Assignments for R and S rotational lines for F 12v = 1 ← ← X 1+v = 0
H 35Cl and for Q rotational lines for V 1+v = 14 ← ← X 1+v = 0 H 35Cl transitions are shown. b Excitation region of 85 320– 85 365 cm−1. Assignments for Q rotational lines for F 12v = 1 ← ← X 1+v = 0 H 35Cl and H 37Cl and for Q rotational lines for V 1+v = 14 ← ← X 1+v = 0 J = 8;
H 35Cl and H 37Cl transitions are shown.
states and will therefore show ion formations according to all
channels i–vii, mentioned above and shown in Fig. 1b.
The lack of Cl+ ions for all resonance transitions except to
v = 1, J = 8 in the F state suggests that negligible coupling
to the V state occurs for these states and that the ionization
follows channel 1 i.e., i and ii in Fig. 1b. The observed Cl+ signals for resonance excitations to F 12v = 1,
J = 8 both for H 35Cl and H 37Cl are consistent with a nearresonance interaction, F 12v = 1, J = 8 ↔ V 1+v = 14,
J = 8 in agreement with earlier reported data on line shift
analysis for H35Cl.14
For convenience and to help with interpretations we
evaluated normalized ion-signal intensities INM+ defined
in the following way: Ion intensities IM+ detected via
Rydberg state excitations were normalized with respect to the
HCl+ ion intensities the main Rydberg state indicator,
IHCl+ to obtain INM+Ry = IM+ / IHCl+Ry. Ion intensities detected via the V ion-pair state excitations were
normalized with respect to the Cl+ ion intensities the V
ion-pair state indicator, ICl+ to obtain INM+v
= IM+ / IHCl+v. Figures 3a–3d show normalized ion
intensities for H 35Cl and H 37Cl for various resonance excitations derived for constant laser power. Figure 3a shows
that not only do Cl+ ions appear, following resonance excitations to F 12v = 1, J = 8, but H+ ion signals are also
found to be enhanced with respect to HCl+ i.e., the main
Rydberg state indicator for resonance excitations to
F 12v = 1, J = 8 compared to J 8. This is due to opening up of the H+ excitation channels iv, vi, and vii via
V 1+v = 14, J = 8, of which channel vi is believed to be
the largest.22 Judging from normalized HCl+ signals for
V 1+v = 14, J = 0 – 9 see Fig. 3b, HCl+ ion formation
also is enhanced for resonance excitations to V 1+v = 14,
J = 8. This is a further indication of the resonance coupling
from the V state side. The relatively large enhancement in the
HCl+ signal is an additional indication see previous arguments that HCl+ is a major indicator for the Rydberg state
contribution. The significantly lower relative signals for
H 37Cl compared to H 35Cl, shown in both Figs. 3a and 3b,
indicate smaller resonance coupling in the former case. The
overall drops in the relative signal strengths observed for
V 1+v = 14 ← ← X 1+v = 0 Fig. 3b with increasing
J for J 2 is due to decreasing nonresonance couplings
between V v = 14 and other Rydberg states, of which the
coupling to the Ev = 1 state plays the major role. An analogous effect is observed for the E 1+v = 1 ← ← X 1+v
= 0 transition, i.e., decreasing ICl+ / IHCl+ and
IH+ / IHCl+ ratios, hence decreasing coupling strength as
J increases J 1 see Fig. 3c.
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164313-5
J. Chem. Phys. 129, 164313 2008
2D REMPI of HCl
FIG. 3. Relative/normalized ion-mass signals. a IH+ / IHCl+ for H 35Cl and H 37Cl, in the case of ionization via the Rydberg state 1 F 12v = 1 as a
function of J; J = 4 – 9. b IHCl+ / ICl+ for H 35Cl and H 37Cl in the case of ionization via the ion-pair state 2 V 1+v = 14 as a function of J; J
= 0 – 9. c IH+ / IHCl+ and ICl+ / IHCl+ for H 35Cl in the case of ionization via the Rydberg state 1 E 1+v = 1 as a function of J; J = 0 – 5. d
ion-mass signals normalized with respect to IHCl+/the F1 state indicator IM+ / IHCl+1; M+ = H+, Cl+, and HCl+ for H 35Cl and H 37Cl, in the case of
ionization via the Rydberg state 1 F 12v = 1, J = 8 on right side of the broken vertical line and for J 8 average of data for J = 4 – 7 on left side of
the broken vertical line.
Laser power dependence vs excitation mechanisms
Ion intensities IM+ and intensity ratios IM+ / IN+
vary with laser power Plaser depending on the number of
photons needed to ionize n , m , . . . and on the transition
probabilities
IM+ = C Plasern ,
1
C is proportionality constant depending on the transition
probability. Based on Eq. 1 the following expressions can
be derived:
ref
log IM+ = n log Plaser
+C
2a
ref
log IM+/IN+ = n − mlog Plaser
,
2b
and
rel
is proportional to the laser power. This permits
where Plaser
easy extraction of photon numbers or photon number differences n − m for ionization processes from the slopes in relevant log-log plots.
Assuming that H+ and HCl+ ion signals, formed via
resonance excitation to a noncoupled Rydberg state, follow
channel 1 Fig. 1b, the sum of the H+ and HCl+ signals
will be a measure of the HCl+ ion formation, whereas the H+
formation is found by direct measurement of H+ signals. Figure 4a shows typical log-log plots relevant to testing these
criteria for the H+ and HCl+ ion formation obtained for resonance excitations via rotational levels other than J = 8, v
= 1 in the F state i.e., for ionizations via noncoupled diabatic Rydberg states. Based on slope evaluations, the numbers
of excitation photons for HCl+ and H+ formations are indeed
found to be 3 and 4, respectively, in agreement with the
model as presented in Fig. 1b.
Figure 4b shows log-log plots derived from a resonance excitation to the coupled Rydberg state F 12v = 1,
J = 8↔V 1+v = 14 , J = 8 by tuning to the S6 rotational line excitation from X 1+v = 0, J = 6, using minimum possible laser power. Assuming the ionization to follow
both channels 1 and 2 Fig. 1b, IH 35Cl+ will increase
with power cubed in the low power limit assuming negligible H+ to be formed by channel ii, in agreement with the
observation. Based on the work of Romanescu and
Loock,11,22 who observed maximum contribution to the H+
formation by channel v three-photon ionization for v
= 12 and gradually lower contribution as v increased from
12 to 15, a minor contribution from channel v is to be
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164313-6
J. Chem. Phys. 129, 164313 2008
Kvaran et al.
FIG. 4. Number of photons needed for ionization processes. a logIH 35Cl+ + IH+ and logIH+ vs
rel
for ionization via the resonance excitation
logPlaser
F 12v = 1 ; J = 4 ← ← X 1+v = 0 ; J = 3 / RJ = 4
rotational line. The numbers of photons needed for
H 35Cl+ and H+ formations are determined from the
slopes indicated as 3 and 4, respectively. See text for
further clarification. b logIH 35Cl+, logIH+, and
rel
for ionization via the resologI 35Cl+, vs logPlaser
nance excitation F 12v = 1 ; J = 8 ← ← X 1+v
= 0 ; J = 6 / SJ = 8 rotational line. See text for further
clarification. Ion intensities are normalized to IM+
rel
= 1.
= 1 for Plaser
expected for v = 14, whereas the major contribution to the
H+ formation is expected to be by the four-photon ionization
channel iii. This is consistent with the observed “photon
number value/n” of 3.82 0.6 for IH+. The reproducible
observation of n 3 for Cl+ formation, however, came as a
surprise. As seen in Fig. 1a, the lowest energy limit for Cl+
formation via a F 12v = 1 excitation requires a minimum
of four photons. A possible explanation for an observed photon number value lower than four could be that the chlorine
ionization occurs via formation of the short-lived Cl*4s
species = 2.0 ns,20 in which case spontaneous decay will
compete with laser excitation which occurs within the approximately 10 ns of the laser pulse duration.
State interactions and contributions vs excitation
mechanisms
The resonance coupling strengths for H 35Cl and H 37Cl
between the F and V states F 12v = 1 , J = 8 ↔ V 1+v
= 14 , J = 8 could be estimated from relevant rotational line
positions combined with estimates of mixing fractions from
ion-signal intensities in the following way. Level to level
interactions are represented by
Ei = 21 E01 + E02 21 4W122 + E01 − E0221/2 ,
E01
c2i =
1 E2 − 4W122
2
2E
5a
are weight factors for the state mixing. Since rotational lines
which belong to the same branch X = O , P , Q , R , S for mixing states equal J quantum numbers are due to transitions
from the same initial state, E1 and E2 can be replaced with
the corresponding transition energies or wavenumbers
ṽ1X and ṽ2X and E can be replaced with ṽ = ṽ1X
− ṽ2X,
c2i =
1 ṽ2 − 4W122
.
2
2ṽ
5b
The wavenumber differences for transitions to the two states
1 F 12v = 1, J = 8 and 2 V 1+v = 14, J = 8, for the
same rotational branches X ṽ1X , J = 8 − ṽ2X , J = 8
= ṽJ=8 = EJ=8 for H 35Cl and H 37Cl see, for example,
Fig. 2b for the Q branch were found to be on average,
H35Cl:
ṽ1Q,J = 8 − ṽ2Q,J = 8
= ṽJ=8 = EJ=8 = 11.3 cm−1 ,
3
E02
where
and
are the zero-order rovibrational level energies for the unperturbed states 1 and 2 and W12 is the matrix
element of the perturbation function/interaction strength.37
E1 and E2 are the resulting level energies of the perturbed
states for the high and low energy states, respectively. The
eigenfunctions of the perturbed levels 1 and 2 are related
to the eigenfunctions of the unperturbed states o1 and o2 as
1 = c1o1 − c2o2 ,
2 = c1o1 + c2o2 ,
where, for normalized wavefunctions and E = E1 − E2,
4
FIG. 5. Weight factors c21 as a function of interaction strength W12 for the
F 12v = 1 ; J = 8 1 state in the F 12v = 1 ; J = 81 ↔ V 1+v
= 14; J = 82 state mixing for H 35Cl solid curve and H 37Cl dotted curve
derived from Eqs. 5a and 5b and the spacing between corresponding Q
branch lines.
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164313-7
J. Chem. Phys. 129, 164313 2008
2D REMPI of HCl
H37Cl:
ṽ1Q,J = 8 − ṽ2Q,J = 8
−1
= ṽJ=8 = EJ=8 = 15.1 cm .
Therefore the fractional contributions c21 corresponding to
the high energy state according to Eqs. 5a and 5b vary
with W12 for 0.5 c21 1, as shown in Fig. 5. This gives
upper limits to the interaction strength, corresponding to a
resonance interaction i.e., E01 = E02 and c21 = 0.5,37 Wmax
12 ,
Wmax
12 =
EJ=8
2
=
ṽJ=8
2
6
as 5.65 and 7.55 cm−1 for H 35Cl and H 37Cl, respectively, in
the case of the F 12v = 1, J = 8 ↔ V 1+v = 14, J = 8
interaction.
Based on Eqs. 5a and 5b the actual interaction
strength W12 could be evaluated if the weight factor c21 for
the F state in the F ↔ V mixing v = 1, J = 8 hence the
weight factor for the V state, c22 = 1 − c21 was known,
W12 = EJ=81 − 4c21 − 1/22/2
= ṽJ=81 − 4c21 − 1/22/2.
7
As an attempt to estimate c21 we made use of the ion
signals as follows. The basic assumption is made that c21 is
equal to the sum of all normalized ion signals formed via the
noncoupled diabatic F1-state excitation iINM +i nc
divided by the total normalized ion signal formed via the
F-state excitations in the coupled adiabatic state F, v = 1,
J = 8 jINM +j c,
c21 =
iINM +i nc
jINM +j c
.
8
As an approximation to represent iINM +i nc we used the
averaged sum of normalized ion signals for ionizations via
