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

i

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

ii

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

1

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!

2

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.

3

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

EH (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 (1.1.1.a)

where I is the moment of inertia, μ is the reduced mass

, 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:

4

zzzyzx

yzyyyx

xzxyxx

III

III

III

I (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:

c

b

a

I

I

I

I

00

00

00

(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.

5

Given the rotational Hamiltonian:

(1.1.1.j)

the rotational constants (in joules) A, B and C can be obtained by:

aI

hA

28 (1.1.1.k)

bI

hB

28 (1.1.1.l)

cI

hC

28 (1.1.1.m)

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:

CA

CAB

2 (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

6

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 dipole-

dipole, quadrupole-dipole, quadrupole-quadrupole, Keesom alignment, dipole-

induced 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

7

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).

8

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 (cavity-

FTMW).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.

9

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.

To Diff.

Pump

10

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 CP-

FTMW 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.

11

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:

(

) (1.3.2)

where is the output frequency, 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

12

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 cavity-

FTMW 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

13

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

14

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 36

Ar-

cyclopentanone 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.

15

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,3H-

perfluoropentane 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 13

C 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

16

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 MP2/6-

31+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

17

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-C

3-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, 3H-

perfluoropentane 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

18

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-C

3-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

19

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 A = 1190.43

B = 335.34

C = 329.05

(R,R) Cis (right well)-

2H,3H-Perfluoropentane

217

1.91

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 A = 1096.55

B = 374.60

C = 359.22

(R,S) Trans (left well)

2H,3H-Perfluoropentane

77

0.26 A = 1203.95

B = 346.20

C = 318.46

(R,S) Trans (right well)-

2H,3H-Perfluoropentane

77

0.26 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.

20

Structure MP2/6-

311++g(2d,2p)

Relative Energies

(cm-1

)

Total Dipole

(Debye)

Predicted

Rotational

Constants (MHz)

(R,R) Trans (left well)-

2H,3H-Perfluoropentane

0 2.02 A = 1204.74

B = 339.94

C = 332.81

(R,R) Cis (right well)-

2H,3H-Perfluoropentane

163

1.91

A = 1108.10

B = 381.24

C = 365.07

(S,S) Trans (left well)-

2H,3H-Perfluoropentane

0 2.02 A = 1204.73

B = 339.94

C = 332.81

(S,S) Cis (right well)-

2H,3H-Perfluoropentane

163 1.91 A = 1108.10

B = 381.24

C = 365.07

(R,S) Trans (left well)

2H,3H-Perfluoropentane

180

0.33 A = 1221.02

B = 350.95

C = 322.89

(R,S) Trans (right well)-

2H,3H-Perfluoropentane

180

0.33 A = 1221.02

B = 350.95

C = 322.89

(S,R) Trans (left well)-

2H,3H-Perfluoropentane

180

0.33 A = 1221.02

B = 350.95

C = 322.89

(S,R) Trans (right well)-

2H,3H-Perfluoropentane

180

0.33 A = 1221.02

B = 350.95

C = 322.89

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) trans-

2H, 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.

21

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, 3H-

perfluoropentane 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 Q-

branch 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 b-

type 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.

22

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.

23

Data for the 13

C 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 cavity-

FTMW.

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 3 5 - 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

8 - 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

24

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 Parent 13

C (1) 13

C (2) 13

C (3) 13

C (4) 13

C (5)

A /MHz 1190.426 1190.129 1189.420 1190.177 1189.649 1190.095

B /MHz 335.329 333.789 334.918 335.325 335.005 333.976

C /MHz 329.645 327.556 328.589 329.024 328.704 327.717

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 Parent

(Obs)

13C (1)

(Scaled)

13C (2)

(Scaled)

13C (3)

(Scaled)

13C (4)

(Scaled)

13C (5)

(Scaled)

A /MHz 1208.3386(1) 1207.980 1207.260 1208.030 1207.490 1207.95

B /MHz 336.90086(5) 335.358 336.492 336.901 336.580 335.546

C /MHz 329.24674(5) 327.756 328.789 329.225 328.905 327.917

Table 2.5.2. The scaled rotational constants of the carbon-13 isotopologues of 2H, 3H-

perfluoropentane 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

25

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 Parent 13

C (1) 13

C (2) 13

C (3) 13

C (4) 13

C (5)

A /MHz 1208.3386(1) 1208.06473(3) 1207.30318(8) 1208.10021(9) 1207.55688(7) 1208.01815(4)

