Wesleyan University
The Honors College
Rotational Spectroscopy with ab initio Calculations of
2H, 3H-Perfluoropentane, its Isotopologues and the
Argon-36 Cyclopentanone van der Waals Complex
by
Chinh H. Duong
Class of 2013
A thesis submitted to the
faculty of Wesleyan University
in partial fulfillment of the requirements for the
Degree of Bachelor of Arts
with Departmental Honors in Chemistry
Middletown, Connecticut
April, 2013
Table of Contents:
Acknowledgements ..................................................................................................... 1
Chapter 1: General Introduction .............................................................................. 2
1.1. Microwave Spectroscopy ................................................................................... 2
1.1.1. The Rigid Rotor and Asymmetric Tops ...................................................... 3
1.1.2. van der Waals Complexes ........................................................................... 6
1.1.3. Centrifugal Distortion Constants ................................................................. 6
1.2. ab initio Computational Method ....................................................................... 7
1.2.1 Moller-Plesset Perturbation Theory (MPPT) ............................................... 7
1.3. Experimentation (Equipment and Programs) .................................................. 8
1.3.1. Chirped-Pulse Fourier Transform Microwave Spectrometer with Laser
Ablation Source ..................................................................................................... 8
1.3.2. Balle-Flygare type Cavity Fourier Transform Microwave Spectrometer
with a Supersonic Nozzle .................................................................................... 10
1.3.3. Spectral Fitting Programs .......................................................................... 12
Chapter 2: 2H, 3H-Perfluoropentane ..................................................................... 15
2.1. Abstract ............................................................................................................ 15
2.2. Project Motivation and Introduction .............................................................. 16
2.3. Computational Predictions.............................................................................. 17
2.4. Experimental ................................................................................................... 21
2.5. Results and Discussion.................................................................................... 23
2.6. Conclusions and Future Work ....................................................................... 28
Chapter 3: Argon-36 Cyclopentanone .................................................................... 30
3.1. Abstract ............................................................................................................ 30
3.2. Project Motivation and Introduction .............................................................. 32
3.3. Computational Predictions.............................................................................. 33
3.4. Experimental ................................................................................................... 33
3.5. Results and Discussion.................................................................................... 35
3.6. Future Work .................................................................................................... 35
Appendix .................................................................................................................... 36
i
A.1. 2H, 3H-Perfluoropentane Charts and Sample Files ..................................... 36
A.1.1. Transition Frequency Assignments for 2H, 3H-Perfluoropentane and its
Isotopologues ....................................................................................................... 36
A.1.2. Sample Input File for KRA.exe for Kraitchman Single Atom Substitution
Analysis ............................................................................................................... 41
A.1.3. Sample Input File for Scanning Coordinate Calculations for the (R,R)
trans-2H, 3H-perfluoropentane Isomer................................................................ 42
A.1.4. Sample Input for MP2/6-31+g(d,p) Optimization with Gaussian O9 ...... 43
A.1.5. Sample Input for MP2/6-311++g(2d,2p) Optimization with Gaussian 09 44
A.1.6. Sample .var Input for SPCAT ................................................................... 45
A.1.7. Sample .int Input for SPCAT.................................................................... 45
A.1.8. Sample .lin Input for SPFIT...................................................................... 45
A.2. Argon-36 Cyclopentanone Sample Files ....................................................... 46
A.2.1. Sample Input for MOMENT .................................................................... 46
A.2.2. Sample Input for LAS ............................................................................... 47
A.2.3. Sample .var Input for SPCAT ................................................................... 48
A.2.4. Sample .int Input for SPCAT.................................................................... 48
A.2.5. Sample .lin Input for SPFIT...................................................................... 48
References .................................................................................................................. 49
ii
Acknowledgements
The journey to reach this point has been exciting and breathtaking. I would
like to extend my gratitude towards the Novick, Pringle, Cooke, Bohn group (to all of
the professors, graduate students and undergraduates). Your lessons on science,
history and life have always been insightful and entertaining. It has been a pleasure
tackling the mysteries of our physical world along your side.
Dr. Novick, thank you for having a hard time saying “no” to me as a naïve
freshman and allowing me to join your research group! Drs. Novick, Pringle, Cooke,
and Bohn, you have all been excellent mentors and I appreciate all of the projects you
have tossed my way.
Dr. Grubbs II, thank you for your wonderful mentorship and daily vigor. You
keep the lab alive! Dan Obenchain, Brittany Long, Dan Frohman, thank you for all of
the answers to my random questions at the oddest times. Whether it was convenient
or inconvenient, I was always treated well (and fed with snacks)!
Most of all, thank you to all of my friends and family who have given me the
time and opportunities to get this far. Our late night conversations and your penchant
for asking hard questions and willingness to challenge views have made me grow.
There are too many of you to name, so I will do one brisk sweep and say THANK
YOU to all of you!
Though I fear heights, I am happy to have known all of you for you have
given me a beautiful glimpse of the world from up high. I do not regret the view.
Cheers!
1
Chapter 1: General Introduction
In preparation for the following discussion on 2H, 3H-perfluoropentane and
argon-36 cyclopentanone, some important “machinery” on quantum mechanics and
rotational spectroscopy will be presented.
1.1. Microwave Spectroscopy
Spectroscopy is defined as the study of the way in which electromagnetic
radiation interacts with matter as a function of frequency.1 The frequencies of
radiation used can vary throughout the electromagnetic spectrum, depending on the
technique employed.
Various methods of spectroscopy are available to probe the physical and
chemical properties of molecules through their geometric and electronic structures
since a molecule’s chemistry is closely related to these parameters.2 In particular,
high-resolution microwave spectroscopy has the potential to probe important
properties that govern a molecule’s chemistry. Additionally, this method can explore
several molecular systems, ranging from monomers and complexes to small clusters
of several molecules,3,4 and can provide precise details about a system’s bond lengths,
torsional angles, and sets of conformations and electronic structures.
Microwave spectroscopy utilizes microwaves (roughly 1mm to 1 meter in
length and 300 GHz to 300 MHz in frequency) to explore the geometric and
electronic structures of molecules in a collision free environment through rotationally
excited states.
2
In particular, rotational spectroscopy studies the rotational transitions that
exist within the vibrational states of a molecule. When these molecules are excited,
three possible branches of rotational transitions can be observed and defined as
follows: P branches ≡ ΔJ = +1, Q branches ≡ ΔJ = 0, R branches ≡ ΔJ = -1. These
transitions are quantized and their energies can be solved with solutions to
Schrödinger’s equation:5,6
H  E
(1.1.a)
where H is a Hamiltonian operator, Ψ is a wave function, and E is the quantized
energy of the system. The Hamiltonian operator can be broken down further and
represented as:
H = Helec + Hvib + Hrot
(1.1.b)
where Helec, Hvib, and Hrot represent the electronic, vibrational and rotational
Hamiltonians respectively.2 Rotational spectroscopy focuses on the Hrot of a system
and its solutions can usually be solved based on a center of mass analysis using the
rigid rotor approximation.
1.1.1. The Rigid Rotor and Asymmetric Tops
The moment of inertia for a diatomic molecule is given by:
I = μr2
where I is the moment of inertia, μ is the reduced mass
(1.1.1.a)
, and r is the bond
length of the molecule. The moment of inertia can also be expressed as a second rank
tensor with the matrix:
3
 I xx

I   I yx
I
 zx
I xy
I yy
I zy
I xz 

I yz 
I zz 
(1.1.1.b)
where the diagonal matrix elements Ixx, Iyy and Izz are given by:
∑
(1.1.1.c)
∑
(1.1.1.d)
∑
(1.1.1.e)
and the off-diagonal terms Ixy, Iyx, Ixz, Izx, Izy and Iyz are represented by:
∑
(1.1.1.f)
∑
(1.1.1.g)
∑
(1.1.1.h)
The diagonalized form of this matrix will produce:
 Ia

I 0
0

0

0
I c 
0
Ib
0
(1.1.1.i)
where the Cartesian coordinates are now rotated by matrix mechanics into the
molecule fixed frame (the principal axis system of the molecule) and the moments of
inertia Ixx, Iyy and Izz are now represented by Ia, Ib, and Ic respectively. These moments
of inertia in the principal axis system are oriented so that Ia defines the axis with the
smallest moment of inertia and Ic defines the axis with the largest moment of inertia.
4
Given the rotational Hamiltonian:
(1.1.1.j)
the rotational constants (in joules) A, B and C can be obtained by:
A
B
C
h
(1.1.1.k)
8 2 I a
h
(1.1.1.l)
8 2 I b
h
(1.1.1.m)
8 2 I c
These rotational constants can be converted into units of MHz by multiplying A, B,
and C by 10-6 or units of cm-1 by multiplying A, B and C by
.7
Usually these rotors or “tops” can be classified as:7
1. Linear molecules, IA = 0, IB = IC.
2. Spherical tops, IA = IB = IC.
3. Prolate symmetric tops, IA<IB=IC, e.g. CH3Cl.
4. Oblate symmetric tops, IA=IB<IC, e.g. BF3.
5. Asymmetric tops, IA<IB<IC.
and can be further understood with Ray’s asymmetry parameter:

2B  A  C
AC
(1.1.1.n)
When K = -1, the molecule is more prolate (cigar shaped), K=0, the molecule is
completely symmetric, and when is K = +1, the molecule is more oblate (disk
shaped). The quantum labels of Ka and Kc denote the prolate and oblate limits of
asymmetry within a molecule. These labels are also useful in denoting the types of
5
transitions contained within a spectrum. The following selection rules can be used to
label the type of transitions within a spectrum:
1. a-type transitions have ΔKa = even (0, 2, 4…) and ΔKc = odd (1, 3, 5...)
