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T h e 1 /1 1 band of cyanuric fluoride and the A *11 - X *E+ transition of aluminum monobromide

Fleming, Patrick E., Ph.D.

The Ohio State University, 1994

UMI 300 N. Zeeb Rd. Ann Arbor, Ml 48106 The vn Band of Cyanuric Fluoride and The A ‘II - X 1S + Transition of Aluminum Monobromide

A Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of the Ohio State University

By

Patrick E. Fleming

* * * * *

The Ohio State University

1994

Approved By: Dissertation Committee:

Prof. James V. Coe Prof. Roger E. Gerkin Prof. C. Weldon Mathews Advisor Department of Chemistry To my students, past and future.

ii Acknowledgements

I wish to express my most sincere gratitude to my preceptor, Professor C. Weldon

Mathews for his continual guidance during the completion of the projects presented in this document. I also wish to thank Professors James Coe, Roger Gerkin, Harry McSwiney and

Russell Pitzer for critical readings of this document and portions thereof and also for many helpful suggestions and discussions concerning the content of this document.

I would like to thank the many former and current members of the research group including Drs. Barbara Sweeting and Michael Armijo. Also, gratitude is due to Kelly

Mahoney and Richard Brett for a great deal of help and advise in recent years.

Further, my survival over the past several years has been greatly aided by the friendship of several colleagues including Kenneth Cowen, Christopher Carter and Timothy

Wright who will always be remembered for saving the new Chemistry Building from the

"Great flood of 1994" and several amusing games of Hacky-Sack. Also, I would like to thank my good friends Cynthia Capp, Deborah McCarthy, Otto Fruedenberg, John Szpylka, Jed

Mellott and Frank Seeley. Their contributions to the quality of my life will not be forgotten.

I must also express my gratitude to all of the fine people at Ohio Wesleyan University who aided me in affording me my first solo opportunity at teaching on the college level.

Lastly, I would like to thank all of the current and past members of the Campus

Dart League and the Wednesday night dart league at Ledos. To all, throw well! Vita

January 16, 1963 Born - Torrance, California

1985 B.S. in Chemistry University of Notre Dame Du Lac Notre Dame, Indiana

1988 M.S in Physical Chemistry The Ohio State University Columbus, Ohio

1985 - 1992 Graduate Teaching Associate Department of Chemistry The Ohio State University Columbus, Ohio

1992 - 1994 Assistant Professor of Chemistry, Department of Chemistry Ohio Wesleyan University Delaware, Ohio

Field of Study

Major Field: Chemistry

Studies in Molecular Spectroscopy Professor C. Weldon Mathews

iv Table of Contents

D edication ...... ii

Acknowledgements ...... iii

V ita ...... iv

Table of Contents ...... v

List of Tables ...... viii

List of Figures ...... ix

CHAPTER I - Introduction ...... I

A. Principles of Fourier Transform Spectroscopy ...... 1

B. Light Collection Optics for the Bruker IFS 120 HR Spectrometer ...... 3

i. Principles of Design ...... 3 ii. Implementation ...... 4

C. Least-Squares fitting of Spectral Data ...... 6

R eferences ...... 18

CHAPTER II - The v„ Band of Cyanuric Fluoride ...... 19

A. Historical Background ...... 19

B. Experimental C o n siderations...... 21 CHAPTER II (Continued)

C. Spectral Interpretation and Analysis ...... 25

i. Vibrational Interpretation ...... 25 ii. Rotational Analysis ...... 26

D. Discussion and Conclusions ...... 30

i. Structural Considerations ...... 32

R eferences ...... 35

CHAPTER III - Aluminum Monobromide ...... 36

A. Introduction ...... 36

B. Experimental Details ...... 38

C. Isotopomer Identification ...... 39

D. Rotational Analysis ...... 44

E. Conclusions ...... 50

R eferences ...... 51

CHAPTER IV - Other Experiments...... 53

A. The Electronic Spectrum of FCN ...... 53

i. Production of FCN ...... 55 ii. Observations in the Laboratory ...... 56

B. Steady State Observation of Radicals Containing C N ...... 58

R eferences ...... 60

CHAPTER V - Conclusions ...... 63

Bibliography ...... 64

vi Appendix A - Assignments for the v„ and vn + v14-vI4 Bands of Cyanuric Fluoride ...... 67

Appendix B - Assignments for the A - X Transition of Aluminum Monobromide ...... 74