rotational levels in the F state close to v = 1, J = 8 see J
= 4 – 7 and 9 in Fig. 3a, i.e., iINM +i J8, where insignificant coupling was observed see Fig. 3d. jINM +j c
was taken to be the sum of the normalized ion signals for
v = 1, J = 8 i.e., jINM +j J=8. Therefore, since normalized ion intensities for HCl+ are equal to 1, c21 is
c21 =
INH+J8 + 1
.
INH+J=8 + INCl+J=8 + 1
TABLE I. H 35Cl: Spacings between observed rotational energy levels E
= E1 − E2 =spacings between transitions of same rotational branches, X
v = ṽ1X − ṽ2X in the F 12v = 1 , J and the V 1+v = 14; J states
for equal J values, coupling strengths as a function of JW12, and fractional population in the state F 12v = 1 , J 1 c21.
9
Thus c21 = 0.60 and 0.75 were obtained for H 35Cl and H 37Cl,
respectively, which gives W12 5.54 and 6.54 cm−1 for
H 35Cl and H 37Cl, respectively see Fig. 5 and Table I. Notice that this assumes that the ion signals HCl+ and Cl+ for
F 12 v = 1, J = 8 originate from ionizations of the diabatic F1 and V2 states, respectively, whereas the H+ signal
originates from both sources according to the ionization procedure above, and presented in Fig. 1b. As mentioned before, a small contribution to HCl+ formation due to excitation
via the V state cannot be excluded, which makes the c21 estimated values c21 = 0.60 and 0.75 upper limit values, hence
the W12 values 5.54 and 6.54 cm−1 lower limit values.
35
5.54 W12 5.64 cm−1 Wmax
12 obtained for H Cl is in
good agreement with the value, 6 2 cm−1, obtained solely
J
E / ṽ
cm−1
W12a
cm−1
c2b
1
2
3
4
5
6
7
8
9
282.9
256.8
224.4
185.2
134.2
70.6
11.3
105.6
1.60
2.28
2.92
3.58
4.23
4.89
5.54
6.19
1.00
1.00
1.00
1.00
1.00
0.99
0.60
0.99
a
From Eq. 10 for W12 = 0.653 cm−1 see text.
Equations 5a and 5b.
b
from relative shifts of rotational lines in the F 12v = 1
← ← X 1+v = 0 spectrum for H35Cl.14
It has been argued that the F 1 state wave function may
be a linear combination of = 1 – 3 components, in which
case the weak perturbation observed is probably due to a
heterogeneous 0 coupling.11,14 Hence W12 will be
proportional to the square root of JJ + 1,38
JJ + 11/2
W12 = W12
10
and W12 0.653 and 0.771 cm−1 for H 35Cl and H 37Cl, respectively, derived from the approximate W12 values for
J = 8. This allows determination of W12 and c21 Eqs. 5a
and 5b values for J 8 see Table I for H 35Cl, J = 2 – 7
and 9. Notice that the weight factors c21 for J 8 are very
close to unity hence c22 0, i.e., negligible V-state contribution, which makes it understandable why insignificant ionization via the V 1+ state is observed in those cases.
Potential energy curves and ab initio REMPI spectra
Major perturbation effects observed in singlet excited
states of HCl are found to be due to interactions between
Rydberg states and the V 1+ = 0 ion-pair state. Some
less obvious mixing between Rydberg states has also been
predicted or observed indirectly.3,11 A rule of thumb is that
state interactions decrease as symmetry differences between
states increase, and with increasing differences between electronic spin and orbital angular momentum quantum numbers.
Thus there is a reason to believe that an ab initio potential
energy curve for the lowest energy singlet delta excited state
= 2 could be used to reproduce the experimental data
without taking into account state interactions, since the weak
mixing is only observed for the v = 1, J = 8 state.
Various ab initio calculations DFT and time-dependent
DFT with the B3LYP and the MPW1PW91 functionals,
MP2, MP4, CC and EOM-CC and completely renormalized
coupled cluster CR-EOM-CC calculations were performed
on the singlet states of HCl, and potential energy curves and
spectroscopic parameters were derived for the ground state
and the lowest energy state. The REMPI spectra for the
corresponding transitions were also evaluated. Potential en-
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164313-8
J. Chem. Phys. 129, 164313 2008
Kvaran et al.
ergy curves were determined using the GAUSSIAN03,39 the
40
41
NWCHEM, and the ACESII program packages. A restricted
Hartree–Fock wavefunction was employed as a reference
function in the MP and CC calculations, with all electrons
being correlated. CCSD and CCSDT calculations were carried out for the ground state and both EOM-CCSD42 and
CR-EOM-CCSDT43 calculations were used for excited
states. The augmented correlation consistent basis sets by
Dunning et al. aug-cc-pVnZ n = T , Q , 5,44 and its corevalence versions aug-cc-pCVnZ n = T , Q,45 were employed
as obtained from the basis set exchange.46 Additionally, the
aug-cc-pVQZ basis set was further augmented by adding 3s,
3p, 2d, and 1f diffuse functions for H exponents in atomic
units of 0.023 630, 0.006 211, 0.000 146, 0.084 800,
0.024 626, 0.002 088, 0.190 000, 0.054 531, 0.136 800, respectively, and 3s, 3p, 2d, 2f, and 2g functions for Cl exponents of 0.051 900, 0.018 823, 0.006 827, 0.037 600,
0.013 337, 0.004 813, 0.095 200, 0.035 681, 0.217 000,
0.082 460, 0.378 000, 0.143 640, respectively, to give the
basis set referred to as AQZ. Ground-state potential energy
curves and lowest energy potential energy curves for delta
orbital symmetry 1 states were fitted by Morse potential
functions Ur to determine average internuclear distances
re Å, dissociation energies De cm−1, vibrational freanharmonicity
parameters
quencies
e cm−1,
exe cm−1, and the rotational parameter Be cm−1,
Ur = T0 + De1 − exp− r − re2 ,
De
e = exe = 2e /4De,
11a
0.121 77,
Be =
h2
,
82r2e
11b
for T0 in cm−1, in g mol−1, and in Å−1. The nuclear
Schrödinger equation was solved numerically on the Morse
potentials to evaluate vibrational wavefunctions v and obtain averaged internuclear distances rv and corresponding
first and second order rotational parameters Bv and Dv as a
function of vibrational quantum number,
rv =
0
r2vdr,
Bv =
h2
,
82rv2
Dv = 4B3v/2e . 12
Finally, two-photon absorption spectra were calculated as has
previously been described.13–15,17 Thus rotational line positions were derived from the expression
ṽJ,v
←J,v
0
= ṽv←v + EJ,J ,
13
0
where ṽ v ←v is the band origin of the vibrational band
and EJ,J is the difference in rotational energies in the
ground and excited states, depending on the relevant rotational parameters. Relative line intensities Irel of spectra at
thermal equilibrium were evaluated from
Irel = CgJ++ 2sJ,Jexp− EJhc/kBT,
14
where gJ is the degeneracy of level J. + and + are the
one-photon perpendicular transition moments for transitions
via a virtual state in the two-photon excitation,14 treated here
as constants. sJ , J are relevant Hönl–London factors,
which depend on the quantum numbers J and J.47 EJ is
the rotational energy in the ground state and C is a constant.
Individual rotational lines were displayed as Gaussianshaped functions of wavenumbers Iṽ and bandwidth
bw cm−1 as48
Iṽ =
4 ln2
Irel
exp −
ṽ − ṽ0 − EJ,J2 .
bw
bw2
15
Assuming the ionization step, following the resonance excitation, to be independent of excitation wavelength, Iṽ as a
function of ṽ can be assumed to represent a 2 + n REMPI
spectrum.
Calculated spectroscopic parameters, experimental values, as well as values derived by or from Bettendorff et al.27
for the ground state and the F 1 state are listed in Tables II
and III. In general, average internuclear distances re , rv,
hence rotational constants Be , Bv, are found to be well reproduced by the DFT, MP2, MP4, and CC calculations for
the ground state, whereas the vibrational frequency e is
found to be slightly overestimated with the exception of
B3LYP calculations, where they are underestimated. For the
F 1 state the internuclear distance re is found to be overestimated by about 0.01– 0.02 Å in most calculations; hence
the rotational constants are slightly underestimated by about
0.5– 0.6 cm−1 for B0. The vibrational frequency is consistently found to be slightly overestimated. The discrepancies
in the rotational and vibrational parameters are larger for the
DFT calculations than for the CC calculations. The electronic
excitation energy T0 is overestimated in the EOM-CC calculations, whereas it is underestimated in the DFT calculations. The latter effect is explained by too rapid decay of
conventional exchange-correlation functionals as opposed to
the theoretical −1 / r asymptotic decay.49 However, as already
the ground-state geometry and thus rotational constant exhibited a larger deviation from the experimental than the
MP/CC results, we opted against improving the TD-DFT excitation energies by asymptotical corrections50 to the functionals. Generally the CC calculations, compared to the TDDFT calculations, were found to give parameters closer to
that observed, as one might expect. All in all, the use of the
largest basis set aug-cc-pV5Z and the completely renormalized equation-of-motion CCSDT calculation for the excited
state gave spectroscopic parameters and potential curve
shape closest to that observed experimentally and slightly
better than those calculated before by Bettendorff et al.27
Ab initio REMPI spectra for the F 12v = 0
← ← X 1+v = 0 process excited state: CR-EOMCCSDT/aug-cc-pV5Z; ground state: CCSD/aug-cc-pV5Z
are shown in Fig. 6 along with the REMPI spectrum obtained
by recording H 35Cl+ ion signal on a relative two-photon
wavenumber scale. The simulated spectrum is also shown in
the same figure. Overall rotational structure shapes, in terms
of band head shadings red/blue and spectral ranges, are
reproduced distinctly, whereas finer details are not always
reproduced well. The fine structure of the calculated REMPI
spectra, presented on a relative two-photon wavenumber
scale, is dependent on the calculated rotational parameters
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164313-9
J. Chem. Phys. 129, 164313 2008
2D REMPI of HCl
TABLE II. Spectroscopic parameters and their basis set dependence for the ground state of H 35Cl, X 1+
derived from various ab initio calculations and experiments.
Experiments
B3LYP/aug-cc-pVTZ
B3LYP/aug-cc-pVQZ
MPW1PW91/aug-cc-pVQZ
MP2/aug-cc-pVTZ
MP2/aug-cc-pVQZ
MP4/aug-cc-pVTZ
MP4/aug-cc-pVQZ
CCSD/AQZ
CCSD/aug-cc-pVTZ
CCSD/aug-cc-pVQZ
CCSD/aug-cc-pV5Z
CCSD/aug-cc-pCVQZ
CCSDT/aug-cc-pVTZ
CCSDT/aug-cc-pVQZ
CR-CCSDT/aug-cc-pVTZ
CR-CCSDT/aug-cc-pVQZ
re Å
e cm−1
exe cm−1
B0 cm−1
1.27455a
1.284
1.282
1.278
1.271
1.272
1.275
1.276
1.273
1.273
1.274
1.268
1.272
1.275
1.276
1.246
1.256
2990.946a,b
2957
2955
3007
3070
3055
3025
3009
3030
3053
3042
3079
3050
3016
3002
3022
3008
52.8186a,b
57
57
56
56
55
58
57
57
53
51
61
52
58
57
58
56
10.439 826c
10.19
10.21
10.27
10.40
10.39
10.33
10.32
10.36
10.36
10.53
10.44
10.38
10.32
10.31
10.33
10.32
a
Reference 52.
Reference 13.
B0 = Be − e1 / 2 for Be and e in Ref. 52.
b
c
and on the temperature, which was found to be about 100 K
from simulation analysis, but independent of the vibrational
e , exe and electronic T0 parameters. Hence the discrepancy between the calculated and experimental data is mainly