2. b-type transitions have ΔKa = odd (1, 3, 5…) and ΔKc = odd (1, 3, 5...)
3. c-type transitions have ΔKa = odd (1, 3, 5…) and ΔKc = even (0, 2, 4...)
These parameters are useful for understanding spectra since certain types of
transitions and molecules will have distinguishing spectral patterns that could be
employed in their spectral fits.8
1.1.2. van der Waals Complexes
Weakly bound complexes are often hard to study with room temperature
experiments since their bonds are elongated (usually ~ 3 Å) and held together by
extremely weak forces. Collision-free environments with low temperatures are
required to observe these interactions on a practical time scale. These intermolecular
forces include many different short-range interactions which can consist of dipoledipole, quadrupole-dipole, quadrupole-quadrupole, Keesom alignment, dipoleinduced dipole, London dispersion, quadrupole-induced dipole and exchange forces
interactions.9 Many of these interactions are not well known (due to their short
lifetimes) even though they are all around us. For this reason, more investigation into
their behaviors is warranted.
1.1.3. Centrifugal Distortion Constants
In refining spectral fits, only using the rotational constants A, B and C are
often not enough to perfectly align a spectrum. Centrifugal distortions due to the
rotations of a molecule need to be applied to the Hamiltonian operator such that it has
6
considerations for Hrot and Hcd. This new addition to the Hamiltonian causes a change
within the rotational energy terms. For instance, the rotational energy for a diatomic
molecule is W = BJ(J+1) now becomes W = BJ(J+1) – DJ2(J+1)2. Though these
distortions do not make a dramatic difference, their subtleties can appear for delicate
molecules that are more prone to perturbations. As such, they usually need to be
included in spectral fits to produced quality results. These distortion constants go up
to the decadic terms in SPCAT and SPFIT with the Watson A reduction and stop at
the octic terms for the Watson S reduction.
1.2. ab initio Computational Method
Computational models have become increasingly relevant to modern
experimentation. Predictive calculations help lead experimentalists in the right
direction and increases in experimental data allow theoreticians to better model future
experiments. These two fields of experimentation and theory operate cohesively in an
ever-growing technological era.
1.2.1 Moller-Plesset Perturbation Theory (MPPT)
Rayleigh and Schrödinger originally made the considerations for many-body
perturbation theory (known as Rayleigh-Schrödinger Perturbation Theory). Their
theory was extrapolated to n-electron systems by Moller and Plesset.10 These
calculations all improved upon Hartree-Fock by adding in electron correlation effects.
Since perfluoroalkanes tend to be heavy and electron dense molecules, Moller-Plesset
(MP2) calculations were selected for the 2H, 3H-perfluoropentane project for their
accuracy and speed in computing good starting geometries while also taking into
account electron correlations (sometimes important for electron dense systems).
7
These levels of computation are fairly standard in most chemical models because they
are accurate and relatively inexpensive. Though higher orders of MPPT exist, such as
MP3 and MP4, they were not necessary for our experiments and not used in the
interest of saving time.
1.3. Experimentation (Equipment and Programs)
High-resolution spectroscopy can be conducted using various types of
spectrometers. Two important instruments in microwave spectroscopy are the
chirped-pulse Fourier Transform Microwave Spectrometer (CP-FTMW)11,12 and the
Balle-Flygare cavity type Fourier Transform Microwave Spectrometer (cavityFTMW).13 In addition to these machines, various spectroscopic prediction and fitting
programs are necessary for the assignments of spectra and geometries. Some of these
programs include Herb Pickett’s SPCAT and SPFIT14, KRA.exe based on the
equations for Kraitchman’s single atom substitution analysis from Gordy & Cook15,
LAS, Moment, and Kisiel’s AABS package.16
1.3.1. Chirped-Pulse Fourier Transform Microwave Spectrometer with Laser
Ablation Source
The original designs of the chirped-pulse Fourier transform microwave
spectrometer (CP-FTMW) for broadband spectroscopy were made by Brooks H.
Pate’s group.11 This technique was adapted by Stephen A. Cooke’s group to study
metal atom chemistry by adding a laser ablation source to the apparatus.12 The
general experimental process of the CP-FTMW is shown and explained in figure
1.3.1.a.
8
To Diff.
Pump
Figure 1.3.1.a. 1) Gas molecules are pulsed into a vacuum chamber. Then a center frequency
between 8-18 GHz is generated from an arbitrary wave generator and sent into a mixer. 2)
The linear frequency sweep 0 – x (an arbitrary span, our experiments usually go to 1 GHz
spans) - “Chirp” is mixed with the center frequency. 3) The mixed frequency is amplified
with a frequency ± x (the span of the chirp), pulsed and then broadcasted into the vacuum
chamber. 4) This broadcasted radiation travels orthogonally to the motion of the sample gas
pulses and excites the molecules. 5) The free-induction decay is collected, amplified and then
digitized on a 40 GS/s oscilloscope, Fourier transformed from the time domain to the
frequency domain and viewed on a computer as spectra. Since the gas pulses are traveling
orthogonal to the motion of the radiation, no splitting in the spectra due to Doppler shifts are
detected. Note: The colored steps correspond to the colors in the diagram.
The power of the CP-FTMW comes from its broadband capabilities, which
allow it to collect large regions of data faster than the cavity-FTMW since it does not
require the same level of scanning and time consumption needed by a cavity-FTMW
to obtain spectra within the same frequency span. However, the speeds of this
experiment make the CP-FTMW less sensitive than the cavity-FTMW. As such,
isotopologues and molecules with weak dipoles or spectral intensities are harder to
study in the CP-FTMW experiments and require the use of the cavity-FTMW.
9
1.3.2. Balle-Flygare type Cavity Fourier Transform Microwave Spectrometer
with a Supersonic Nozzle
A general experiment for the Balle-Flygare cavity type-FTMW13 is given as
follows: a supersonic jet pulse of molecular sample and carrier gas (usually argon is
used in our experiments, but any inert gas will work) is sent into a vacuum chamber
in between the mirrors of a Fabry-Parot microwave cavity. These mirror cavities have
low frequency antennas with tunable frequencies from 5 to 26 GHz (though our
experiments usually go from 8 to 18 GHz due to poor cavity modes beyond those
frequencies). These gas pulses are sent through a supersonic nozzle into a high
vacuum chamber and undergo a supersonic expansion which produces a collision free
environment that greatly reduces the rotational temperatures of the molecules (to 1
Kelvin - 5 Kelvin). In this collision free expansion, molecules that usually have short
lifetimes, such as van der Waals complexes, can be formed and studied.
Microwaves are emitted shortly after the gas expansion has entered the
chamber (optimal timings vary upon experiments) in order to excite the molecules
into a rotationally excited state. Once the radiation is turned off, these molecules
undergo free-induction decay (FID) and are detected within a few hundred kHz of the
tuned frequency. A Fourier transformation interprets the signals produced by the FID
in the time domain and translates the data into the frequency domain. A pictorial view
of the experiment is shown in figure 1.3.2.a. These experiments differ from the CPFTMW experiments through the use of Fabry-Perot cavity mirrors rather than
chirped-pulse horns and the use of a coaxial nozzle design rather than a perpendicular
nozzle design.
10
Figure 1.3.2.a. A simplified schematic of the experiment. A supersonic nozzle sends a gas
pulse into a vacuum chamber. The gas pulse cools to low rotational energies. Then,
microwaves are used to excite the gas pulse to specific rotational energy levels. After the
radiation has stopped, the molecules undergo an FID and their spectra is recorded in the time
domain and Fourier transformed into the frequency domain to yield the spectra of the
molecule on a computer screen as frequency peaks.
Due to the coaxial configuration of the nozzle17 with respect to the direction
of the microwave pulses (the gas pulse travels in the same direction as the microwave
pulse), Doppler shifts in the frequency are observed. Single peaks in a perpendicular
nozzle set up (where the microwave pulses travel in an orthogonal direction to the gas
pulses), will appear as a doublet in the coaxial nozzle arrangement. The Doppler
broadening effect for non-relativistic velocities can be described by:
(
where
is the output frequency,
)
(1.3.2)
is the input frequency, ν is the velocity of the gas
pulse (this value can be negative or positive) and c is the speed of light.
Before the microwaves are introduced into the system, they are generated
outside of the cavity by an arbitrary wave generator, mixed down and processed
through several synthesizers, filtered and then that final frequency is amplified before
11
injection into the cavity. The circuit diagram and picture of the cavity-FTMW for our
lab with a laser ablation source is shown in figure 1.3.2.b.
Figure 1.3.2.b. Dr. Novick’s Balle-Flygare type cavity Fourier Transform Microwave
Spectrometer (Cavity-FTMW)13 which exchanges between the use of a supersonic gas nozzle
and laser ablation system to study gas phase molecules or metal atom chemistry. This
chamber’s high-resolution and sensitivity make it ideal for finding weak spectra, as well as
strong ones.
One of the major strengths with the cavity-FTMW is its varied flexibility to
study several different chemical systems depending on the type of nozzle used.
Though the experiments in this thesis only used the supersonic nozzle, other types of
nozzles such as high temperature, fast mixing, pulsed discharge and laser ablation
source nozzles18 also exist for a myriad of other experiments. These traits, along with
the high-resolution capabilities and sensitivity of the technique, make the cavityFTMW a wonderful tool for studying weakly bound van der Waals complexes in
natural abundance and gas phase chemistry.