B /MHz 336.90086(5) 335.35054(4) 336.5028(1) 336.9168(1) 336.59273(8) 335.54314(5)

C /MHz 329.24674(5) 327.76270(6) 328.8067(1) 329.2456(1) 328.9161(1) 327.92366(7)

ΔJ /kHz 0.00550(6) 0.0045(2) 0.0048(4) 0.0045(3) 0.0044(4) 0.0045(2)

ΔK /kHz 0.063(3) [0.063] [0.063] [0.063] [0.063] [0.063]

ΔJK /kHz 0.0167(3) [0.0167] [0.0167] [0.0167] [0.0167] [0.0167]

δJ /kHz -0.00010(2) [-0.00010] [-0.00010] [-0.00010] [-0.00010] [-0.00010]

δK /kHz 0.148(6) [0.148] [0.148] [0.148] [0.148] [0.148]

Lines used 182 11 12 20 12 11

Microwave

RMS /kHz

6.0 0.3 0.8 1.3 0.7 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.

26

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 Calc.

C(3)

Obs.

C(3)

Calc.

C(4)

Obs.

C(4)

Calc.

C(5)

Obs.

C(5)

a -0.113 [-0.113] 1.178 1.150(1) 2.471 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

27

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 Calc.

(Staggered)

MP2/6-31+g(d,p)

Calc.

(Helical)

MP2/6-31+g(d,p)

Obs.

Results

(Helical)

Rotational Constants (MHz) A = 1159.9

B = 334.9

C = 332.0

A = 1190.4

B = 335.3

C = 329.0

A = 1208.3386(1)

B = 336.90086(5)

C = 329.24674(5)

Second Moments Paa

= 1275.9

Pbb

= 246.3

Pcc

= 189.4

Paa

= 1309.2

Pbb

= 226.7

Pcc

= 197.9

Paa

= 1308.3973(3)

Pbb

= 226.5579(3)

Pcc

= 191.6850(3)

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 perfluoropentane

20 that reveal

perfluorinated alkanes with four or more carbons within the chain have helical

geometries. In the case of perfluoropentane, a helical angle ~15o – 17

o 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-17

o from the

staggered conformation. This indicated that although hydrogen substituents exist in

28

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 (19

F).

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, 3H-

perfluoropentane 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, 3H-

perfluoropentane conformers. Additionally, since these conformers were not seen in

the CP-FTMW and difficult to observe in the cavity-FTMW experiments due to their

29

low dipoles and higher relative energies than the (S,S) and (R,R) trans-2H, 3H-

perfluoropentane 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 13

C 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, 3H-

perfluoropentane.

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

30

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, 3H-

perfluoropentane 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

40Ar-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 36

Ar-cyclopentanone (36

Ar-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 40

Ar-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 36

Ar isotope has a natural abundance of 0.33% and the 18

O isotope has a natural

abundance of (0.21%). This would imply that although the 36

Ar-C5H8O complex

approximately 300 times weaker than the main 40

Ar-C5H8O isotopomer, it should be

31

visible using the cavity-FTMW and also be easier to detect in natural abundance than

the 40

Ar-C5H818

O complex. Since the spectrum of the 40

Ar-C5H818

O complex was

observed in natural abundance, it was expected that the 36

Ar-C5H8O complex would

also be observable within the cavity-FTMW in natural abundance.

Previously determined spectral and structural data of the 40

Ar-C5H8O complex

combined with scaling calculations and Kraitchman analysis were used to predict the

spectra and structure of the 36

Ar-C5H8O complex. A visualization of the Ar-

cyclopentanone 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 36

Ar-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 36

Ar in the same position as

the 40

Ar 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 20

Ne- C5H8O and 22

Ne-C5H8O indicated that the position of the neon atoms

between the two complexes were almost identical.31

32

Figure 3.1.1. Argon Position in 40

Ar-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 40

Ar-

cyclopentanone 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, 40

Ar complex and the 13

C and 18

O isotopologues. The

spectra and structure of the 36

Ar isotopomer was and has never been studied in natural

abundance. With the known 40

Ar coordinates in the principal axis system and

33

replacement of the mass of 40

Ar with 36

Ar, a theoretical prediction of the rotational

constants (A, B and C) for the 36

Ar 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 40

Ar 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 36

Ar-

complex 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

34

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 40

Ar-

cyclopentanone spectra in the time and frequency domain is shown in figure 3.4.1.

Figure 3.4.1. The spectrum of the 40

Ar-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 36

Ar-cyclopentanone lines will be

roughly 0.097 mV, which is about 300 times weaker than the parent compound.