due to the underestimation of the rotational constant in the
upper state.
The slight but consistent deviations in the calculated
compared to the experimentally determined parameters, the
internuclear distances rcalc rexp, the rotational constants
Bcalc Bexp, the electronic parameters, and the vibrational
frequencies calc exp for the excited singlet state suggest that an extra bond stability factor is not taken into account in the calculation procedure. This could be due to
Rydberg-Rydberg state interactions. First, the weak perturbation mentioned above for the F 12v = 1, J = 8 state has
been attributed to a state mixing to give the F 12 state a
slight = 1 character, hence a heterogeneous coupling with
the V 1+ = 0 state.11,14 Second, spin-orbit coupling is
found to mix the F 12 and the f 32 states.12,51
TABLE III. Spectroscopic parameters and their basis-set dependence for the lowest energy singlet delta state, F 12, of H 35Cl, derived from various ab initio
calculations and experiments.
Experiments
Bettendorff et al.
e
TD-DFT B3LYP/aug-cc-pVTZ
TD-DFT B3LYP/aug-cc-pVQZ
TD-DFT MPW1PW91/aug-cc-pVQZ
EOM-CCSD/AQZ
EOM-CCSD/aug-cc-pVTZ
EOM-CCSD/aug-cc-pVQZ
EOM-CCSD/aug-cc-pV5Z
EOM-CCSD/aug-cc-pCVQZ
CR-EOM-CCSDT/aug-cc-pVTZ
CR-EOM-CCSDT/aug-cc-pVQZ
CR-EOM-CCSDT/aug-cc-pV5Z
CR-EOM-CCSDT/aug-cc-pCVQZ
T0 cm−1
re Å
e cm−1
81 555.3875a
1.295b
2608.3b
e
1.314
77 810
76 079
78 037
81 391
84 924
84 219
84 023
84 635
84 058
83 141
82 707
83 109
1.304
1.303
1.300
1.317
1.311
1.314
1.308
1.315
1.309
1.312
1.306
1.311
79 930
e
exe cm−1
49.35b
e
2715 /
2813e,f
2916
2881
2906
2681
2731
2711
2736
2719
2758
2736
2755
2740
69e,f
75
73
68
58
58
58
63
59
55
56
61
57
Be cm−1
B0 cm−1
B1 cm−1
10.415/
10.412c
9.96e
9.68e,f
10.12
10.14
10.18
9.92
10.02
9.97
10.06
10.01
10.05
9.99
10.09
10.02
10.3246/
10.3228d
10.143/
10.1447d
9.42e,f
9.83
9.86
9.90
9.65
9.75
9.71
9.79
9.74
9.79
9.74
9.81
9.76
8.90e,f
9.27
9.30
9.36
9.13
9.24
9.19
9.25
9.22
9.29
9.24
9.28
9.25
a
T0 = v0 − e / 2 − exe / 4; v0 from Ref. 6; e, exe from Ref. 14.
Reference 14.
Derived from fitting Bv vs v according to Bv = Be − ev + 1 / 2 for Bv from Ref. 6.
d
Reference 6.
e
Reference 27.
f
Derived from Morse potential fitting of a published potential curve in Ref. 27.
b
c
Downloaded 27 Oct 2008 to 130.208.167.39. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
164313-10
J. Chem. Phys. 129, 164313 2008
Kvaran et al.
FIG. 6. 2 + n REMPI spectra for HCl corresponding to the two-photon
excitation region of 82 730– 83 070 cm−1 on a relative two-photon wavenumber scale; experimental REMPI spectrum for H 35Cl+ top; simulated
two-photon absorption spectrum for the F 12v = 0 ← ← X 1+v = 0
transition, using rotational constants derived from experimental data Ref.
14 and rotational temperature, Trot = 100 K middle; ab initio REMPI spectrum for the F 12v = 0 ← ← X 1+v = 0 transition derived from the use
of potential curves calculated for the basis set aug-cc-pV5Z and the CRCCSDT calculation for the excited state bottom. Numbers for rotational
lines refer to J quantum numbers.
= 14, J = 8 mixing for H 35Cl and H 37Cl. The fraction evaluations coupled with a perturbation treatment for a level-tolevel interaction further allowed state interaction strengths to
be evaluated. We performed ab initio calculations at several
levels with a number of basis sets to derive potential energy
curves for the ground and excited singlet states. Morse fit
analysis of the ground state and the lowest energy 1 state
was used to evaluate the vibrational and rotational spectroscopic parameters, as well as to calculate two-photon absorption spectra. Calculated parameters and spectra were compared with experimentally evaluated parameters and REMPI
spectra as well as with older ab initio calculations. Slight but
significant variations in parameters and finer detailed spectroscopic structures are attributed partly to lack of state interaction assumptions in the calculations.
ACKNOWLEDGMENTS
The financial support of the University Research Fund,
University of Iceland and the Icelandic Science Foundation,
is gratefully acknowledged.
1
CONCLUSIONS
Ion-mass spectra were recorded as a function of twophoton wavenumbers corresponding to 2 + n REMPI to obtain 2D REMPI data for HCl for natural abundance isotopomers H 35Cl: H 37Cl 75: 25. Mass-resolved REMPI
spectra were obtained for the ion species H+, 35Cl+, H 35Cl+,
37 +
Cl , and H 37Cl+ in the two-photon wavenumber region of
82 600– 88 100 cm−1. Contour representations of the data are
found to be very useful for assigning the fine structure of
rotationally resolved REMPI spectra for both isotopomers.
Emphasis was placed on analysis of data relevant to ionizations via resonance excitation to the F 12v = 0 , 1 , 2
Rydberg states and the V 1+ ion-pair states close in energy,
in order to explore the mechanisms of photorupture photodissociation and photoionization channels. H iCl+; i = 35, 37
and H+ but no iCl+; i = 35, 37 ions were observed for excitations via all the rovibrational states F 12v = 0 , 1 , 2 except for F 12v = 1, J = 8, with H iCl+ ions as the dominating product. For F 12v = 1, J = 8 significant amount
of all ions were detected. This effect, along with anomalies
observed in relative ion intensities for excitations via the
V 1+v = 14, J = 8, as well as observed rotational line
shifts, is in agreement with a near-resonance state interaction, F 12v = 1, J = 8 ↔ V 1+v = 14 , J = 8, and gives
an important indication of how photoionization channels depend on the resonance intermediate states. Power dependence measurements for ion signals further support the proposed photorupture mechanism as presented schematically in
Figs. 1a and 1b and described above.
Cl+ ion formation is characteristic for ion-pair state involvements in the ionization processes of HCl. HCl+ ion formation is largely indicative of the Rydberg state involvement. This rather clear distinction between the two ionization
channels in terms of measurable signals allowed estimates of
the state fractions in the F 12v = 1, J = 8 ↔ V 1+v
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Paper VI
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of
acetylene: Gerade Rydberg states and photorupture channels, Chemical
Physiscs Letters, 458 (1-2), 58 (2008).
105
Chemical Physics Letters 458 (2008) 58–63
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
(2 + n) REMPI of acetylene: Gerade Rydberg states and photorupture channels
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran *
Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavík, Iceland
a r t i c l e
i n f o
Article history:
Received 27 February 2008
In final form 23 April 2008
Available online 29 April 2008
a b s t r a c t
Mass analysis studies were performed of ions detected after (2 + n) REMPI of acetylene for resonance
excitations to various gerade Rydberg states as a function of laser power. These data, along with
STQN/DFT calculations for dissociation of acetylene to C2 + H2, allowed an estimate of a threshold for photodissociation via gerade Rydberg states near 75 000–77 000 cm�1. Mechanisms are proposed regarding
+
+
(2 + 3) REMPI of acetylene to form Cþ
2 as well as C and H . Simulation analysis of partly-resolved rotational structured spectra recorded for different jet cooling allowed determinations of precise spectroscopic parameters and lifetime estimates for the Rydberg state, 4p 1Dg00.
2008 Elsevier B.V. All rights reserved.
1. Introduction
UV spectroscopy, photochemistry and photophysics of acetylene (C2H2) have been widely studied over the recent years. This
is partly due to its importance in interstellar space and cometary
atmospheres, where it is one of the most abundant species observed. There it has been considered to be a reservoir molecule
for the production of carbon-containing radicals which, in turn,
are involved in formation of larger organic compounds [1–3]. Furthermore, being the simplest unsaturated hydrocarbon, acetylene
is a fundamental unit in various organic photochemistry processes
and synthesis work.
Photodissociation of C2H2 has been the subject of numerous
experimental investigations, among which are studies by single[1,2,4–8], two- [9,10] and three- [2,4] photon resonance excitations. Photodissociation in acetylene is almost exclusively found
to occur via excitations to high-lying Rydberg states C2 H�2 . Due to
the strict u M g selection for excitation per photon interaction only
ungerade Rydberg states are accessed by one- and three- (odd
number) photon excitations from the 1 Rþ
g electronic ground state,
whereas gerade Rydberg states are accessible by two-photon (even
number) excitation. In view of this, and the additional restriction
on possible intersystem crossings based on the selection rules
u M u and g M g, it is not surprising that the mechanism and outcome of photodissociation differ in accord with on odd- or evennumber photon excitations. Fragmentation of C2H2 into C2H and
H is found to be dominant following single- and three-photon excitations [1,6,10]. Thus single-photon excitations of the Rydberg
states below the first ionisation potential reveal only the C2H product by emission spectra [6]. Two distinct dissociation channels, fol* Corresponding author. Fax: +354 552 8911.
E-mail address: [email protected] (Á. Kvaran).
URL: http://www.hi.is/�agust/ (Á. Kvaran).
0009-2614/$ - see front matter 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2008.04.104
lowing single-photon excitations, have been observed [7,8],
showing major differences with respect to internal energies and
angular distributions of the fragments C2H and H. In both channels
the observed decay dynamics are found to depend strongly on the
excited state of the parent molecule, C2 H�2 . In the case of a predissociation of the C2H2 (H1Pu) Rydberg state, it has been proposed
that it occurs via the bent valence state A1Au [7]. From less extensive two-photon excitation studies, on the other hand, fragmentations both into C2 + H2 and into C2H + H, are found to occur [9,11].
3
1
3
Thus C2 molecules in the X1 Rþ
g , a Pu, A Pu and d Pg states, H
atoms and H2 molecules have been identified by time-resolved
photofragment and emission detection studies [9,11]. Both
sequential bond-rupture mechanisms and concerted two-bond fission processes have been proposed to explain the C2 and H2 fragment formations [11]. Furthermore, long-lived bent isomers of
C2H2, as well as C2H intermediates, have been revealed experimentally. Tsuji et al. concluded from detailed REMPI analysis [9] that
ion fragment formations are predominantly due to ionisation of
neutral molecular fragments after predissociation. Because of the
characteristic predissociation channels, the ungerade and gerade
Rydberg states of acetylene are found to be short-lived, with lifetimes ranging from 50 fs to more than 10 ps [4,9]. Despite extensive experimental and theoretical studies on the photochemistry