1.3.3. Spectral Fitting Programs
SPCAT takes (name).var input files with rotational constant and centrifugal
distortion parameters, their errors and a variety of other parameters necessary for the
molecular system’s spectra to be fit and generates a (name).cat file which produces
12
the frequency predictions for the rotational transitions of the molecule, as well as their
relative intensities and errors (based on the errors of the (name).var file). An
(name).int file is required to run the (name).var file. This (name).int file contains the
dipoles moments of the molecule in the principal axis system along the a, b, and c
axes and can be used to dictate the minimum and maximum J quantum numbers, the
upper and lower frequency cutoffs for the (name).cat file outputted from SPCAT.
Additionally, the (name).int file can also predict the appearance of the spectra at
various temperatures (based on the partition functions relevant to the molecule being
studied).
SPFIT utilizes a (name).par, (name).lin file to fit rotational spectra. The
(name).par file is almost identical to the (name).var file with the exception that the
parameters in the (name).par file are allowed to vary for the sake of spectral fitting,
whereas the parameters in the (name).var file are generally precise. The (name).lin
file consists of experimental line frequencies, their quantum transition assignments
and weights that determine the accuracy of the frequencies fitted. A (name).fit file is
outputted from SPFIT that contains the updated rotational constants based on the fit
of the molecule, the errors within the rotational constants and observed minus
calculated values for each of the fitted lines and the microwave root-mean-square of
the fit. Usually 6-7 kHz fits are good for CP-FTMW data and 0.5-3 kHz fits are good
for cavity-FTMW data.
KRA.exe utilizes Kraitchman’s equations for single atom isotopic substitution
directly from Gordy & Cook15 to confirm the positions of the these atoms based on
13
their experimental rotational constants. The program can be found on the PROSPE
website.19
Schoeffler’s Line Assigner (LAS) was designed by Aaron Schoeffler and used
to assign quantum transitions to unassigned spectral frequencies by producing
possible fits of the frequencies and their errors through direct variation of the
rotational constants. These computations can be time consuming depending on the list
of unassigned lines and the convergence criterions. Large lists of unassigned lines
result in an exponential time increase, while loose convergence criterions produce
nonsense results. On the contrary, too narrow of a convergence criterion may not
allow the fit to fluctuate enough to fit the spectral frequencies listed.
MOMENT calculates the rotational constants of a molecule, given a set of
masses and their Cartesian coordinates. The masses in the Cartesian coordinates are
rotated into the principal axis system and the moment of inertia tensors are
diagonalized to yield rotational constants for the molecule being studied. This
program is vital in providing isotopic substitution predictions for atoms. Similarly,
STRGEN is a program that behaves in a similar fashion to provide predicted
rotational constants for a given molecule. MOMENT was used for the 36Arcyclopentanone studies, while STRGEN was used for the 2H, 3H-perfluoropentane
studies.
AABS package16 was designed to help visualize spectral data from a
(name).csv file which lists the frequencies of the lines and their intensities. This
program can also be used in conjunction with SPCAT and SPFIT to view the
predictions from the (name).cat files and fits in real time.
14
Chapter 2: 2H, 3H-Perfluoropentane
2.1. Abstract
Previous structural studies of alkanes and perfluoroalkanes have concluded
that alkanes have staggered structures where the hydrogen atoms along the H-C-C-H
dihedral angle are separated by180o, meanwhile perfluoroalkanes with four or more
carbons along the carbon chain display a helical C2 geometry where the fluorine
atoms along the F-C-C-F dihedral angle are separated by approximately 15-17o.20
These results have led to interest in identifying the structure of fluorinated alkane
chains with various substituents. In this study, the pure rotational spectrum of 2H,3Hperfluoropentane was observed and assigned using a chirped-pulse Fourier Transform
Microwave Spectrometer. Given a racemic sample of four available structural
isomers, only the (S,S)/(R,R) structure was observed in the broadband spectrum.
Examination of all five 13C isotopologues on a Balle-Flygare type cavity spectrometer
and their complete spectral assignments will be presented, along with a comparison of
the theoretical predictions for the structure and rotational constants of the molecule
against their experimental values. Structural results of the monomer will also be
compared with those of the helical structure of C2 perfluoropentane.20
Figure 2.1.1. Cross-sectional view of structural results from previous studies: staggered
pentane, helical perfluoropentane and nonhelical perfluoropropane.20
15
2.2. Project Motivation and Introduction
Previous studies have shown that alkane chains of any length generally
assume a staggered geometry, as shown in Fig. 2.1.1 for C5H12. Meanwhile,
perfluoroalkane chains with four or more carbons tend to have helical geometries (ex.
Fig. 2.1.1 C5F12) and only perfluoroalkanes with three or fewer carbons along the
chain show a staggered structure (ex. Fig. 2.1.1 C3F12) consistent with regular
alkanes.20
In this study, 2H,3H-perfluoropentane structures were predicted using ab
initio calculations from Gaussian 0921 on the MP2/3-21g basis set and then the lowest
potential wells for each unique conformer were optimized on a larger basis set. A fast
scanning coordinate calculation at the low level MP2/3-21g basis set was used to
identify possible minimum energy conformations of the 2H,3H-perfluoropentane. The
two lowest energy conformations from each of the four scanning coordinate
calculations (one for each isomer) were then initially optimized with an MP2/631+g(d,p) basis set. These previously refined structures (eight in total) were then
tightly optimized further with an MP2/6-311++g(2d,2p) basis set to more rigorously
consider the electrostatic and dispersion interactions for each conformer.
Afterwards, the rotational constants from these optimized calculations were
used to predict the spectrum of the molecule. Predictions and fits were made with
SPFIT and SPCAT14 (respectively) and the AABS package16 was used to visualize
the spectrum. Kraitchman analysis22 was conducted to verify the accuracy of the
predictions against their experimental values for the positions of the carbon atoms and
predict the rotational constants of the isotopologues. This analysis also established the
16
carbon atom backbone of the molecule with their correct relative positions and bond
distances. Comparisons of the molecule’s observed planar moment versus the planar
moments of the helical and staggered structures of 2H, 3H-perfluoropentane from ab
initio calculations were also completed to confirm the geometry of the structure.
Additionally, structural dependence on the hydrogen substituents and the
impact of the dipole repulsions on the helical nature of 2H, 3H-perfluoropentane were
examined for eight possible conformers. The conformers consist of four isomers, each
with two minimum energy conformers.
2.3. Computational Predictions
Figure 2.3.1. The carbon labeling scheme for (S, S) trans-2H, 3H-perfluoropentane.
A scanning coordinate calculation was conducted for each of the four isomers
of 2H, 3H-perfluoropentane around the H-C2-C3-H dihedral angle to determine the
possible minimum energy structures of each isomer. A sample result of the scanning
coordinate calculations is shown in figure 2.3.2. The results showed two minimum
energy wells for each of the four isomers. The (R,R) and (S,S) 2H, 3Hperfluoropentane compounds converged into two different conformations, an all
trans structure (left well) and a cis structure (right well). In contrast, the (R,S) and
(S,R) 2H, 3H-perfluoropentane structures converged into only one minimum energy
17
conformation of the all trans structure (the left and right potential wells were
equivalent for these structures).
Figure 2.3.2. Sample results for the scanning coordinate calculation at the MP2/3-21g basis
set around the H-C2-C3-H dihedral angle for the (S,S) 2H, 3H-perfluoropentane conformer.
This calculation shows two minimum energy conformers indicated by the red brackets and
labeled with their predicted rotational constants.
These minimum energy conformers from the scanning coordinate calculations
were then optimized with an MP2/6-31+g(d,p) and MP2/6-311++g(2d,2p) basis set to
further refine the structures and rotational constants of the prediction. The
optimization calculations were able to provide better geometries for the computed
structures with better consideration for electrostatic and dispersion interactions of the
hydrogens, fluorines and carbons. A difference in the rotational constants from the
MP2/6-31+g(d,p) calculations to the MP2/6-311++g(2d,2p) calculations was noticed.
This difference showed more structural accuracy in the MP2/6-311++g(2d,2p)
calculation after the values were compared with experimental results discussed in
section 2.5. A summary of the optimizations are summarized below in table 2.3.1 and
table 2.3.2. Sample input calculations for the scanning coordinate calculations and the
18
geometry optimizations for MP2/6-31+g(d,p) and MP2/6-311++g(2d,2p) are shown
in appendix A.1.3, A.1.4 and A.1.5 respectively.
Structure
MP2/6-31+g(d,p)
Relative Energies
(cm-1)
Total Dipole
(Debye)
Predicted
Rotational
Constants (MHz)
(R,R) Trans (left well)2H,3H-Perfluoropentane
0
2.02
(R,R) Cis (right well)2H,3H-Perfluoropentane
217
1.91
A = 1190.43
B = 335.34
C = 329.05
A = 1096.57
B = 374.58
C = 359.22
(S,S) Trans (left well)2H,3H-Perfluoropentane
0
2.02
A = 1190.42
B = 335.33
C = 329.04
(S,S) Cis (right well)2H,3H-Perfluoropentane
217
1.91
(R,S) Trans (left well)
2H,3H-Perfluoropentane
77
0.26
(R,S) Trans (right well)2H,3H-Perfluoropentane
77
0.26
A = 1096.55
B = 374.60
C = 359.22
A = 1203.95
B = 346.20
C = 318.46
A = 1203.95
B = 346.20
C = 318.46
(S,R) Trans (left well)2H,3H-Perfluoropentane
77
0.26
A = 1203.97
B = 346.23
C = 318.47
(S,R) Trans (right well)2H,3H-Perfluoropentane
77
0.26
A = 1203.97
B = 346.23
C = 318.47
Table 2.3.1. Results from ab initio calculations optimized at the MP2/6-31+g(d,p) basis set
for the eight possible conformations of 2H, 3H-perfluoropentane.