35

Using the known rotational constants and centrifugal distortion constants for

each of the isotopomers, SPCAT prediction files of the monomer, complex and the

13C and

18O isotopomers were created to make sure that the observed lines used for

our fits were unique to the 36

Ar. 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 36

Ar-cyclopentanone is

still being refined. Our closest fits for the 36

Ar complex have produced the following

constants: A=2617.744, B =1177.707, C=1021.683, which closely matched the

position of the 40

Ar 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 36

Ar-

cyclopentanone van der Waals complex has not been completely resolved.

3.6. Future Work

Further investigation and analysis of the spectrum for the 36

Ar 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 36

Ar-cyclopentanone complex.

36

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

J' Ka' Kc' J'' Ka'' Kc'' ν (MHz) ν (MHz) ν (MHz) ν (MHz) ν (MHz) 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

37

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

38

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

39

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

40

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

8 4 5 7 3 5 11455.947 NM NM 11454.351 NM NM

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

41

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

42

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

0 1

C 1.24999996 3.90449432 0.00000000

C 1.76331567 2.45256217 0.00000000

C 1.24997638 1.72660693 1.25740676

H 1.60665206 2.23100617 2.13105650

C 1.76329093 0.27467437 1.25740605

C 1.24995263 -0.45127910 2.51481423

F 1.70000775 4.54088456 -1.10227059

F -0.10000004 3.90451096 0.00000000

F 1.70000775 4.54088456 1.10227059

F -0.10002362 1.72662434 1.25741070

F 1.31330532 1.81617102 -1.10226902

F 1.31327805 -0.36171715 0.15513828

F 3.11329093 0.27465597 1.25740083

F -0.10004508 -0.44912064 2.51605630

F 1.70198270 0.18368475 3.61707996

F 1.69791603 -1.72478892 2.51357938

H 2.83331567 2.45254899 -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

43

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

0 1

C -2.59072500 -0.20604000 0.20680300

C -1.32328500 0.61104200 0.06185100

C -0.09958500 -0.29015100 0.05433600

H -0.18452100 -1.00335400 0.87185900

C 1.17068500 0.50126600 0.27768700

C 2.42465100 -0.31707700 -0.00735100

F -3.68831100 0.60720200 0.30491800

F -2.77002500 -1.07046900 -0.83802300

F -2.48418600 -0.94556000 1.37256300

F 0.00930200 -0.96904700 -1.18717200

F -1.41305600 1.35313400 -1.13990800

F 1.20306900 1.65393600 -0.49500200

F 1.17191400 0.87204900 1.62729100

F 2.64749800 -0.41947300 -1.34828000

F 2.24713000 -1.57356400 0.52495600

F 3.51574100 0.26268300 0.58304500

H -1.25760100 1.27109900 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

44

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

0 1

C 2.63040500 -0.25579000 -0.20219400

C 1.34564600 0.56629300 -0.19744700

C 0.11285400 -0.28937500 0.06953000

H 0.14714700 -1.18640600 -0.55143000

C -1.17814500 0.45539700 -0.26492900

C -2.47142300 -0.34418300 -0.00703200

F 3.68937600 0.53077900 -0.47922800

F 2.85628300 -0.87378800 0.96916300

F 2.54355900 -1.20444500 -1.17355700

F 0.07618800 -0.66665700 1.40349800

F 1.47436300 1.54224700 0.77607500

F -1.27615000 1.62853000 0.41239200

F -1.14051100 0.73425300 -1.61033600

F -2.68473100 -0.51124200 1.30548700

F -2.36989500 -1.55954100 -0.59261300

F -3.52089900 0.30381000 -0.53898200

H 1.26511800 1.04433600 -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

45

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 25.0 3.0

2 0.5500000/ b dipole moment

3 2.2300000/ c dipole moment

(*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

46

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

47

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

48

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 1 0

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 -6. -6. 26.5 5.0

1 1.00 / a dipole

2 2.00 / b dipole

3 0.00 / c dipole

A.2.5. Sample .lin Input for SPFIT

6 0 6 5 1 5 12166.44864 .005 1.

6 1 6 5 0 5 13314.14010 .005 1.

3 3 1 2 2 0 14182.73660 .005 1.

3 3 0 2 2 1 14195.27690 .005 1.

5 1 5 4 0 4 11443.21810 .005 1.

3 2 2 2 1 1 10917.81300 .005 1.

7 0 7 6 1 6 14396.14800 .005 1.

7 1 7 6 0 6 15201.04300 .005 1.

49

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