of acetylene, many unsettled questions remain regarding the
mechanism of its photodissociation [9].
Rotational spectra due to electronic transitions recorded by
resonance-enhanced-multiphoton-ionisation (REMPI) [4,9,12,13],
absorption [4,14] or as fluorescence excitation spectra [9] suffer
from line broadenings depending on the Rydberg state lifetimes.
Hence either nonresolved or partly-resolved rotational structures
are observed, limiting detailed studies of the excited states involved. A number of rotationally-structured spectra due to transitions to ungerade Rydberg states have been recorded and analysed
to derive rotational parameters [13,14] and/or lifetime values [4]
59
K. Matthíasson et al. / Chemical Physics Letters 458 (2008) 58–63
Table 1
Band origins (m0) rotational parameters (B and D) and lifetimes (s) for C2H2 electronic states
Species
m0/cm�1
C2H2 ground state C2H2** Rydberg states
0
79 933
80 111h
80 154i
81 695h
82 562d
82 556 ± 2l
85 229h
85 425h
87 054h
87 884i
88 852i
89 266i
89 751i
90 630i
91 956n
C2H2+ ground ion state
a
b
c
d
f
h
i
j
k
l
m
n
o
u-States;
1
l
3dd, Uu
G 4sr, 1Puh
G 4sr, 1Pui
F0 3dd, 1Uuh
I 5sr, 1Puh
J 4dd, 1Puh
I 5sr, 1Puh
g-States;
X 1 Rþ
g
4p, 1Dgd
4p, 1Dg
v
B/cm�1
b
v=0
v = 0h
v4 = 1i
v2 = 1h
v=0
v=0
v = 0h
v = 0h
v2 = 1h
I 5sr, 1Pui
v2 = 2i
M 8sr, 1Pui
N10sr, 1Pui
X2Pu
v = 0i
v = 0i
v=0
1.17660a,b,c,d
1.105b
1.1023(1)i,j
1.100(1)i,j
1.104(1)i,j
(1.115)d,f
1.110 ± 0.001l
1.09955(54)i
1.107(2)i,j
1.0933(4)i,j
1.076(3)i,j
1.084(1)i,j
1.097(5)i,j
1.0932(7)i,j
1.1006(6)i,j
1.104d,o
D/10�6 � cm�1
1.61a,b,c
(1.5)b,f
1.5(2)i,j
(1.5)f,i
(1.5)f,i
–
0.99 ± 0.02l
2.1(7)i,j
5.5(33)i,j
0.9(5)i,j
(0) i,3
–10(2)i
26(20)i,j
(0)i,f
–6.0(5)i,j
s (lifetimes)
>10 psm
>10 psh,k
�1 psb,h
(>2.1 ps)d
>2.6 psl
�3 psh,m
�2 psh,m
�2 psh,i
Ref. [22].
Ref. [13].
Ref. [32].
Ref. [9].
Imposed value.
Ref. [4].
Ref. [14].
Errors (in parentheses) are expressed in units of the last digits.
Ref. [1].
This work.
Ref. [2].
Ionization potential [3].
Ref. [33].
for the excited states (see Table 1). Analyses of one-photon absorption spectra allowed determinations of fairly precise rotational
parameters [14] whereas more tentative values have been obtained from three-photon resonance excitation experiments [13].
Lifetimes of very short-lived states have been determined by
means of photofragment action spectroscopy [7]. Only spectra
due to transitions to one gerade Rydberg state with partially resolved rotational structures, have been reported for C2H2. Tentative
analyses of these spectra have been performed with an emphasis
on assigning the corresponding Rydberg states. Lifetimes of gerade
Rydberg states have been estimated from spectral bandwidths [9].
Rotational parameters have been derived for states with lifetimes
larger than about 1 ps only.
In this Letter we emphasise two-photon resonance excitations
of acetylene to gerade Rydberg states followed by ionisation, i.e.
(2 + n) REMPI. We present ion mass-analysis as a function of laser
excitation frequencies and laser power, combined with DFT/STQN
[15,16] calculations on C2H2 ? C2 + H2 surfaces, which, together
with energetic interpretations, allows determination of important
thresholds for fragmentation processes. Furthermore we report a
thorough analysis of partly rotationally-resolved structured specX 1 Rþ
tra due to the 4p 1Dg
g transition recorded for different
jet cooling, which allows a derivation of precise rotational and
vibrational parameters for the 4p 1Dg Rydberg state.
2. Experimental
Resonance-enhanced-multiphoton-ionisation (REMPI) of jetcooled C2H2 gas was performed in an ionisation chamber. Ions
were directed into a time-of-flight tube by electric lenses and detected by MCP plates to record ion yield as a function of flight time,
hence mass, and/or as a function of laser radiation wavenumber.
The apparatus has been described elsewhere [17–19].
Tunable excitation radiation in the wavelength region 227–
278 nm was generated by an Excimer laser-pumped dye laser sys-
tem, using a Lambda Physik COMPex 205 Excimer laser, a Lumonics Hyperdye 300 laser and frequency doubling with BBO crystals.
The repetition rate was typically 5 Hz for about 10 ns laser pulses.
The bandwidth of the dye laser beam was about 0.05 cm�1. Laser
pulse energies used were in the range 0.05–0.32 mJ/pulse. The
radiation was focused with a 200 mm focal-length quartz lens into
an ionisation chamber between a repeller and an extractor separated by 19 mm. Gas samples, either pure C2H2 (AAS Acetylene
2.6 from Linde gas) or mixtures of C2H2 and argon (typically in ratios ranging from 1:1 to 1:9 = C2H2:Ar) were pumped through a
500 lm pulsed nozzle from a typical total backing pressure of
about 0.6–1.8 bar into the ionisation chamber, which was maintained at lower than about 10�5 mbar pressure during experiments. The distance from the nozzle to the centre between the
repeller and the extractor was about 6 cm. The nozzle was held
open for about 200 ls and the LASER beam was typically fired
about 450 ls after opening the nozzle. Ions were extracted into a
70 cm-long time-of-flight tube and focused with an electric lens
onto a MCP plate detector. Voltage outputs as a function of flight
time were fed into a LeCroy 9310A 400 MHz storage oscilloscope.
Average voltage outputs for a fixed number of laser pulses were
evaluated and recorded on a computer to produce mass spectra.
Either mass peak heights or integrals were measured and averaged
for a fixed number of laser pulses as a function of laser radiation
wavenumbers to obtain REMPI-TOF spectra. Typically spectral
points were obtained by averaging over 200 pulses.
Wavelength calibration was achieved by recording iodine atomic lines [20] or by measurements of the strongest hydrogen chloride
rotational lines and comparison with those reported by Green et al.
[21]. The accuracy of the calibration was found to be about
±1.0 cm�1 on a two-photon wavenumber scale. Care was taken to
correct for possible drifts in signal intensity during long scans. Spectra intensities were corrected for possible intensity drift during the
scan. Furthermore, the effect of varying laser power was corrected
for by dividing the measured intensity by the power squared.
60
K. Matthíasson et al. / Chemical Physics Letters 458 (2008) 58–63
3. Results and analysis
3.1. Mass spectra: analysis and interpretations
Fig. 1, left, shows some REMPI spectra for two-photon resonance excitations obtained by recording maximum ion signals as
a function of excitation wavenumbers. The main spectral features,
all due to resonance transitions to gerade Rydberg states, have
been identified before [9,12], and are assigned accordingly. No
Rydberg states could be detected for higher energies, whereas
X1 Rþ
weak (1 + n) REMPI due to the transition A1Au
g was observed in the region 84 000–88 000 cm�1 on the two-photon wave�1
number scale, corresponding to the 42 000–44 000 cm region on
the one-photon wavenumber scale [22], here reported for the first
time. Ion mass spectra for ‘intermediate’ (see explanation below)
strength laser power is shown in Fig. 1, right, for the main spectral
features. These were obtained by subtracting mass spectra, for
background signals close by, from those recorded for the Rydberg
spectra in order to obtain contributions due to the resonance
excitations.
The parent molecular ion, C2 Hþ
2 , was found to be the dominant
ion species formed for the lowest energy 3p-Rydberg resonances (i)
72 744–74 554 cm�1 showing an increase with laser power, while
negligible or no other fragment ions were detected. This is analogous to what others have found [12]. The resonance signals at (ii)
75 760 cm�1 and 76 085 cm�1 (3p Rydberg states) show a number
+
of ion-fragment signals such as H+, C+, CH+, Cþ
2 , C2H , as well as
+
the parent molecular ion C2 Hþ
2 . The ratios of ion signals for H ,
þ
+
C , and C2 to that of the parent ion were found to increase proportionally with laser power for all the fragment ions. The Rydberg
resonance signals for the 4p states at (iii) 82 561 cm�1 and
83 006 cm�1 were far weaker than those for the 3p states, showing
the fragment ions dominating the parent ion. Only a weak C2H2+
ion signal is observed at 82 561 cm�1, and the fragment ion signals
all increased proportionally relative to that of the parent ion. No
�1
. The mass specsignificant C2 Hþ
2 could be observed at 83 006 cm
tra shown in Fig. 1, right, were chosen for ‘intermediate’ laser powers suitable to demonstrate the main features observed and trends
mentioned. These observations will now be interpreted and discussed with reference to the schematic energy diagrams in Fig. 2
and relevant observations made by others.
Lifetime [ps]
4p1Σg00
83006 cm
80
4p1Δg00
0.14
-1
82561 cm
>2.1
-1
C2H2+
79
3p1Σg21
76085 cm
3p1Δg2142
75760 cm
-1
0.35
-1
0.20
x1 0
3
H+
78
74554 cm
3p1Σg00
77
C2+
~0.1
-1
74279 cm
-1
73969 cm
3p1Δg42
C+
0.58
-1
0.47
76
72744 cm
3p1Δg00
Intensity
-20
-1
Mass [amu]
0
0.24
Mass
40
Fig. 1. REMPI spectra and corresponding mass spectra for acetylene; Rydberg state
assignments and lifetimes as well as REMPI spectra wavenumber values are
indicated.
All the Rydberg states in question are known to be predissociated. Both fragmentations into C2 + H2 and into C2H + H have been
postulated [9,11]. This has either been deduced from detections
of fragment species [9,11] or based on spectral bandwidth measurements, hence lifetime estimations [9]. Thus C2 in the excited
d3Pg state has been identified from detection of the fluorescence
due to the transition d3Pg ? a3Pu (Swan band) in all cases. The formation of C2 d3Pg has been interpreted as being due to predissociation of the gerade Rydberg states to C2H, followed by a further
photodissociation of C2H [9,11]. According to Tsuji et al. [9] there
is reason to believe that the fragment ions detected in REMPI, under comparable conditions to our cases (see above), are generally
formed from ionisation of neutral fragments rather than from
photofragmentation of the parent ion. In the case of excitation to
the 3p1Rg00 Rydberg state (74 279 cm�1 band), Hsu et al. propose
long-lived intermediates after predissociation [11]. Thus, for exam3
ple, C2 X1 Rþ
g and C2 d Pg molecules are believed to be formed primarily by a sequential bond-rupture mechanism via excitation of
long-lived C2H fragments, whereas some C2 in a3Pu is formed by
a concerted two-bond fission process via excitation of a long-lived
cis isomer (see Fig. 2a). Insignificant fragment ion formation observed for the (i) 72 744–74 554 cm�1 region could be due to slow
fragment formation processes on the timescale of the laser detection (about 10 ns laser pulses), causing only direct ionisation of
the Rydberg excited molecules to be observed. The sudden alteration from dominant parent ion formation to ion fragments, as well
as the parent ion-formation, as excitation increased to (ii)