19
Structure
MP2/6311++g(2d,2p)
Relative Energies
(cm-1)
0
Total Dipole
(Debye)
Predicted
Rotational
Constants (MHz)
2.02
(R,R) Cis (right well)2H,3H-Perfluoropentane
163
1.91
(S,S) Trans (left well)2H,3H-Perfluoropentane
0
2.02
(S,S) Cis (right well)2H,3H-Perfluoropentane
163
1.91
(R,S) Trans (left well)
2H,3H-Perfluoropentane
180
0.33
(R,S) Trans (right well)2H,3H-Perfluoropentane
180
0.33
(S,R) Trans (left well)2H,3H-Perfluoropentane
180
0.33
(S,R) Trans (right well)2H,3H-Perfluoropentane
180
0.33
A = 1204.74
B = 339.94
C = 332.81
A = 1108.10
B = 381.24
C = 365.07
A = 1204.73
B = 339.94
C = 332.81
A = 1108.10
B = 381.24
C = 365.07
A = 1221.02
B = 350.95
C = 322.89
A = 1221.02
B = 350.95
C = 322.89
A = 1221.02
B = 350.95
C = 322.89
A = 1221.02
B = 350.95
C = 322.89
(R,R) Trans (left well)2H,3H-Perfluoropentane
Table 2.3.2. Results from ab initio calculations optimized at the MP2/6-311++g(2d,2p) basis
set for the eight possible conformations of 2H, 3H-perfluoropentane.
Spectral predictions were made using the rotational constants for the (R,R)
and (S,S) trans-2H, 3H-perfluoropentane conformer based on its low relative energy
to the other conformations of 2H, 3H-perfluoropentane and its strong dipole. Since
the rotational constants for the (R,R) trans-2H, 3H-perfluoropentane and (S,S) trans2H, 3H-perfluoropentane structure were almost identical, the predictions yielded
similar results. The other conformations were not believed to be visible, at least in the
broadband due to their higher relative energies and weak dipole moments and were
thus not pursued during the experimentation and spectral fitting process.
20
2.4. Experimental
A racemic mixture of 2H, 3H-perfluoropentane was purchased from SynQuest
Laboratories. The all carbon-12 data for the parent 2H,3H-perfluoropentane
compound was collected using a chirped-pulse Fourier transform microwave
spectrometer (CP-FTMW). None of the carbon-13 isotopologues for this molecule
was observed in the broadband spectrum using the CP-FTMW. Higher sensitivity and
resolution was required to obtain data on the carbon-13 isotopologues and thus a
Balle-Flygare type cavity spectrometer13 was used to collect data for these
compounds in natural abundance.
In the CP-FTMW, approximately 2mL of a racemic mixture of 2H, 3Hperfluoropentane sample was injected into a polyethylene tube and isolated from air
to prevent contamination of the spectra due to atmospheric gases. Afterwards, argon
gas was bubbled through the sample at ≈ 50 psi and the spectrum was collected at an
average of 10,000 gas pulses per 2 GHz section from 7-15 GHz. A sample broadband
spectrum of the 2H, 3H-perfluoropentane is shown below in figure 2.4.1. Several Qbranch transitions were also observed within the broadband spectrum and an example
of one of the Q-branches, along with their transition assignments, around 7872 MHz
is shown in figure 2.4.2 through an expansion of the spectrum in figure 2.4.1. The
broadband spectrum consisted predominantly of c-type transitions, although some btype transitions were possibly observed in very weak intensities. No spectral doubling
was observed in the broadband spectrum, which indicates that the (R,R) trans-2H,
3H-perfluoropentane and (S,S) trans-2H, 3H-perfluoropentane structures may be
indistinguishable in our experiments.
21
Figure 2.4.1. A sample broadband spectrum of 2H, 3H-perfluoropentane from 7-9 GHz
visualized using the AABS package.
Figure 2.4.2. An expanded view of the broadband spectrum with a close up of the Q-branch
transitions around 7872 MHz. The experimental data is in blue and white (the first three
spectrums), while the predictions are in black and yellow (the last spectrum with sharp
lines).The transitions shown from left to right are as follows: 19 5 15 – 19 4 15, 19 5 14 – 19 4 16, 18
5 14 – 18 4 14, 18 5 13 – 18 4 15, 17 5 13 – 17 4 13, 17 5 12 – 17 4 14, 16 5 12 – 16 4 12, 16 5 11 – 16 4 13, 15 5 11 –
15 4 11. It is also unique to note that the difference between the peaks of the 16 5 12 – 16 4 12 and
16 5 11 – 16 4 13 transitions is 89 kHz apart, which means that the CP-FTMW instrument can be
fairly well resolved.
22
Data for the 13C isotopologues were obtained on the cavity-FTMW under
fairly similar conditions at selected regions, although the polyethylene tubing was
substituted with Teflon tubing. Additionally, the argon pressure was increased to ≈ 55
psi. The parent and all five carbon-13 isotopologues were visible within the cavityFTMW.
Spectral predictions and fits were made using SPCAT and SPFIT. Sample
input files for these programs for the 2H, 3H-perfluoropentane molecule can be found
in appendix A.1.6, A.1.7 and A.1.8.
2.5. Results and Discussion
Originally, fits were made based on the Q-branches, but these did not lead to
conclusive results. Future fits for the broadband spectra were based on a harmonic
pattern within the spectra where rotational transitions (in the form J’ Ka’ Kc’ – J’’ Ka’’
Kc’’)
such as 4 3 1 - 3 2 1 (7040.787 MHz) with 4 3 2 - 3 2 2 (7041.041 MHz) and 5 3 2 - 4 2 2
(7706.646 MHz) with 5 3 3 - 4 2 3 (7707.392 MHz) appeared in pairs separated by 665
MHz (approximately the value of the B + C rotational constants for the molecule).
These pairs of lines within the same rotational energy block also displayed an
increase in separation as the rotational energy increased in J. The pattern continued
for the following pairs of transitions: 6 3 3 - 5 2 3 with 6 3 4 - 5 2 4, 7 3 4 - 6 2 4 with 7 3 5 - 7 2
5,8 358-
7 2 5 with 8 3 6 - 7 2 6 , 9 3 6 - 8 2 6 with 9 3 7 - 8 2 7 , 10 3 7 - 9 2 7 with 10 3 8 - 9 2 8 , 11 3
10 2 8 with 11 3 9 - 10 2 9, and 12 3 9 - 11 2 9 with 12 3 10 - 11 2 10. These harmonics were
also observed within the spectrum of the isotopologues and used as a starting point
for the initial fits of the isotopologues. The harmonic patterns seem to be observable
in some asymmetric prolate molecules with b and c type spectra (in this case, the b
23
and c type transitions were directly on top of one another).8 After this pattern was
fitted, the Q-branch transitions for the predicted and experimental results became
aligned and easily assigned.
Once the parent structure was fitted, calculations for rotational constants of
the carbon-13 isotopologues based on the parent’s geometry were completed and
scaled based on the ratio of:
(2.5.1)
where X1 (Obs) is the observed rotational constant (A, B or C) for the parent, X1
(Calc) is the calculated rotational constant (A, B or C) for the parent, X2 (Calc) is the
calculated rotational constant (A, B or C) for the isotopologue and X2 (Obs) is the
expected observed rotational constant (A, B or C) for the isotopologue. These
predictions and their scalings are shown in table 2.5.1 and table 2.5.2, respectively.
Parameter
A /MHz
B /MHz
C /MHz
Parent
1190.426
335.329
329.645
13
C (1)
1190.129
333.789
327.556
13
C (2)
1189.420
334.918
328.589
13
C (3)
1190.177
335.325
329.024
13
C (4)
1189.649
335.005
328.704
13
C (5)
1190.095
333.976
327.717
Table 2.5.1. The predicted rotational constants for 2H, 3H-perfluoropentane and its
isotopologues arbitrarily recorded to three significant figures. Significant figures in these
predictions do not hold much weight.
Parameter
A /MHz
B /MHz
C /MHz
Parent
(Obs)
1208.3386(1)
336.90086(5)
329.24674(5)
13
C (1)
(Scaled)
1207.980
335.358
327.756
13
C (2)
(Scaled)
1207.260
336.492
328.789
13
C (3)
(Scaled)
1208.030
336.901
329.225
13
C (4)
(Scaled)
1207.490
336.580
328.905
13
C (5)
(Scaled)
1207.95
335.546
327.917
Table 2.5.2. The scaled rotational constants of the carbon-13 isotopologues of 2H, 3Hperfluoropentane arbitrarily recorded to three significant figures. Significant figures in these
scaled predictions do not hold much weight.
Since these scaled predictions closely agree with the experimentally fitted
constants for the parent molecule and its isotopologues in table 2.5.3, it can be
24
inferred that the original (S,S) or (R,R) all trans-2H, 3H-perfluorpentane helical
geometry of the parent molecule was accurate. A summary of the fitted rotational
constants and centrifugal distortion constants for the all carbon-12 parent and
isotopologues are shown on table 2.5.3 and their complete list of the assigned
transition frequencies can be viewed in appendix A.1.1.