Appendix C - VIB-DIST.BAS ...... 97

Appendix D - ABC.BAS and related program s ...... 113

Appendix E - CHEW.BAS and CHEW-MER.BAS ...... 131

Appendix F - SIM.BAS and related program s ...... 141

vii List of Tables

Table

1. Chemicals Used in the Preparation of Cyanuric Fluoride ...... 21

2. Occupancy of Vibrational Levels of Cyanuric Fluoride ...... 26

3. Rotational Constants for Cyanuric Fluoride ...... 29

4. Band Origins for Cyanuric Fluoride Near 820 cm'1 ...... 30

5. Isotopic shifts of band origins in the A-X transition of A lB r ...... 43

6. Band-by-band fitting results for the A-X transition of A lB r ...... 46

7. Merged constants for the A state of AlBr ...... 48

8. Equiibrium constants for A lBr ...... 49

9. Electronic states of SF2 observed by REMPI spectroscopy ...... 56

viii List of Figures

Figure

1. A simplified Michelson interferometer ...... 2

2. Overhead view of light collection optics for emission spectroscopy on the Bruker IFS 120 HR Fourier transform Spectrometer ...... 5

3. The structure of cyanuric fluoride as optimized by semi-empirical calculation at the AMI level ...... 20

4. v,. Band of Cyanuric Fluoride near 820 cm1 ...... 23

5. R-branch Region of v,, Band of Cyanuric Fluoride ...... 24

6. Occupancy of Vibrational Levels in Cyanuric Fluoride ...... 27

7. Q-branch region of v,, Band of Cyanuric Fluoride ...... 28

8. Geometry of Cyanuric Fluoride ...... 32

9. ZCNC as a Function of rCF in Cyanuric Fluoride ...... 33

10. A -X Transition of AlBr near 2 8 0 0 A ...... 41

11. A portion of the 0-0 band of the A-X transition of AlBr ...... 42

ix CHAPTER I

Introduction

Spectroscopic studies in the microwave, infrared and ultraviolet regions provide direct measurements of differences between discrete energy levels of molecules. These measurements can yield information about the states of electrons in the molecule or of the vibrations and rotations of the nuclei. This information can then be used to determine bonding and structural parameters such as bond dissociation energies and molecular geometries. Also, the study of molecular spectra provides probes for investigating chemical reactions on a microscopic scale by monitoring reactants, products, or intermediates.

A. Principles of Fourier Transform Spectrometry

Fourier transform spectroscopy is a technique which has found increasing popularity recently. This technique allows for the use of very sensitive detectors and offers vei^ high resolution. Also, since all wavelengths are sampled at the same time with high optical throughput, data can be acquired very rapidly using this method. Further, the introduction recently of commercially available high resolution Fourier transform spectrometers has produced a rapid growth in the use of this technique in many research laboratories.

A simplified schematic diagram of a Michelson interferometer is shown in Fig. 1. Light emitted by the source is split into two beams by the partially reflective surface of the beamsplitter. These beams

are reflected by the moving

and fixed mirrors and then

Fixed Mirror rejoined at the beamsplitter.

If the difference in path

length traversed by the two

beams is an integral

multiple of the wavelength Figure 1. A simplified Michelson interferometer. of the light, constructive interference will occur. Thus, for monochromatic light, the intensity observed at the detector will oscillate sinusoidally with a frequency which is determined by the wavelength of the light and the velocity of the moving mirror. For polychromatic light, the intensity observed at the detector will follow the form

oo 1(8) = Js(v)[l + cos (2ti\?8)]dv (1)

where 6 refers to the path difference and v refers to the wavenumber of the light. B(v) is the intensity distribution emitted from the source as a function of wavenumber. B(v) is the dispersed spectrum of the source and is obtained by taking the Fourier transform of 1(6)

B($) = 2^I (8)cos(2nV8)d8 (2) 3

Due to the very large number of data points collected in a high resolution Fourier transform spectrum, a powerful computer must be dedicated to the instrument to handle the

Fourier transform of the signal. Also, the moving mirror must be carefully calibrated so that the path difference is known very precisely. This is accomplished by using a highly stabilized laser. The intensity and wavelength of the laser beam must be stable so that all fluctuations in the detected intensity result from interference patterns caused by the moving mirror only.

<

B. Modifications to the Spectrometer System

Recent advances in the construction of interferometers have led to a major increase in the use of interferometry in molecular spectroscopy. Commercial Fourier transform spectrometers are available which provide coverage over a very wide portion of the electromagnetic spectrum at very high resolution. Typically, such a spectrometer will provide several light sources for routine absorption spectroscopy. The Bruker IFS 120 HR also provides two ports for recording molecular spectra in emission. Unfortunately, the emission source must be very small or the user must provide efficient light collection optics.