75 760 cm�1 and 76 085 cm�1, could in principle be due to a sudden alteration in ionisation cross sections. Based on the energetics
�
for Cþ
2 formation from ionisation of C2 (or excited states C2 ), however, three additional photons (five photons in total; see Fig. 2b)
are needed in all cases; hence no sudden alteration in ionisation
is to be expected. Therefore this observation is probably due to
the opening up of new and/or faster dissociative channel(s) between 74 554 cm�1 and 75 760 cm�1. Dominant fragment ion formations via excitations to the high-lying Rydberg states (iii)
82 561 cm�1 and 83 006 cm�1) and comparable power dependence
of ion signals suggests that the dissociative channel(s) is of still
greater importance at higher energies. Slight parent ion formation
in the case of 82 561 cm�1 excitation is due to the relatively long
lifetime of the relevant Rydberg state (4p 1Dg00; s > 2.1 ps).
In an attempt to search for a threshold energy for C2 + H2 fragment formation we performed quantum-chemical calculations
based on DFT, using a QST- (quadratic synchronous transit [23])
based method and tracked energy paths starting from various singlet and triplet states of C2H2, via an intermediate cis-conformer, to
the ground state molecular fragments. Thus we looked for transition states in terms of energy and molecular shape. The calculations were performed using the software package GAUSSIAN 98
[24] and the STQN method [15,16] for B3LYP level of calculations
and various basis sets (3-21G, 6-31G, 6-31G*, 6-31G**). The lowest
energy transition states were obtained for the lowest energy singlet and triplet states of C2H2, but with some variation from one
calculation level to another. Comparable energies, for the transition states, were obtained for singlet and triplet states. The lowest
transition state energies obtained were about 75 000 cm�1 as seen
in Fig. 3 for the 6-31G* basis set. The structure for the singlet
transition state is shown in the figure. This result and the abovementioned experimental data lead us to believe that a faster dissociation process, leading to formations of C2 and H2, occurs in region
(ii) (75 760 cm�1 and 76 085 cm�1) compared to that in region (i)
(72 744–74 554 cm�1), involving atom migration to a cis configuration and crossing over a transition state (E = 76 000 ± 1000 cm�1)
on the lowest energy singlet surface for the cis conformer
(Fig. 3). The Cþ
2 observed in REMPI for excitations larger in energy
than 75 000 cm�1, will hence be formed after that, by three-photon
61
K. Matthíasson et al. / Chemical Physics Letters 458 (2008) 58–63
a
C2H2**
80x103
1
b
+ 0
4p Σg 0
1
0
1
1 2
4p Δg0
(6)
3p Δg2 4
1
#
H2C 2
+ 1
3p Σg 2
1
1
+ 0
3p Σg 0
H
C
H
C-C
1
(5)
+
H2
180
1
3p Δg2
2
3p Δ g4
H
+
CH 2
3
70
H2 + C2(d Πg)
1
+
(5)
(5)
160
+
(4)
0
3p Δ g0
3
140
E / cm-1
C( P)+CH2(X)
C 2H
+
C2
+
(4)
x10
3
(4)
120
(3)
60
(3)
+
1
H2 + C2(A Πu)
C2 H2
-1
100
80
3
H2 + C2(a Πu)
3p
C2H2**
50
(3)
4p
(3)
(2)
H 2+C 2 (d)
C + CH 2
60
H2 + C 2(X)
H + C2H(X)
H+C 2 H(X) H + C (X)
2
2
Fig. 2. (a) Energy diagram for neutral species (molecules, intermediates and atoms) relevant to photodissociation processes of gerade Rydberg states of acetylene, discussed
in the text. Broken lines (arrows) represent major intersystem crossing paths for 3p gerade Rydberg states 72 744–74 554 cm�1. Uncertainty limits for the energy of C + CH2
are indicated [25]. Transition corresponding to the Swan band is shown by a vertical arrow. (b) Energetics of ion- and excited state- species and photon excitations relevant to
two-photon excitations of acetylene by 72 744 cm�1 and 83 006 cm�1. Proposed fast dissociation channels for gerade Rydberg states 75 760–83 006 cm�1 are indicated by
broken arrows. Numbers in brackets represent the total number of photons needed for excitations.
100x10
-1
E / [cm ]
80
60
3
C —C
1.27 Å ± 0.025 Å
C —H
2.68 Å ± 0.05 Å
C —H
2.34 Å ± 0.05 Å
H —H
1.94 Å ± 0.04 Å
HCC
84°± 1°
CCH
109°± 1°
HCCH
6°± 1°
H1
C1
H2
C2
C2 + H2
40
20
0
H-C
2
C2 H2 ! Cð3 PÞ þ CH2 ðXÞ
C-H
4
tively, the reason could be that hot H2 species, formed by
dissociation, simply fly out of the ionisation region.
Comparable power dependence of the C+ and H+ ion fragment
�1
sugsignals and the Cþ
2 signal for excitations above 75 000 cm
gests that same number of photons is needed for all these ion formations, i.e. five photons in total. Hence, possible explanations for
C+ and H+ ion formations are as follows:
C+: Based on experimental determinations of bond strengths for
acetylene and vinylidine, the energy of dissociation of acetylene to
the ground state C and CH2 fragments,
6
8
10
12
14
16
18
Tracking points
Fig. 3. Minimum energy paths derived for STQN tracking [15,16] (6-31G* basis sets,
B3LYP calculation level) from the lowest energy singlet (solid curve) and triplet
(broken curve) states of C2H2 towards C2 + H2 dissociation via cis-conformer transition states. Structure of the cis-conformer transition-state on the singlet state
surface is shown.
ionisation of the C2 fragments (Fig. 2b). The explanation for Hþ
2 not
being observed could be that one more photon (four photons in total) is needed to ionise H2 in the ground state (see Fig. 2b). Alterna-
is found to be 72 800 ± 2100 cm�1 [25]. Considering the large uncertainty limit and/or possible barrier towards dissociation it could be
that a threshold (transition state) for transformations of Rydberg
excited states of acetylene, C2 H��
2 , via a trans conformer, leading to
formation of the neutral fragments C(3P) and CH2 (X), could be close
to the energy range 74 554 cm�1 and 75 760 cm�1 (see Fig. 2). Hence
C+ formations for excitations via Rydberg states higher than
75 000 cm�1 could be due to additional three-photon ionisation of
C(3P), thereafter.
H+: The observation of H+ ions for excitation energies higher
than 75 000 cm�1 could be associated with the energetics of the
H-atom ionisation step. Four photons are needed to ionise H-atoms
in its ground state (H(n = 1)), formed by photodissociation of C2H2
62
K. Matthíasson et al. / Chemical Physics Letters 458 (2008) 58–63
to H(n = 1) + C2H, for excitations into the lowest Rydberg states,
whereas three photons are needed to ionise H(n = 1) for Rydberg
states higher in energies than 75 000 cm�1 (see Fig. 2b).
Relative line intensities (Irel) of spectra at thermal equilibrium
were evaluated from
3.2. REMPI spectra for 4p 1Dg00
simulation analysis
where gJ00 is the degeneracy of level J00 . l+ and l0þ are the onephoton perpendicular transition moments for transitions via a
virtual state in the two-photon excitation [27], treated here as constants. s(J , DJ) are relevant Hönl-London factors, which depend on
the quantum numbers J0 and J00 [30]. E(J00 ) is the rotational energy in
the ground state (in cm�1). h, c, kB and T have the usual meanings
and C is an arbitrary constant. Individual rotational lines were
displayed as Gaussian-shaped functions of wavenumbers ðIð~mÞÞ
and bandwidth (bw/cm�1) as [31]
X 1 Rþ
g vs. rotational temperature;
Fig. 4a and b (top) show REMPI spectra due to the resonance
X 1 Rþ
transition 4p 1Dg00
g for different argon:acetylene ratios
and/or backing pressures, hence different jet cooling conditions.
We performed simulation analysis of a number of such spectra,
based on least square analysis of intensities using spectroscopic
parameters, bandwidth as well as rotational temperatures as variables, and searched for an unified solution in terms of the parameters and the bandwidth. This method allowed derivations of
precise parameter values despite only partly resolved rotational
structures.
A simulation analysis method analogous to that used before
[26–29] for analysis of two-photon absorption in diatomic molecules, based on derivations of line-strengths for linear molecules
[30], was used. Thus rotational line positions were derived from
the expression
~mJ0 ;v0
J 00 ;V 00
¼ ~m0v0
v00
þ DEJ0 J00
where ð~m0v0 v00 Þ is the band origin of the vibrational band and DEJ0 ,J00 is
the difference in rotational energies in the ground and excited
states, depending on the relevant rotational parameters [29].
a
Irel ¼ Cg J00 ðlþ l0þ Þ2 sðJ; DJÞ expð�EðJ 00 Þhc=kB TÞ
Ið~mÞ ¼
2
Irel
4lnð2Þ ~m � ~m�0 � DEJ0 J00
exp �
2
bw
bw
Finally the lifetime was derived from the relation
Bwðcm�1 Þ ¼ fwhmðcm�1 Þ ¼ 5:3=sðpsÞ
Spectra recorded for limited cooling could be simulated by
assuming a thermal distribution (i.e. Boltzmann distribution) as
seen in Fig. 4a, whereas a better fit was obtained for ‘colder’ spectra
by assuming two temperature components (see Fig. 4b). This latter
effect we attribute to a nonthermal/nonequilibrium rotational energy distribution in the beam showing as a population tail to higher J levels, as spacing between levels increases and relaxation slows
down. Results of simulations are shown in Table 1. A slight but significant difference in parameter values, compared to that derived
tentatively by others, was obtained. In order to further test the significance, we used the parameters derived by Tsuji et al. [9], and
obtained worse fits for experimental and calculated spectra.
Exp.
Intensity
4. Conclusions
Q
Calc
P
R
S
O
82.52
82.54
82.56
2xhν / cm-1
82.58
82.60x103
b
Intensity
-1
-2
Exp.
Calc.
-3
Calc.150K
-4
82.52
Calc.12K
82.53
82.54
82.55
82.56
82.57 82.58x103
2xhν / cm-1
Fig. 4. Simulations of jet-cooled REMPI spectra due to the 4p 1Dg00
X 1 Rþ
g transition (a) Simulation of a REMPI spectrum; rotational temperature, T = 220 K, Top:
experimental spectrum, middle: calculated spectrum, bottom: calculated rotational
line contributions. (b) Simulation of a REMPI spectrum assuming two rotational
temperature components (two Boltzmann rotational distribution components): (1)
T = 12 K; (93%), (2) T = 150 K, (7%).
Ions formed by (2 + n; n P 1) resonance-enhanced-multiphoton-ionisation (REMPI) of acetylene, via gerade Rydberg states,
were recorded as a function of laser power and frequency corresponding to the two-photon resonance excitation range 72 500–
83 100 cm�1. The parent molecular ion, C2 Hþ
2 was found to be the
main product for the excitations to the 3p Rydberg states in the
range 72 500–75 000 cm�1, while competition between parent ion
and fragment ion formations was found for the 3p Rydberg states
in the excitation region 75 500–76 200 cm�1. Fragment ion formations, on the other hand, were dominant in REMPI of the highest
observed gerade 4p Rydberg states between 82 500 and
83 100 cm�1. Fragment ion signals for H+, C+ and Cþ
2 all showed
analogous power dependence, different from that for the parent
ion. Tracking potential energies for dissociation of various triplet
and singlet energy-states of acetylene to C2 and H2, via a cis-conformer using the STQN method for various basis sets and the
B3LYP level of calculations, revealed energy minima for corresponding transition states in the energy region 75 000–
77 000 cm�1. In light of the work of Hsu et al. [11], who identified