Parameter
A /MHz
B /MHz
C /MHz
ΔJ /kHz
ΔK /kHz
ΔJK /kHz
δJ /kHz
δK /kHz
Lines used
Microwave
RMS /kHz
Parent
1208.3386(1)
336.90086(5)
329.24674(5)
0.00550(6)
0.063(3)
0.0167(3)
-0.00010(2)
0.148(6)
182
6.0
13
C (1)
1208.06473(3)
335.35054(4)
327.76270(6)
0.0045(2)
[0.063]
[0.0167]
[-0.00010]
[0.148]
11
0.3
13
C (2)
1207.30318(8)
336.5028(1)
328.8067(1)
0.0048(4)
[0.063]
[0.0167]
[-0.00010]
[0.148]
12
0.8
13
C (3)
1208.10021(9)
336.9168(1)
329.2456(1)
0.0045(3)
[0.063]
[0.0167]
[-0.00010]
[0.148]
20
1.3
13
C (4)
1207.55688(7)
336.59273(8)
328.9161(1)
0.0044(4)
[0.063]
[0.0167]
[-0.00010]
[0.148]
12
0.7
C (5)
1208.01815(4)
335.54314(5)
327.92366(7)
0.0045(2)
[0.063]
[0.0167]
[-0.00010]
[0.148]
11
0.4
Table 2.5.3. The rotational and quartic centrifugal distortion constants fitted to experimental
data using SPFIT. The parameters are all well determined to 6 kHz or less. Deviations in
accuracy are due to changes in instruments. The CP-FTMW has slightly higher errors (these
are usually around 6-7 kHz for a good fit) than the cavity-FTMW errors (these range from
0.5-3 kHz for a good fit).
Kraitchman substitution analysis22 was completed with KRA.exe to confirm
the accuracy of the substituted atoms and their positions based on the experimental
rotational constants of the parent molecule and its isotopologues. A sample input file
for KRA.exe is shown in appendix A.1.2. The results of these substitution analyses
are tabulated in table 2.5.4 and table 2.5.5. When the ab initio coordinates of the
atoms in the principal axis system are compared to their observed values, it is clear
that the heavy atom carbon backbone of the 2H, 3H-perfluoropentane closely match
between calculated and experimental results. This further reinforces the accuracy of
helical structure of (R,R) and (S,S) trans-2H, 3H-perfluoropentane.
25
13
Isotopologue
Calc.
C(1)
Obs.
C(1)
Calc.
C(2)
Obs.
C(2)
a
-2.630
-2.6265(6)
-1.346
-1.317(1)
b
-0.256
-0.235(6)
0.566
0.565(3)
c
-0.202
-0.200(8)
-0.198
-0.200(7)
Table 2.5.4. A comparison of the calculated and experimental coordinates of the first and
second carbon atoms within (R,R) and (S,S) trans-2H, 3H-perfluoropentane in the principal
axis system where a, b and c are coordinates of the atom along the a, b and c axes
respectively.
Isotopologue
a
Calc.
C(3)
-0.113
Obs.
C(3)
[-0.113]
Calc.
C(4)
1.178
Obs.
C(4)
1.150(1)
Calc.
C(5)
2.471
Obs.
C(5)
2.4656(6)
b
-0.289
-0.282(5)
0.455
0.469(3)
-0.344
-0.343(4)
c
0.070
0.06(3)
-0.265
-0.226(7)
-0.007
[-0.007]
Table 2.5.5. A comparison of the calculated and experimental coordinates of the third, fourth
and fifth carbon atoms within (R,R) and (S,S) trans-2H, 3H-perfluoropentane in the principal
axis system where a, b and c are coordinates of the atom along the a, b and c axes
respectively.
One final computational analysis between the staggered and helical
geometries of the (R,R) and (S,S) trans-2H, 3H-perfluoropentane compared against
the experimental values showed that the experimental rotational constants are in
better agreement with the helical geometry than the staggered geometry. The
staggered geometry has a much lower A rotational constant and higher C rotational
constant than the observed values, whereas the helical structure’s rotational constants
for A, B and C are very similar to the observed values. This difference in agreement
is definitive when the second moments of each structure are compared to the
experimental values. The agreement between the second moments of the calculated
26
helical geometry and observed values are much closer than that of the calculated
staggered structure and experimental results. The staggered computed structure’s
lower Paa value than the observed indicates that the computed structure was too short
along the a-axis, meanwhile the helical computation produced very similar planar
moments compared with the observed, indicating that the bond lengths and bond
angles of the calculated helical structure better resemble the observed geometry of
(R,R) and (S,S) trans-2H, 3H-perfluoropentane. Table 2.5.6 summarizes the results of
these computations.
Structure
Rotational Constants (MHz)
Second Moments
Calc.
(Staggered)
MP2/6-31+g(d,p)
A = 1159.9
B = 334.9
C = 332.0
P = 1275.9
Calc.
(Helical)
MP2/6-31+g(d,p)
A = 1190.4
B = 335.3
C = 329.0
P = 1309.2
Obs.
Results
(Helical)
A = 1208.3386(1)
B = 336.90086(5)
C = 329.24674(5)
P = 1308.3973(3)
P = 246.3
P = 226.7
P = 226.5579(3)
P = 189.4
P = 197.9
P = 191.6850(3)
aa
bb
aa
bb
cc
cc
aa
bb
cc
Table 2.5.6. The rotational constants and second moments of the staggered and helical
geometries of 2H, 3H-perfluoropentane from ab initio calculations compared with the
observed rotational constants and second moments.
These results are consistent with the a variety of computational methods23,24,
25,26,27
and experimental studies conducted on perfluoropentane20 that reveal
perfluorinated alkanes with four or more carbons within the chain have helical
geometries. In the case of perfluoropentane, a helical angle ~15o – 17o from the trans
completely staggered structure is observed, as shown in figure 2.1.1. Our study
indicates that the helical angle of (R,R) and (S,S) trans-2H, 3H-perfluoropentane is
close to that of perfluoropentane, within the same range of ~15o-17o from the
staggered conformation. This indicated that although hydrogen substituents exist in
27
the 2H, 3H-perfluoropentane, these substituents still allow for the formation of a
helical geometry rather than form a partly staggered conformation. The exact helical
angle cannot be determined without Kraitchman analysis of the fluorine atoms, but
this is currently impossible since fluorine has only one observed isotope (19F).
2.6. Conclusions and Future Work
Based on the fitted parameters and the comparisons of the ab initio
calculations with experimental results, the evidence indicates that the (R,R)/(S,S)
2H,3H-perfluoropentane is helical. This helical geometry is shown in figure 2.6.1.
Figure 2.6.1. Planar views of the (R,R) trans-2H,3H-perfluoropentane structure from
computational results along the XY, XZ, and YZ planes, respectively.
The structure of the (R,S) and (S,R) 2H,3H-perfluoropentane cannot be
confirmed since only ab initio predictions are available for these enantiomers. The
broadband spectrum was assigned to the (S,S) and (R,R) trans-2H, 3Hperfluoropentane conformers (which are spectroscopically identical in our
experiments) and no other conformations of 2H, 3H-perfluoropentane were observed
with the CP-FTMW. Thus, no broadband data was available to fit the (R,S) and (S, R)
trans-2H, 3H-perfluoropentane or (R,S), (S,R), (R,R) and (S,S) cis-2H, 3Hperfluoropentane conformers. Additionally, since these conformers were not seen in
the CP-FTMW and difficult to observe in the cavity-FTMW experiments due to their
28
low dipoles and higher relative energies than the (S,S) and (R,R) trans-2H, 3Hperfluoropentane structures, they were not pursued because of their potentially low
intensity spectra.
Although the CP-FTMW is a powerful technique, it’s resolution and
sensitivity only allowed for the (R,R) and (S,S) isomers to be observed in the
broadband. All of the 13C measurements for the isotopologues had to be made with
the cavity-FTMW.
The hydrogen substituents still generate an overall helical structure. Although
the exact angle of this helical geometry could be refined with studying the
Kraitchman positions of the hydrogens and their deuterium derivatives. This was
attempted shortly, but was postponed due to the low intensity spectrum of the
deuterium species in natural abundance. More work on the deuterium derivatives and
H2O clusters could be conducted to further refine the helical structure of 2H, 3Hperfluoropentane.
The enantiomers of the (R,R) and (S,S) isomers, as well as the (R,S) and (S,R)
isomers cannot be separated by rotational spectroscopy since the enantiomers produce
the same rotational constants. As a result, they are spectroscopically
indistinguishable.
Further studies on longer perfluoroalkane chains may be conducted to confirm
the helical trends of perfluoroalkanes with four or more carbon chains. More data on
these geometries as the perfluoroalkane chains extend could lead to better
approximations for the helical angle of these compounds and possible trends that
could refine the position of the fluorine atoms. These refined geometries could also
29
provide insights into the reactivity of these compounds based on steric effects or their
electronic structures.
Additionally, since perfluorinated compounds have been increasingly applied
to many commercial and industrial processes,28 their usage has led to increases in
environmental concerns. Due to their longer lifetimes, these compounds could be
potential atmospheric or water contaminants and studies on water clusters of 2H, 3Hperfluoropentane or its complexion with various atmospheric gases may provide more
details about this compound’s potential as an environmental pollutant.
Chapter 3: Argon-36 Cyclopentanone
3.1. Abstract
The microwave spectrum and structure of the cyclopentanone monomer,29
40
Ar-cyclopentanone (40Ar-C5H8O) and its isotopomers have been assigned by
previous research.30,31,32 This work builds upon previous studies to further investigate
the spectrum of 36Ar-cyclopentanone (36Ar-C5H8O) in natural abundance. The focus
of this project is to test the sensitivity limits of the cavity-FTMW and understand van
der Waals forces and their influences on the structure of organic molecules.