In either case, the design of the spectrometer typically limits the user to a single experiment per port. This section describes an optical system which uses the external source port of the

Bruker IFS 120 HR spectrometer.

i. Principles of Design

For an interferometer to work, light passing through it must be collimated. This is achieved by a concave mirror which is placed at a distance from the entrance aperture which is equal to the mirror’s focal length. In the Bruker IFS 120 HR, this mirror is 7 cm in diameter and has a focal length of 42 cm. These parameters yield an f-number, defined as 4 the focal length divided by the diameter, of f/6. For maximum collection of photons, the element which focuses an experimental emission source on the entrance aperture must match this f-number and thus sample the same solid angle as the collimating element in the spectrometer.

At the same time, the focusing element in the external light collection optics must not introduce excessive geometrical aberrations as this will reduce the effectiveness of the collimating element. Ideally, this is accomplished using an off-axis parabaloid mirror or a lens transmitting light directly along the lens’ optical axis. However, such mirrors are expensive and difficult to align and a lens system limits the effective range of the spectrometer because of the transmission characteristics of the particular lens. The system described in this work uses reflection optics to minimize sacrifices in the spectral throughput of the spectrometer.

ii. Implementation

The system is designed to accept collimated light from the emission experiment.

Also, the system uses a kinematically mounted rotating mirror to select emission from several different positions reproducibly. In this manner, several emission sources may be in use and each selected separately with no impact on any of the experimental setup itself.

The system was designed to use the external emission port of the Bruker IFS 120

HR spectrometer. The intent in designing the system was to provide the maximum coverage of the spectrum by using first-surface aluminum reflection optics. The focusing mirror was chosen to be spherical rather than parabaloid in order to reduce cost. The orientation of the mirrors is shown in Fig. 2. 5

______e s s

W/////s/'Y's/ ssS/SSA

M2

Figure 2. An overhead view of the optics used for light collection on the Bruker IFS 120 HR Fourier transform spectrometer. An angle between the normal to spherical mirror (Ml) and the optical axis is necessary, but is kept small to minimize the introduction of spherical aberration. The plane mirror, M2, is placed in a fixed position which minimizes the angle formed between the normal axis of Ml and the true optical axis of the system. The plane mirror M3 sits on a kinematic mount which allows for the mirror to be rotated between several orientations with maximum reproducibility.

The focussing mirror, Ml, has a diameter of 5 cm since this matches other optics available in our laboratory. This choice dictates that the mirror must be located 30 cm from the entrance aperture. To properly focus collimated light onto the aperature, the mirror must have a focal length of 30 cm. This combination of mirror size and placement limits the compactness of the apparatus since mirror M3 must be placed in a position which allows a 5 cm wide collimated beam of light to pass around the mount holding the spherical mirror

Ml. The entire set-up sits on a table surface which is 30 cm by 38 cm. This system could be vacuum coupled to the spectrometer although such a vacuum system has not been implemented in our system.

C. Least-Squares Fitting of Spectral Data

Least-squares fitting of spectral data is central to the problem of determining molecular constants from observed molecular spectra. In many cases, the Hamiltonian chosen to determine the eigenstates of a molecule will contain adjustable parameters which are linear functions of the positions of measured spectral lines. When this is the case, the problem of fitting the spectrum is straight forward.

Albritton, Schmeltekopf and Zare (1) treat this problem of determining "minimum- variance, linear, unbiased" (MVLU) estimates of molecular parameters from observed spectral data. Their solution requires that all three of these criteria are reasonable. These properties will be discussed briefly.

The criterion of "minimum-variance" indicates that fits of successive sets of measurements taken under identical experimental conditions and subject only to random experimental error will result in parameters which yield deviations scattered randomly about the "true" values with the smallest possible mean squared deviation. The mean squared deviation is defined to be the variance.

The property of linearity will hold if the model function F(x) (where x is the set of independent variables corresponding to a single observation) to which data are to be fittted can be expressed as a linear combination of linearly independent functions fj(x).

m F(X) = £ Pjfj (x) (3) >1 This insures that the partial derivative of the model function F(x) with respect to any of the adjustable parameters p, is independant of any of the adjustable parameters pk or

32F(*> = 0 (4 ) a p ,a p * for all j and k. Many models in molecular spectroscopy will have this property. However, when Hamiltonians are required which contain off-diagonal elements (such as Jahn-Teller interactions of spin-orbit angular momentum coupling) the criterion of linearity will not hold for the model equation. In such cases, an iterative fitting method is required so that the criterion can be satisfied with a small range of error.