a long-lived intermediate, most probably a cis-conformer, after
two-photon excitation to the 3p1Rg00 Rydberg state
(74 279 cm�1), our observations suggest that the lowest energy
transition state for the cis-conformer is a threshold for photodissociation of gerade Rydberg states to C2 and H2. Hence, Cþ
2 will be
formed by additional three-photon ionisation of C2 or by (2 + 3) REMPI of C2H2. Mechanisms are postulated involving (2 + 3) REMPI of
C2H2 to form C+ as well as H+ for resonance excitations larger than
about 75 000 cm�1.
REMPI spectra of partly-resolved rotational structured spectra
X 1 Rþ
corresponding to the transition 4p 1Dg00
g , recorded for
K. Matthíasson et al. / Chemical Physics Letters 458 (2008) 58–63
different jet cooling conditions, were simulated by a least square
analysis procedure. A search was made for a unified solution, in
terms of spectroscopic parameters and bandwidth, hence lifetime
estimate. This method allowed determination of precise parameter
values for the relevant excited Rydberg state.
Acknowledgements
The financial support of the University Research Fund, University of Iceland, and the Icelandic Science Foundation is gratefully
acknowledged. We would also like to thank Dr. Andras Bodi for
useful help with this project.
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[26] Á. Kvaran, H. Wang, J. Mol. Spectrosc. 228 (2004) 143–151.
[27] Á. Kvaran, H. Wang, B.G. Waage, Can. J. Phys. 79 (2001) 197.
[28] Á. Kvaran, H. Wang, Á. Logadóttir, J. Chem. Phys. 112 (2000) 10811.
[29] Á. Kvaran, Á. Logadóttir, H. Wang, J. Chem. Phys. 109 (1998) 5856.
[30] R.G. Bray, R.M. Hochstrasser, Mol. Phys. 31 (1976) 1199.
[31] Á. Kvaran, H. Wang, J. Ásgeirsson, J. Mol. Spectrosc. 163 (1994) 541.
[32] K.F. Palmer, K.N. Rao, Mickelso Me, J. Mol. Spectrosc. 44 (1972) 131.
[33] M.F. Jagod, M. Rosslein, C.M. Gabrys, B.D. Rehfuss, F. Scappini, M.W. Crofton, T.
Oka, J. Chem. Phys. 97 (1992) 7111.
5
Ion formation through multiphoton processes for HCl35-39,77
The photoionization of HCl is a complex multiprocess mechanism that
entails perturbations, photodissociations and predissociations. In this
chapter I will go over the ionization mechanism that are know or have
been suggested. Figure 17 shows all the mechanics discussed collected
into a single figure.
5.1 Formation of HCl+
HCl+ ions are generally only formed through ionization via a Rydberg
state via mechanism (1) shown in figure 17 a). However, electrons
excited to an ion-pair state are able to access Rydberg states by
perturbation.
5.1.1 Ionization via Rydberg states
The formation of HCl+ via a Rydberg state is the simplest of the
ionization mechanisms. HCl+ is formed by a simple two-step process, i.e.
the formation of excited HCl# followed by the direct ionization of the
excited molecule, forming HCl+.
5.1.2 Ionization via ion-pair state
HCl+ ions are probably never formed directly via ion-pair states, or at
most only a small fraction. However, HCl+ in considerable quantity has
been observed from ionizations via ion-pair states.19-21,39,40 The cause of
this is found to be a perturbation of the ion-pair state.
When two rotational levels with similar energy are perturbed, the
wavefunctions are overlapped allowing the electron to move from one
state to the other, thus being observed to have characteristics of both
states. The electron can therefore be excited into the ion-pair state, be
perturbed into a Rydberg state, and from there follow channel (i) and (ii)
shown in figure 17 a) forming an ion.
113
a)
(2+n)
HCl+*
(4)
HCl+*
H+ + Cl
H+ + Cl
(v)
(iv)
(ii)
HCl**
(T)
HCl+
(3)
H+
Cl+
HCl+
(vi)
HCl**
1+
HCl**[A]1+
H+ Cl*
H* +Cl
H+Cl*
(i)
H+ + Cl(vii)
(iii)
(2)
HCl*
(Ry, v´,J´)
H+Cl(V1+, v´,J´)
W12
(2)
(1)
(2+n)
(2+n)
b)
HCl+*
H+ Cl+
(5)
Cl+
H+ +Cl
(4)
HCl+
(3)
(ii)
(ix)
(4)
HCl**
(viii)
HCl*
(RyG, v´,J´)
(3)
(i)
(SO)
(2)
HCl*
(Ry, v´,J´)
SO
HCl*
3+
(3)
H+ Cl*
H + Cl(J =1/2,3/2)
(1)
Figure 17: Main ionization mechanisms of HCl. Figures a) and b) show possible
ionization channels via Rydberg (HCl*) and ion-pair states (H+Cl-). The
predissociation gateway mechanism forming H + Cl is included. Necessary
amount of photons for ionization are shown.
114
Since the rotational levels of the ion-pair state in HCl are generally
always perturbed by the Rydberg states close in energy, HCl+ is observed,
in different amounts though, for almost every observed rotational line of
the ion-pair state. Due to this fact there is a possibility that HCl+ is
formed directly from the ion-pair state as has been suggested as shown
for channel (iii) in figure 17 a).35-38 This should however be in small
amounts compared to the HCl+ formed via perturbation, as most low level
ion-pair rotational lines, which are perturbed the least, show only a very
limited HCl+ formation and the v’=4 ion-pair vibrational level shows no
discernable HCl+ at all.
5.2 Formation of H+
H+ ions are formed by several possible channels depending on whether
the ionization is through a Rydberg or ion-pair state.
5.2.1 Ionization via Rydberg states
For unperturbed rotational levels the formation of H+ is initially the same
as for HCl+ followed by a single-photon process that forms the H+ ion.
For perturbed rotational levels the electron is initially excited by a
multiphoton process into an energetically excited Rydberg state. Due to
the perturbation the rotational level gains ion-pair characteristics and the
electron can follow the same ionization mechanism as outlined for ionpair states (in other words it is perturbed into the ion-pair state).
However, one must bear in mind that the proportion of HCl# that is not
perturbed can continue to form H+ as outlined above.
5.2.2 Ionization via ion-pair state
The electron is initially excited to the ion-pair state by a multi-photon
process. The unperturbed electron then undergoes a single-photon
excitation to an unbound state, causing the molecule to dissociate into a
Cl atom and energetically excited H# atom which is ionized as shown in
figure 17 a) channel (vi).
For an electron perturbed into a Rydberg state the ionization mechanism
is the same as outlined for Rydberg states, i.e. excitation to HCl+
followed by a single-photon excitation forming H+.
115
Additionally it has been suggested that H+ can be formed directly from
the ion-pair state by a photodissociation of H+Cl- into H+ and Cl- as
outlined in figure 17 a) channel (vii).
5.3 Formation of Cl+
Cl+ ions are generally only formed through ionization via an ion-pair
state. However, electrons excited to a Rydberg state are able to access
ion-pair states by perturbation.
5.3.1 Ionization via Rydberg states
Cl+ in considerable quantity has been observed from ionization via
Rydberg states.19-21,39,40 The cause of this is found to be a perturbation
between the Rydberg state and a neighbouring ion-pair state. The electron
is perturbed into the ion-pair state followed with a single-photon
excitation to an unbound state, causing the molecule to dissociate into an
H atom and an energetically excited Cl# atom which is ionized as shown
in figure 17 a) channel (v).
Typically the rotational levels in the Rydberg states of HCl are perturbed
by the ion-pair state only in few specific cases. Thus, Cl+ is only observed
in considerable amount in cases where the energy difference of
comparable rotational levels is small, with the exception of the 1 states,
which show Cl+ formation for all observed rotational levels. This
selective appearance of the Cl+ ion is found to be an excellent diagnostic
tool when characterising new states.41,78
However there are observable Cl+ signals for rotational levels that should
not be perturbed by the ion-pair state. These signals are most likely due to
a predissociation of the HCl molecule, followed by the ionization of the
Cl atom as shown for channel (viii) figure 17 b). It is know that Cl atoms
are formed by predissociation in the HCl molecule, specifically through
the C-state. Therefore it is quite possible that these minute amounts of Cl+
ions that are formed are indeed formed via predissociation. It has also
been suggested that Cl+ can form directly via Rydberg states by
photoexcitation to inner walls of bound superexcited states as shown for
channel (ix) in figure 17 b), where the molecule is dissociated into H +
Cl* followed by ionization of the chlorine.
116
5.3.2 Ionization via ion-pair state
Like the formation of H+ via the Rydberg state, the formation of Cl+ via
an ion-pair state is somewhat straightforward. The electron is excited to
the ion-pair state by a multi-photon process. What follows is then a
single-photon excitation to an unbound state, causing the molecule to
dissociate into an H atom and an energetically excited Cl# atom which is
ionized ( channel (v)).
117
6
The use of mass analysis to
determine interaction constants
Based on this overall ionization scheme presented above, Cl+ ions are
characteristic indicators for the ion-pair state contribution, H+ formation clearly
is both indicative of the ion-pair and the Rydberg state contribution and HCl+
formation is the main ion formation channel via Rydberg state excitation under
low power conditions. There are reasons to believe that the HCl+ contribution
to ion formation, via excitation to the V1 state, is rather small.39 Therefore, it
has been found to be useful to define and work with normalized ion intensities
for Cl+ (IN(Cl+) and HCl+ (IN(HCl+)) as indicators for the separate (diabatic)
Rydberg and ion-pair states respectively, where IN(Cl+) is the Cl+ ion signal
intensity normalized to (divided by) the HCl+ ion signal intensity and vice
versa, i.e.:
IN(Cl+) = I(Cl+)/I(HCl+); Rydberg state indicator
IN(HCl+) = I(HCl+)/I(Cl+); ion-pair state indicator
In addition to the photofragmentation channels, mentioned above, further
dissociation of resonance-excited Rydberg states to form H + Cl and/or H
+ Cl* via predissociation of some gateway states could be important, as
predicted by Alexander et al.77 In such cases, further photoionization of
the Cl, Cl* and H fragments could also occur. Whereas the interactions
between the states involved could be of various kinds77, spin-orbit
couplings most probably are dominant.
Assuming a level-to-level interaction scheme to hold for the Rydberg-toion-pair states interactions, weight factors (fractions) for the state mixing
can be expressed as
1
c  
2
2
i
2
E  4 W12
2 E
2
(34)
for E = E1 - E2, where E1 and E2 are the resulting level energies of the
perturbed states (1 and 2) and W12 is the matrix element of the
119
perturbation function / interaction strength.39,72 In the case of
homogeneous ( = 0) interaction W12 is independent of the total angular
momentum quantum number, J´, whereas for heterogeneous ( > 0)
interactions W12 is expressed as28,39,79
W12 W12' ( J ´(J ´1))1 / 2 (35)
'
for constant W12 . W12 is related to the resulting level energies and the
0
0
zero-order level energies for the unperturbed state ( E1 and E2 ;
E 0  E10  E20 ) by
Ei 