Additionally, this study will confirm the position of the argon in the 40Ar-C5H8O van
der Waals complex. This experiment may also give insights into argon’s higher
potential for polarization and behavior as a Lewis base in van der Waals complexes.
The 36Ar isotope has a natural abundance of 0.33% and the 18O isotope has a natural
abundance of (0.21%). This would imply that although the 36Ar-C5H8O complex
approximately 300 times weaker than the main 40Ar-C5H8O isotopomer, it should be
30
visible using the cavity-FTMW and also be easier to detect in natural abundance than
the 40Ar-C5H818O complex. Since the spectrum of the 40Ar-C5H818O complex was
observed in natural abundance, it was expected that the 36Ar-C5H8O complex would
also be observable within the cavity-FTMW in natural abundance.
Previously determined spectral and structural data of the 40Ar-C5H8O complex
combined with scaling calculations and Kraitchman analysis were used to predict the
spectra and structure of the 36Ar-C5H8O complex. A visualization of the Arcyclopentanone complex can be seen in figure 3.1.1 and figure 3.1.2. These
predictions were then used in conjunction with a cavity-FTMW to obtain the data for
the microwave transitions of the 36Ar-C5H8O. The predicted results determined the
rotational constants to be: A = 2616.10 MHz, B = 1176.62 MHz and C = 1022.89
MHz. Kraitchman analysis of these constants placed the 36Ar in the same position as
the 40Ar within the complex (which is to be expected since they are correlated). The
predicted rotational constants were assumed to be accurate since previous studies of
the 20Ne- C5H8O and 22Ne-C5H8O indicated that the position of the neon atoms
between the two complexes were almost identical.31
31
Figure 3.1.1. Argon Position in 40Ar-cyclopentanone (viewed from the a, b, c axes
respectively).32
(XZ Plane)
(XY Plane)
(YZ Plane)
Figure 3.1.2. Gaussian depictions with the relative atom sizes to scale of the 40Arcyclopentanone complex optimized from the skeleton of the monomer. The position of the
36
Ar-cyclopentanone complex is predicted to be in a similar position.
3.2. Project Motivation and Introduction
Cyclopentanone has been previously studied by Kim, Gwinn, Brooks, and
Lin. Their research has thoroughly assigned the spectra and structure for the
cyclopentanone monomer, 40Ar complex and the 13C and 18O isotopologues. The
spectra and structure of the 36Ar isotopomer was and has never been studied in natural
abundance. With the known 40Ar coordinates in the principal axis system and
32
replacement of the mass of 40Ar with 36Ar, a theoretical prediction of the rotational
constants (A, B and C) for the 36Ar complex was generated with a program called
MOMENT. A sample input file for MOMENT can be found in appendix A.2.1. These
coordinates were further refined by an extreme Kraitchman analysis that gave better
predictions for the rotational constants by adjusting the rotational constants to agree
more closely with the exact position of the 40Ar in the complex. When these rotational
constants are then scaled by equation 2.5.1, a usable set of A, B and C for the 36Arcomplex was produced. This method had previously worked for all of the other
isotopologues31 and was expected to work for this experiment. The scaled rotational
constants produced predictions that did not lead to any conclusive fit. Sample input
files for SPCAT and SPFIT are shown in appendix A.2.3, A.2.4, and A.2.5.
3.3. Computational Predictions
No major ab initio computations were used for my part of this experiment.
Most of the calculations employed were based on scaling methods from previous
studies.31 Programs such as MOMENT and LAS were employed to predict rotational
constants from an initial geometry and fit possible combination of spectral lines to
their rotational transitions, respectively.
3.4. Experimental
A U-tube of 1 mL of 99% cyclopentanone was prepared with one end attached
to a tank of argon and the other end attached to the pulse nozzle of the spectrometer
(with pressure gauges in between each attachment). This set up allows for the
formation of argon van der Waals complexes with cyclopentanone once the gas
expansion is inside the vacuum chamber. Initially, optimization tests indicated that
33
the argon gas generated the strongest observed intensities with low pressures of -40
kPa (below 1 atm) and detection parameters that consisted of a gas expansion width
of 1000 μs, an excitation width of 1.5 μs with 0.1 μs delay after each microwave
pulse and a detection source width of 750 μs. But, secondary experiments a year later
indicated that the molecule was very pressure dependent and generated the best
signals at 101.325 kPa (1 atm) and detection parameters that consisted of a gas
expansion width of 1295 μs, an excitation width of 1.5 μs with 0.1 μs delay after each
microwave pulse and a detection source width of 1075 μs. Spectral data for this
compound was collected from 7.6 GHz to 22 GHz.33 A sample of the 40Arcyclopentanone spectra in the time and frequency domain is shown in figure 3.4.1.
Figure 3.4.1. The spectrum of the 40Ar-cyclopentanone complex at 11438 MHz in the time
domain (top) and frequency domain (bottom picture). The roughly 29 mV intensity of the
40
Ar-cyclopentanone line indicates that the intensities of the 36Ar-cyclopentanone lines will be
roughly 0.097 mV, which is about 300 times weaker than the parent compound.
34
Using the known rotational constants and centrifugal distortion constants for
each of the isotopomers, SPCAT prediction files of the monomer, complex and the
13
C and 18O isotopomers were created to make sure that the observed lines used for
our fits were unique to the 36Ar. Several line checks in neon were also completed to
make sure the molecules were of dependent on argon, to confirm that they were argon
complexes.
3.5. Results and Discussion
The proper quantum assignment and structure of the 36Ar-cyclopentanone is
still being refined. Our closest fits for the 36Ar complex have produced the following
constants: A=2617.744, B =1177.707, C=1021.683, which closely matched the
position of the 40Ar in the complex when analyzed with a Kraitchman analysis for
isotopic substitution. However, this fit does not perfectly predict new lines and is thus
not conclusive. The lack of agreement between predicted results and experimental
data (as well as a lack of available lines for fitting) make this experiment extremely
difficult. As a result of these experimental hurdles, the spectrum of the 36Arcyclopentanone van der Waals complex has not been completely resolved.
3.6. Future Work
Further investigation and analysis of the spectrum for the 36Ar complex will
be done to refine the value of the rotational constants A, B, C and centrifugal
distortion constants. Other computational approaches and methods to predicting
accurate van der Waals geometries will be explored. Once a good set of initial
rotational constants can be predicted to guide the structural fit, it will be easier to
determine the spectrum and geometry of the 36Ar-cyclopentanone complex.
35
Appendix
A.1. 2H, 3H-Perfluoropentane Charts and Sample Files
A.1.1. Transition Frequency Assignments for 2H, 3H-Perfluoropentane and its