Finally, a fit is "unbiased" if the model F(x) does not introduce a systematic shift in the estimated parameters. If this criterion holds, successive fits to the same appropriate equations F(x) of successive sets of data taken under identical conditions and subject only 8 to random experimental error will yield constants Pj which will average to the "true" values of the parameters. This will be the case if neither more nor fewer basis functions fj(x) are needed to improve the fit.

The MVLU fit of a set of experimental data consisting of n measured values to a model containing of m linear parameters can be found as the solution to the over­ determined matrix equation

y = 2rp + e (5) where y, P and e are the column vectors given by

y = (yx, y2, yn) T P = (Px, P2 P J r <«> e = (ex, e2, . . ., e J T where the superscipt T is used to indicate the transpose of a matrix, n gives the number of observations, m gives the number of adjustable parameters in the model, y( is the i'h experimentally measured value, p, is the j'h adjustable parameter and e, gives the deviation of the i,h observation from its estimated "true" value. X is an n by m matrix which relates the experimental observations to the adjustable parameters. The fitting procedure involves selecting a vector p such that the squared magnitude of e is a minimum.

The best estimate of the parameters p which minimize the squared magnitude of e is given by

p = (X TX)-xXTy (7)

As an example, consider the fitting of nine experimentally determined band origins in an electronic transition of a diatomic molecule in order to determine the five spectroscopic constants Tc, to/, ope/, to/' and ope/'. Let the band origins correspond to those involving states for which v’ = 0, 1, 2 and v" = 0, 1,2. The p vector will contain the unknown values of the spectroscopic constants.

P = (Te, J e, to", <8>

The y vector will contain the measured values of the nine band origins.

y~ (V00' V01' V02' V10' Vl l ' V12' V20' V21' V22)T

In order to construct the X matrix it is necessary to write down the model F(x) which relates the observations to the parameters.

F{x) = Te + u>'e(v'+Vz) - w ex|l(v/+ 1/2)2 - (d'gi v"+Vz) + 0) gx'i (v"+Vz)2 ( 10) The X matrix will be a 5 by 9 matrix and will look as follows

1.0 0.5 -0.25 -0.5 0.25 1.0 0.5 -0.25 -1.5 2.25 1.0 0.5 -0.25 -2.5 6.25 1.0 1.5 -2.25 -0.5 0.25 1.0 1.5 -2.25 -1.5 2.25 1.0 1.5 -2.25 -2.5 6.25 1.0 2.5 -6.25 -0.5 0.25 1.0 2.5 -6.25 -1.5 2.25 1.0 2.5 -6.25 -2.5 6.65

The elements of this matrix, X,j, are given by 10 substituting the appropriate quantum numbers v,’ and v" for the i,h band origin, e will contain the differences between the measured values for the band origins and those calculated from the fitted constants. For example, one element of e is given by

®1 = ^00 “ [Te + C/2 ) " - (0//g(V2) + CH gX" {Va )\ (12)

The values of the elements of p, Pjt are chosen such that the squared magnitude of e is minimized.

It is important to note that the matrix X is independent of the parameters p. This is a consequence of the criterion of linearity. This is obvious since

d2F(x) _ q ( 1 ?) f P / P , ‘ ’ for all Pj. The model is unbiased if neither more nor fewer members of p are needed to provide the best description of the data. Finally, minimum-variance is achieved by adjusting the spectroscopic constants in order to yield the smallest squared magnitude of e.

An algebraically equivalent solution is obtained by solving a set of simultaneous linear equations. These equations, the so-called "normal equations" are constructed by applying the criterion of minimizing the variance with respect to each adjustable parameter.

The result will be a set of m equations in m unknowns (where m is the number of adjustable parameters) and the equations will be linear if the model is linear in all of the adjustable parameters.

For convenience, let the spectroscopic constants be represented as above The model function Ffy’.v") consists of a linear combination of the five linearly independent functions fj(v’,v") as defined by

f ^ v '. v " ) = 1 f 2{vl,v") = (v;+Vz) f 2(v',v//) = -(v'+Vz)2 (1 5 ) v") = - (v/!+Vz) f 5 ( v 1, v") = (v"+Vz) 2

The partial derivative of the sum of the deviations is taken with respect to each P; and set equal to zero.