1/ 2
1 0
1
2
E1  E20  4 W12  (E 0 ) 2
(36)
2
2
Assuming the mechanism discussed above to hold, we make the
following assumptions: Cl+ ion intensity observed (I(Cl+)) is proportional
2
to the fraction of HCl* in the ion-pair state (2; c2 ) as well as its fraction
2
in the Rydberg state (1; c1 ),
I (Cl  )   2 c22  1c12 (37)
Similarly the HCl+ intensity (I(HCl+)) is assumed to be proportional to
the same fractions,
I ( HCl  )   1c12   2 c22
(38)
For    2 /  1 ,   1 /  2 ,   1  (  2 /  1 ) and c1 1 c2 , the ratio
of I(Cl+) over I(HCl+) now can be expresses as
2

  c22 (1   )
I (Cl  )


I ( HCl  )
1  c22



2
(39)
There is a reason to believe that the contribution to the HCl+ formation by
excitation from the diabatic ion-pair state is small39, hence, that the ratio
of its proportionality factor (  2 ) to that for the HCl+ formation from the
diabatic Rydberg state,  1 , (i.e.  2 /  1 ) is negligible and  ~1. By
combining equations (34), (35) and (39) and assuming  =1 the
following expression is derived:
120
2



E ( J ´)  4 W12´2 J ´(J ´1) 
1


   
(1   )

2 E ( J ´)

 2

I (Cl  )




2
I ( HCl )

E ( J ´)  4 W12´2 J ´(J ´1) 
1


1 

2
2 E ( J ´)


(40)
for excitations via a Rydberg state.
Here  (   1 /  2 ), is a measure of the rate of formation of Cl+ via the
diabatic Rydberg state (the “gateway channel”) to that of its formation
from the diabatic ion-pair state, which is one of the major/characteristic
ionization channels. Hence  is a relative measure of the importance of
the “gateway channel”.
Comparably  (   2 /  1 ) measures the relative rate of the two
major/characteristic ionization channels, i.e. for the Cl+ formation for excitation
from the diabatic ion-pair state (  2 ) to the HCl+ formation from the diabatic
Rydberg state (  1 ). Considering the general fact that Cl+ ion signals via
excitations to the ion-pair states and HCl+ ion signals via excitations to the
Rydberg states, signals are comparable or certainly of the same order of
magnitude (See Figs. 2-3) it is concluded that  should be somewhat close to
unity and certainly in the range 10-1 <  < 10.
By multiplying  and  (*) we get a measure of the actual rate of
formation of Cl+ via the diabatic Rydberg state (the “gateway channel”)
to that of its formation from the diabatic ion-pair state
This expression allows relative ion signal data to be fitted for known E
'
values using the variables  ,  and W12 as has been previously
accomplished40,41 and are here gathered together in Table 2.
Table 2: State interaction parameters.
State
max
W '12