Isotopologues
Note: Comments are surrounded by: (* text *) and should be removed from the input files
prior to their usage.
Transition
All-12C
α-13C
β-13C
γ-13C
δ-13C
ε-13C
ν (MHz)
ν (MHz)
ν (MHz)
ν (MHz)
ν (MHz)
J'
Ka'
Kc'
J''
Ka''
Kc''
ν (MHz)
14
1
13
13
2
11
7021.645
4
3
1
3
2
1
7040.787
4
3
2
3
2
2
7041.041
9
1
8
8
0
8
7049.335
17
2
15
16
3
13
7079.911
7
2
5
6
1
5
7214.756
7
2
6
6
1
6
7369.155
13
0
13
12
1
11
7431.351
23
4
20
22
5
18
7463.618
23
4
19
22
5
17
7465.140
16
1
16
15
2
14
7495.761
18
2
17
17
3
15
7553.853
5
3
2
4
2
2
7706.646
5
3
3
4
2
3
7707.392
15
1
14
14
2
12
7719.283
10
1
9
9
0
9
7757.640
18
2
16
17
3
14
7775.666
29
5
25
29
4
25
7832.089
28
5
24
28
4
24
7838.530
29
5
24
29
4
26
7841.839
27
5
23
27
4
23
7844.174
28
5
23
28
4
25
7845.925
26
5
22
26
4
22
7849.106
27
5
22
27
4
24
7849.721
26
5
21
26
4
23
7853.220
25
5
21
25
4
21
7853.407
25
5
20
25
4
22
7856.433
24
5
20
24
4
20
7857.152
8
2
6
7
1
6
7858.375
36
24
5
19
24
4
21
7859.340
23
5
19
23
4
19
7860.401
23
5
18
23
4
20
7861.972
22
5
18
22
4
18
7863.219
22
5
17
22
4
19
7864.321
21
5
17
21
4
17
7865.643
21
5
16
21
4
18
7866.405
20
5
16
20
4
16
7867.717
20
5
15
20
4
17
7868.236
19
5
15
19
4
15
7869.499
19
5
14
19
4
16
7869.844
18
5
14
18
4
14
7871.008
18
5
13
18
4
15
7871.232
17
5
12
17
4
14
7872.423
17
5
13
17
4
13
7872.282
16
5
12
16
4
12
7873.338
16
5
11
16
4
13
7873.437
15
5
11
15
4
11
7874.251
15
5
10
15
4
12
7874.251
14
5
10
14
4
10
7874.920
14
5
9
14
4
11
7875.003
13
5
8
13
4
10
7875.542
13
5
9
13
4
9
7875.542
12
5
7
12
4
9
7876.006
12
5
8
12
4
8
7876.006
11
5
6
11
4
8
7876.373
11
5
7
11
4
7
7876.373
10
5
5
10
4
7
7876.655
10
5
6
10
4
6
7876.655
9
5
5
9
4
5
7876.866
8
5
4
8
4
4
7877.026
21
3
19
20
4
17
7880.678
21
3
18
20
4
16
7907.286
14
0
14
13
1
12
8030.566
8
2
7
7
1
7
8062.120
17
1
17
16
2
15
8093.341
19
2
18
18
3
16
8205.976
6
3
3
5
2
3
8372.179
6
3
4
5
2
4
8373.917
27
5
23
26
6
21
8378.474
37
27
5
22
26
6
20
8378.623
16
1
15
15
2
13
8415.121
11
1
10
10
0
10
8471.243
19
2
17
18
3
15
8475.301
9
2
7
8
1
7
8500.000
22
3
20
21
4
18
8548.885
22
3
19
21
4
17
8583.657
15
0
15
14
1
13
8622.466
18
1
18
17
2
16
8686.669
9
2
8
8
1
8
8758.954
4
4
0
3
3
0
8791.436
25
4
22
24
5
20
8802.639
25
4
21
24
5
19
8805.539
20
2
19
19
3
17
8855.917
7
3
4
6
2
4
9037.219
9023.583
9030.431
9036.094
9028.254
9022.242
7
3
5
6
2
5
9040.681
9027.013
9033.919
9039.576
9031.761
9025.644
17
1
16
16
2
14
9108.475
10
2
8
9
1
8
9140.133
20
2
18
19
3
16
9178.829
12
1
11
11
0
11
9190.456
16
0
16
15
1
14
9206.763
23
3
21
22
4
19
9216.977
13
1
13
12
0
12
9220.773
19
1
19
18
2
17
9275.735
5
4
1
4
3
1
9457.593
10
2
9
9
1
9
9459.671
21
2
20
20
3
18
9503.488
26
6
21
26
5
21
9614.081
26
6
20
26
5
22
9614.150
25
6
20
25
5
20
9616.063
25
6
19
25
5
21
9616.063
23
6
18
23
5
18
9619.338
23
6
17
23
5
19
9619.338
22
6
17
22
5
17
9620.676
22
6
16
22
5
18
9620.676
21
6
16
21
5
16
9621.853
21
6
15
21
5
17
9621.853
20
6
15
20
5
15
9622.880
20
6
14
20
5
16
9622.880
19
6
14
19
5
14
9623.769
38
19
6
13
19
5
15
9623.769
18
6
13
18
5
13
9624.529
17
6
12
17
5
12
9625.172
17
6
11
17
5
13
9625.172
16
6
11
16
5
11
9625.721
16
6
10
16
5
12
9625.721
15
6
10
15
5
10
9626.174
14
6
9
14
5
9
9626.553
13
6
8
13
5
8
9626.859
12
6
7
12
5
7
9627.105
11
6
6
11
5
6
9627.297
10
6
5
10
5
5
9627.451
9
6
4
9
5
4
9627.567
8
6
3
8
5
3
9627.650
8
3
5
7
2
5
9701.584
9685.280
9694.140
9700.458
9691.754
9683.600
8
3
6
7
2
6
9707.802
9691.433
9700.398
9706.705
9698.044
9689.703
11
2
9
10
1
9
9779.269
18
1
17
17
2
15
9798.682
20
1
20
19
2
18
9860.556
24
3
22
23
4
20
9884.876
21
2
19
20
3
17
9886.177
13
1
12
12
0
12
9915.599
6
4
2
5
3
2
10123.734
6
4
3
5
3
3
10123.734
11
2
10
10
1
10
10164.288
18
0
18
17
1
16
10351.540
9
3
6
8
2
6
10365.028
10346.069
10356.927
10363.904
10354.329
10344.059
9
3
7
8
2
7
10375.349
10356.284
10367.313
10374.271
10364.769
10354.188
12
2
10
11
1
10
10417.913
NM
NM
10417.045
NM
NM
21
1
21
20
2
19
10441.174
19
1
18
18
2
16
10485.086
22
2
20
21
3
18
10597.190
14
1
13
13
0
13
10646.980
NM
NM
10648.013
NM
NM
7
4
3
6
3
3
NR
NM
NM
10788.228
NM
NM
7
4
4
6
3
4
10789.853
NM
NM
10788.243
NM
NM
12
2
11
11
1
11
10872.825
19
0
19
18
1
17
10911.682
22
1
22
21
2
20
11017.547
10
3
7
9
2
7
11027.300
11005.702
11018.541
11026.176
11015.722
NM
10
3
8
9
2
8
11043.440
11021.675
11034.778
11042.388
11032.044
11019.210
39
13
2
11
12
1
11
11056.693
11025.567
11046.579
11055.824
11043.127
11022.295
20
1
19
19
2
17
11167.063
5
5
0
4
4
0
11208.101
11203.873
11200.743
11205.959
11198.359
11204.115
26
3
23
25
4
21
11309.859
23
2
21
22
3
19
11311.622
13
7
7
13
6
7
11377.709
12
7
6
12
6
6
11377.855
11
7
5
11
6
5
11377.977
15
1
14
14
0
14
11384.909
8
4
4
7
3
4
11455.888
NM
NM
11454.303
NM
NM
NM
NM
11454.351
NM
NM
8
4
5
7
3
5
11455.947
20
0
20
19
1
18
11463.534
13
2
12
12
1
12
11585.303
23
1
23
22
2
21
11589.777
11
3
8
10
2
8
11688.130
NM
NM
11686.998
NM
NM
14
2
12
13
1
12
11696.188
NM
11685.438
11695.334
NM
NM
11
3
9
10
2
9
11712.201
11687.730
NM
11711.175
11699.995
11684.888
21
1
20
20
2
18
11843.993
6
5
1
5
4
1
11874.254
11867.349
11866.261
11872.132
11863.679
11867.238
21
0
21
20
1
19
12007.126
9
4
5
8
3
5
12121.913
9
4
6
8
3
6
12121.992
16
1
15
15
0
15
12129.670
14
2
13
13
1
13
12301.727
15
2
13
14
1
13
12337.024
12
3
9
11
2
9
12347.233
12
3
10
11
2
10
12381.754
22
1
21
21
2
19
12515.299
7
5
2
6
4
2
12540.405
22
0
22
21
1
20
12542.563
10
4
6
9
3
6
12787.797
10
4
7
9
3
7
12787.984
17
1
16
16
0
16
12881.499
16
2
14
15
1
14
12979.812
40
A.1.2. Sample Input File for KRA.exe for Kraitchman Single Atom Substitution
Analysis
(* Reminder: Comments are made between (* and *) and should be removed in the actual file
when running KRA.exe *)
2h3hpfp (*title*)
c
c parent species (*table for the parent species*)
c
1 -2
3 -1
1208.3386 336.90086, 329.24674 (*rotational constants A, B and C for the parent species*)
0.0001 , 0.00005, 0.00005 (*errors in the rotational constants for the parent species*)
251.9993823 (*mass of the parent species*)
c
c C(5) (*label of carbon 5*)
c
1208.01815 , 335.54314 , 327.92366 (*rotational constants A, B and C for the isotopologue*)
0.00004 , 0.00005 , 0.00007 (*errors in the rotational constants for the isotopologue*)
1.003354826 (*change in mass for the isotopologue from the parent species*)
c
c C(4) (*similar to C(5), format is continued for all of the isotopologues that need substitution*)
c
1207.55688 , 336.59273 , 328.9161
0.00007 , 0.00008 , 0.0001
1.003354826
c
c C(3)
c
1208.10021 , 336.9168 , 329.2456
0.00009 , 0.0001 , 0.0001
1.003354826
c
c C(2)
c
1207.30318 , 336.5028 , 328.8067
0.00008 , 0.0001 , 0.0001
1.003354826
c
c C(1)
c
1208.06473 , 335.35054 , 327.76270
0.00003 , 0.00004 , 0.00006
1.003354826
1 -3
41
A.1.3. Sample Input File for Scanning Coordinate Calculations for the (R,R)
trans-2H, 3H-perfluoropentane Isomer
%chk=\home\cduong\gaussian.chk
# opt=modredundant MP2/3-21g geom=connectivity
Title Card Required
01
C
C
C
H
C
C
F
F
F
F
F
F
F
F
F
F
H
1.24999996
1.76331567
1.24997638
1.60665206
1.76329093
1.24995263
1.70000775
-0.10000004
1.70000775
-0.10002362
1.31330532
1.31327805
3.11329093
-0.10004508
1.70198270
1.69791603
2.83331567
3.90449432
2.45256217
1.72660693
2.23100617
0.27467437
-0.45127910
4.54088456
3.90451096
4.54088456
1.72662434
1.81617102