*
f 32
0.4
0
4
0
f 31
0.7
0.002
0.5
0.001
g  (1)
1.0
0.5
0.6
0.3
j 3(1)
2.7
0.004
3.5
0.014
-
0.031
2.1
0.065
3 
3 
+
j  (0 )
121
It is interesting to note that the * values are considerably different
between  and  states. There’s also a increase by an order of magnitude
between the g 3(1) state and the j 3(0+) and j 3(1) states. This opens
up the possibility that the values are characteristic for certain states and
could be used to assist in state assigments. Further experiments are
needed to determine this as no data exists for  states.
For instances of off-resonance interaction we can assume, to a first
approximation, that the ion intensity ratio is a sum of contributions due to
interactions from the ion-pair states to the Rydberg state. In such cases
common  and  parameters for I(Cl+)/I(HCl+) can be expressed as

 

   c 22,n (1   )   c 22,m (1   ) 
I (Cl  )

 

2
I ( HCl  )
(1  c 22,m ) 
 (1  c 2 ,n )
2
2
(41)
where c 2,n and c 2,m are the fractional mixing contributions for the
interacting ion-pair states respectively.
122
7
Ionization of acetylene and
methyl bromide compared to HCl
It is interesting to compare the ionization mechanics of HCl on one hand
and of acetylene and methyl bromide on the other. As HCl has been well
covered in the previous parts of this dissertation, let us look at the organic
molecules a little closer.
The acetylene ion is formed by an ionization process similar to the
formation of HCl+, i.e. excitation of the acetylene molecule followed by
ionization. The formation of fragment ions are somewhat more
complex.12 However, they generally go through a rearrangement followed
by a predissociation of the parent molecule and a subsequent ionization
of the fragments, forming H+, C+, C2+, C2H+ and CH+.
For methyl bromide a similar story unfolds. Again the methyl bromide
ion is formed by an ionization process similar to the formation of
acetylene and HCl+, i.e. excitation of the methyl bromide molecule
followed by ionization. The formation of fragment ions is again much
more complex than of the parent molecule. In this case two rather
predominant predissociations occur forming CH3 and Br atoms on one
hand and C, H2 and HBr on the other, followed by ionization. Further
dissociation of the fragments can occur in addition to several other
ionization pathways.
To emphasise, for methyl bromide and acetylene this is a simplified
account of the ionization processes of the molecules. What is noteworthy,
however, is that in all these cases the formation of ion fragments goes
through a predissociation process of some sort. This would suggest that
predissociation plays a much more important role in spectroscopy than
hitherto believed.
For HCl, predissociation also plays a key part in the W12 model presented
above. It is interesting to note that it may be possible to use the  and 
values of uncharacterised states to assist in their assignment.41 However,
more research is needed to ascertain a correlation between the  values of
known states and their assignment.
123
8
Unpublished work
8.1 C1-State
The C1 state of HCl is of interest due to its heavy predissociation. The
spectrum shown in Figure 18 has a typical form suggesting short lifetimes
due to predissociation. The mass spectrum analysis in Figure 19 confirms
this theory as a much higher ratio of Cl+ is formed for all rotational levels
than expected for a Rydberg state. Most likely the HCl molecule is
predissociating into neutral H and Cl followed by a direct three-photon
ionization of Cl to Cl+.
1
C ' = 0, R
00
2
00
4
1
6
1
C ' = 0, S
C ' = 0, Q
2
1
C ' = 0, P
00
4
6
1
6
0
3
1
1
C ' = 0, O
00
3
1
77300
77400
00
00
00
77500
77600
77700
-1
[cm ]
Figure 18: (2+n) REMPI of C1 ←← X1+ (0,0) excitation. The figure shows a
diffused spectrum of the H35Cl isotopologue.
A mass spectrum also shows an interesting difference between mass peaks
belonging to the R and P series on the one hand and those belonging to the S
series on the other hand. The J’ = 4 peak of the S series diverges from the
almost linear mass ratios of the other rotational peaks. This divergence is
typically due to perturbation with an ion-pair state.
125
I(35Cl+)/I(H35Cl+) ratio
0.12
0.1
0.08
0.06
0.04
0.02
0
1
2
3
J'
4
5
6
Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white columns
represent the P-series, the black columns the R-series and the gray columns the
S-series. An increased I(Cl+)/I(HCl+)ratio is observed for the J’=4 rotational
level. A small increase in I I(Cl+)/I(HCl+) for the R-series at J’=4 is most likely
due to an overlap with the J’=2 peak of the S-series.
By using equation (40) it is possible to calculate the position of the J’=4
line of the ion-pair state. A comparison of this calculation with the ionpair states measured by Jacques and Barrow80 suggests however that this
cannot be as the energy difference between the rotational lines would
need to be much smaller.
This perturbation effect may therefore be due to a previously undetected state,
possibly a gateway state, as the increased ratio of I(Cl+)/I(HCl+)suggests.
8.2 E1-State
The E1 state of HCl is of interest due to its extended perturbation via off
resonance interaction. Figure 20 shows the I(Cl+)/I(HCl+)and
I(H+)/I(HCl+)ratio of individual rotational peaks for the E1 ←← X1+ (1,0)
excitation.
126
I(H+)/(HCl+) and I(Cl+)/(HCl+)
1,4
2,5
a)
b)
1,2
2
1
Cl+
Cl+
H+
1,5
0,8
H+
0,6
1
0,4
0,5
0,2
0
0
0
1
2
J´
3
4
5
0
1
2
3
J´
4
5
5
6
7
Figure 20: (2+n) REMPI of E1 ←← X1 + (1,0) and V1 ←← X1 + (14,0)
excitations. The figure shows the HCl+/Cl+ ratio of individual rotational peaks.
Table 3 shows the E values for the rotational peaks shown in figure 20.
Interestingly the mass ratio for E1 J’=0 and J’=1 appear to have
reached a perturbation “saturation” point as one would expect to see an
increased Cl+ formation for J’=0 compared with J’=1. Perturbation
“saturation” refers to a 50% mixture of the perturbed states.
Table 3: E values for the rotational peaks of the E1 ←← X1
←← X1 + (14,0) excitations.
J’
E1
+
(1,0) and V1
E; [cm-1]
(v’=1) ↔ V1 (v’=14)
0
246.00
1
247.70
2
251.30
3
260.40
4
280.20
5
319.80
By assuming a 50% state mixing equation (34) can be used directly to
evaluate the W12 constant for this interaction. By doing so a value of
W12=124±2 cm-1 is found. For further studies it would be interesting to
use equation (41) to evaluate W12 using mass ratios and assuming a
considerable off reasonance interaction.
127
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Appendix A: Conference
presentations
Posters
(2+n) REMPI of Acetylene; Gerade Rydberg States and Photorupture
Channels.The 20th International Conference on High Resolution
Molecular Spectroscopy, Prague, Czech Republic, September 2-6, 2008.
MATTHIASSON K., KVARAN A., WANG V.H.
Two dimensional (2+n) REMPI of HCl; Photorupture Channels via the
F1 2 Rydberg state and Ab Initio; The 20th International Conference on
High Resolution Molecular Spectroscopy, Prague, Czech Republic,
September 2-6, 2008, MATTHIASSON K., KVARAN A., WANG V.H.
Two Dimensional (2+n) REMPI of HCl; Photorupture Channels via
Various Rydberg States; The 20th International Conference on High
Resolution Molecular Spectroscopy, Prague, Czech Republic, September
2-6, 2008, MATTHIASSON K., WANG H., KVARAN A.
HCl Photorupture Studies, Raunvísindaþing 2008, 14. og 15. mars í
Öskju, Náttúrufræðahúsi Háskóla Íslands, Kristján Matthíasson.
HCl Photorupture Studies, 4. ráðstefna Efnafræðifélags Íslands á Hótel
Loftleiðum, 2007; Kristján Matthíasson, Victor Huasheng Wang og
Ágúst Kvaran.
Rannsóknir á vetnistengdum sameindaþyrpingum: HF-þyrpingar.
Raunvísindaþing 2006, 3. og 4. mars í Öskju, Kristján Matthíasson,
Victor Huasheng Wang, Ómar F. Sigurbjörnsson og Ágúst Kvaran.
Three photon absobtion of open shell structured molecules. Annual NordForsk
Network Meeting 2005; Fundamental Quantum Processes in Atomic and
Molecular Systems, Sandbjerg, Denmark, 18. Agust – 22. August, 2005,
Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
137
Multiphoton absorption: LASER ionization and mass analysis, 3.
ráðstefna Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september,
2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran.
Fjölljóseindagleypni
niturmonoxíð-sameindarinnar,
3.
ráðstefna
Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september, 2004;
Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran.
Multiphoton absorption: LASER ionization and mass analysis,
Raunvísindaþing 2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17.
apríl 2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran.
Fjölljóseindagleypni niturmonoxíð-sameindarinnar, Raunvísindaþing
2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17. apríl 2004;
Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran.
Talks
Resonance enhanced multiphoton ionization and time of flight mass
analysis of C2H2, Annual NordForsk Network Meeting 2007;
Fundamental quantum processes in atomic and molecular systems,
Nesbúð, near Reykjavík, Iceland, 30. June – 2. July, 2007, Kristján
Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
Research on Hydrogen Bonded Molecular Clusters: HF-Clusters .Annual
NordForsk Network Meeting 2006; Fundamental quantum processes in
atomic and molecular systems, Petursburg, Russia.17-19 June 2006
Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
Research on Hydrogen Bonded Molecular Clusters: HF-Clusters
Raunvísindaþing 2006 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 3. - 4.
mars. 2006; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran
Resonance Enhanced Multiphoton Ionization and Time of Flight Mass
Analysis of C2H2, Annual NordForsk Network Meeting 2005;
Fundamental Quantum Processes in Atomic and Molecular Systems,
Sandbjerg, Denmark, 18. Agust – 22. August, 2005, Kristján
Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
138