-0.36171715
0.27465597
-0.44912064
0.18368475
-1.72478892
2.45254899
0.00000000
0.00000000
1.25740676
2.13105650
1.25740605
2.51481423
-1.10227059
0.00000000
1.10227059
1.25741070
-1.10226902
0.15513828
1.25740083
2.51605630
3.61707996
2.51357938
-0.00000249
1 2 1.0 7 1.0 8 1.0 9 1.0
2 3 1.0 11 1.0 17 1.0
3 4 1.0 5 1.0 10 1.0
4
5 6 1.0 12 1.0 13 1.0
6 14 1.0 15 1.0 16 1.0
7
8
9
10
11
12
13
14
15
16
17
D 1 2 3 5 S 71 5.000000
42
A.1.4. Sample Input for MP2/6-31+g(d,p) Optimization with Gaussian O9
%chk=\home\cduong\gaussian.chk
# opt mp2/6-31+g(d,p) geom=connectivity output=pickett
optRRtrans
01
C
C
C
H
C
C
F
F
F
F
F
F
F
F
F
F
H
-2.59072500
-1.32328500
-0.09958500
-0.18452100
1.17068500
2.42465100
-3.68831100
-2.77002500
-2.48418600
0.00930200
-1.41305600
1.20306900
1.17191400
2.64749800
2.24713000
3.51574100
-1.25760100
-0.20604000
0.61104200
-0.29015100
-1.00335400
0.50126600
-0.31707700
0.60720200
-1.07046900
-0.94556000
-0.96904700
1.35313400
1.65393600
0.87204900
-0.41947300
-1.57356400
0.26268300
1.27109900
0.20680300
0.06185100
0.05433600
0.87185900
0.27768700
-0.00735100
0.30491800
-0.83802300
1.37256300
-1.18717200
-1.13990800
-0.49500200
1.62729100
-1.34828000
0.52495600
0.58304500
0.92869300
1 2 1.0 7 1.0 8 1.0 9 1.0
2 3 1.0 11 1.0 17 1.0
3 4 1.0 5 1.0 10 1.0
4
5 6 1.0 12 1.0 13 1.0
6 14 1.0 15 1.0 16 1.0
7
8
9
10
11
12
13
14
15
16
17
D 1 2 3 5 S 71 5.000000
43
A.1.5. Sample Input for MP2/6-311++g(2d,2p) Optimization with Gaussian 09
%chk=\home\cduong\gaussian.chk
# opt=verytight mp2/6-311++g(2d,2p) geom=connectivity output=pickett
optRRtranstransHnearZPE
01
C
C
C
H
C
C
F
F
F
F
F
F
F
F
F
F
H
2.63040500
1.34564600
0.11285400
0.14714700
-1.17814500
-2.47142300
3.68937600
2.85628300
2.54355900
0.07618800
1.47436300
-1.27615000
-1.14051100
-2.68473100
-2.36989500
-3.52089900
1.26511800
-0.25579000
0.56629300
-0.28937500
-1.18640600
0.45539700
-0.34418300
0.53077900
-0.87378800
-1.20444500
-0.66665700
1.54224700
1.62853000
0.73425300
-0.51124200
-1.55954100
0.30381000
1.04433600
-0.20219400
-0.19744700
0.06953000
-0.55143000
-0.26492900
-0.00703200
-0.47922800
0.96916300
-1.17355700
1.40349800
0.77607500
0.41239200
-1.61033600
1.30548700
-0.59261300
-0.53898200
-1.17551300
1 2 1.0 7 1.0 8 1.0 9 1.0
2 3 1.0 11 1.0 17 1.0
3 4 1.0 5 1.0 10 1.0
4
5 6 1.0 12 1.0 13 1.0
6 14 1.0 15 1.0 16 1.0
7
8
9
10
11
12
13
14
15
16
17
44
A.1.6. Sample .var Input for SPCAT
(*The .par file for SPFIT is similar to the .var file, but the rotational constants are allowed to
vary, rather than be confined to tight values.*)
ss-2h-3h-PFP-60 MP2/6-311+G(2d,2p)
Wed JMon Jun 11 17:36:14 2012
8 1000 250 0 0.0000E+000 1.0000E+006 1.0000E+000 1.0000000000
a 1 1 0 30 0 1 1 1 0 1 0
10000 1.208338699166590E+003 2.60003741E-004 / A
20000 3.369008644855941E+002 6.99150590E-005 / B
30000 3.292467492312164E+002 7.43742741E-005 / C
200 -5.503100870489122E-006 8.24839847E-008 / DJ
2000 -6.312264525593489E-005 4.93983368E-006 / DK
1100 -1.672616019794120E-005 4.18775513E-007 / DJK
40100 1.080448425755044E-007 3.02668399E-008 / dj
41000 -1.480970071158974E-004 9.11810811E-006 / dk
A.1.7. Sample .int Input for SPCAT
03 ss1662h3hPFP
0000 00001 2391 0 29 -8.5 -8.5
2 0.5500000/ b dipole moment
3 2.2300000/ c dipole moment
25.0
3.0
(*The a dipole moment was ignored because computational results showed that this value
was too small and unlike to be detected.*)
A.1.8. Sample .lin Input for SPFIT
14 1 13 13 2 11 0 0 0 0 0 0 7021.645298 0.008000 1.00000
4 3 1 3 2 1 0 0 0 0 0 0 7040.786774 0.008000 1.00000
4 3 2 3 2 2 0 0 0 0 0 0 7041.040885 0.008000 1.00000
9 1 8 8 0 8 0 0 0 0 0 0 7049.334807 0.008000 1.00000
17 2 15 16 3 13 0 0 0 0 0 0 7079.910792 0.008000 1.00000
7 2 5 6 1 5 0 0 0 0 0 0 7214.756459 0.008000 1.00000
7 2 6 6 1 6 0 0 0 0 0 0 7369.154501 0.008000 1.00000
13 0 13 12 1 11 0 0 0 0 0 0 7431.350760 0.008000 1.00000
23 4 20 22 5 18 0 0 0 0 0 0 7463.617622 0.008000 1.00000
23 4 19 22 5 17 0 0 0 0 0 0 7465.140300 0.008000 1.00000
16 1 16 15 2 14 0 0 0 0 0 0 7495.760656 0.008000 1.00000
18 2 17 17 3 15 0 0 0 0 0 0 7553.852643 0.008000 1.00000
45
A.2. Argon-36 Cyclopentanone Sample Files
A.2.1. Sample Input for MOMENT
(*The first row lists the number of atoms on the molecule (15) the other three
parameters were not used in this experiment. The first column after the first row
indicates the mass of the atom, and the second, third and fourth columns are the
coordinates of the atoms in the principal axis system along a, b, and c respectively.*)
Ar Cyclopentanone b3lyp/6-311G+(d,p)
15 0 0 0.0
12.00000 0.850641 0.000000 0.000001
12.00000 -0.044519 1.235399 -0.125819
12.00000 -1.456658 0.740010 0.223368
12.00000 -1.456656 -0.740011 -0.223372
12.00000 -0.044518 -1.235398 0.125825
1.00783 0.012821 1.567998 -1.170018
1.00783 0.333192 2.052500 0.491240
1.00783 -1.615302 0.799457 1.305411
1.00783 -2.246964 1.323084 -0.252926
1.00783 -2.246965 -1.323086 0.252915
1.00783 -1.615209 -0.799457 -1.305417
1.00783 0.012815 -1.567987 1.170027
1.00783 0.333196 -2.052504 -0.491224
15.99491 2.057406 0.000000 -0.000003
35.96755 0.945000 0.804000 3.459000
46
A.2.2. Sample Input for LAS
Ar-cyclopentanone second fit - LAS V1.2c
500.0000 1.000 3 8 8 8 1 200 0
5000.000 26500.000 1.300 3.200 0.000 1.000 0.000100
10 0 8 11 1 1 4
c Frequency-MHz J^ K^ #ON %Error
Rotational Parameter
.2618306000D+04
1 20.000000 A
.1177491000D+04
1 20.000000 B
.1021392000D+04
1 20.000000 C
c Frequency-MHz J^ K^ #ON Max Mag.-MHz Perturbing Parameter
.3919300000D-03
0 10.000000 dJ
.4891000000D-02
0 10.000000 dK
.0000000000D+00
0 0.000000 HJ
.0000000000D+00
0 0.000000 HJK
.0000000000D+00
0 0.000000 HK
.7151300000D-02 1 1 0 10.000000 Delta JK
.2573240000D-02 2 0 0 10.000000 Delta J
.1321800000D-02 0 2 0 10.000000 Delta K
c
c Frequency
Omit QN? >1? J' KA' KC' J'' KA'' KC''
.8901363280D+04 1 0 0
.1010433640D+05 1 0 0
.1060504566D+05 1 0 0
.1060896900D+05 0 0 0
.1077562004D+05 1 0 0
.1216488500D+05 1 0 0
.1324296341D+05 1 0 0
.1418455500D+05 1 0 0
47
A.2.3. Sample .var Input for SPCAT
(*The .par file for SPFIT is similar to the .var file, but the rotational constants are allowed to
vary, rather than be confined to tight values.*)
36-Ar cyclopentanone with errors estimate 7-22-10
Wed Jan 09 22:36:32 2013
8 8 150 0 0.0000E+000 1.0000E+006 1.0000E+000 1.0000000000
'a' 1 1 0 30 0 1 1 1
0 10
10000 2.617750189197834E+003 6.51172666E-004 / A
20000 1.177670387134323E+003 5.75572325E-004 / B
30000 1.021715827685689E+003 2.00167511E-004 / C
200 -2.573200000000000E-003 1.00000000E-036 / DJ
2000 -1.321000000000000E-003 1.00000000E-036 / DK
1100 -7.151000000000002E-003 1.00000000E-036 / DJK
40100 -3.919000000000000E-004 1.00000000E-036 / dj
41000 -4.890000000000000E-003 1.00000000E-036 / dk
A.2.4. Sample .int Input for SPCAT
36-Ar Cyclopentanone 6-6-10
112 00001 1108.1625 0 20
1
1.00 / a dipole
2
2.00 / b dipole
3
0.00 / c dipole
-6. -6.
26.5
A.2.5. Sample .lin Input for SPFIT
6
6
3
3
5
3
7
7
0
1
3
3
1
2
0
1
6
6
1
0
5
2
7
7
5
5
2
2
4
2
6
6
1
0
2
2
0
1
1
0
5
5
0
1
4
1
6
6
12166.44864
13314.14010
14182.73660
14195.27690
11443.21810
10917.81300
14396.14800
15201.04300
.005
.005
.005
.005
.005
.005
.005
.005
48
1.
1.
1.
1.
1.
1.
1.
1.
5.0
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