/ 5 ' 2 (1 6 ) = 0 y ± ~ E p 2 = 1 j= i

This can be rearranged into a set of five simultaneous linear equations

= £ P j £ v") f k(v'i , v") (1 7 ) i=l j=l i=l or in the general case of a function F(x) which is the linear combination of m linearly independent functions f^x), the least-squares solution for a fit of n data points is given by the solution to the set of simultaneous linear equations defined by where Xj is a vector containing the independent variables corresponding to each y(.

This solution can be condensed into a convenient matrix notation by defining an m by m matrix A whose elements are given by

n AJk = <*,>/,(*,) (19) i-1 and a vector h whose elements are defined by

** = (20) i=1

The problem is then stated by the matrix equation

h = AP (2 1 ) and the solution is given by

P = A-Xh (22)

This statement of the problem is related to the earlier statement by noting that

A = X*X (23) h = X Ty

Weighting of data can be incorporated into the fitting procedure by defining the matrix A and the vector y as 13

AJk = E "ifjixj fk(x±) i = l ^n (24) y* = E 1 = 1

This is equivalent to defining an n by n diagonal matrix G» whose elements are given as the reciprocals of the weights w^ In this caseA and y are given by

A = X ^ X (25) y = X Tfb-xy

The usual choice of weighting factors is ws = 1/Oj2 where of is the estimated variance of the ilh measurement The variance of the fit o2 is given by

o2 = ( n-m) _1 (y - Ap) T'1 (y - XP) (26)

The matrix A is of significant importance as it contains a wealth of information. The matrix A is related to the variance-covariance matrix © by

© = a2 A'1 <27>

The diagonal elements of 0, 0^, give the estimated variances of in the parameters Pj which are useful in estimating the uncertainty of the parameter as determined from the fit. The off-diagonal elements ©Jk 0*^) give the covariances ojk2 between the parameters p, and pk.

The degrees to which pairs of the parameters are correlated are given by the elements of the correlation matrix C as defined by

© -ik . c ik = ------2]s— ir <28> O J A * * 4

The values of CJk will fall within the limits -1 s CJk s 1 and will be unity along the diagonal.

It is possible to remove any correlation between the parameters p, by taking linear 14 combinations such that the matrix C is diagonal, but it is unlikely that the linear combinations of the parameters will hold any physical significance with regard to the physical parameters of the molecule.

D. Merging of Data

The usual method of fitting spectroscopic data is to reduce spectra to a set of molecular constants which are determined band by band. This can lead to redundancies in determined constants. The redundancy is an advantage as multiple determinations of parameters will enable "merging" of fits. Albritton, Schmeltekopf and Zare (1,2) have outlined a method for merging several band-by-band fits of spectral data into a set of "best" constants. The method is no more than a correlated weighted least-squares fit and yields results identical to a simultaneous fit of all the data.

For purposes of discussion, consider the 0-0 band of the A ‘II - X ‘S + transition of

AlTOBr near 2700 A. The "best" estimate of the molecular constants will take full advantage of the fact that highly precise measurements of rotational levels in the lower state are available from microwave spectroscopy (3).

Reduction of the ultraviolet data will yield the constants v0, B’, D \ H ’, Bu" and Du".

Reduction of the microwave data will yield the constants Bm" and Dm". (The subscript u is used to denote the value of this constant as determined from the ultraviolet data and the subscript m denotes constants determined from microwave data.) The lower state constants should agree to within experimental uncertainty, but those determined from microwave data will certainly be determined to greater precision. Further, it is important to note that there are several correlations between the constants as determined in the individual band-by-band fits. The merged fit will satisfy the matrix equation 15

y = X$ + 6 (29) by minimizing the vector 8 subject to the known interrelations between the constants. In this procedure, y will contain the constants determined from the band-by-band fits

y = (V0, B', D', H'. b “, d ", b ", d") t (30)

The merged "best" set of constants will be contained in the vector p

P = Dm, Hm, Bm, Dm) t (31)

where the subscript M is used to denote the merged value of the constant. Note that the merged values of the upper state constants may not be the same as those from the reduction of the ultraviolet band due to the correlations with the lower state constants. The matrix

X will relate the band-by-band constants to the final merged constants. In this case, it will be an 8 by 6 matrix

1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 X = 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1

The vector 5 will contain the residuals. Examples of the members of this vector are

,// „//

// // <32> 67 = B" -

The solution to this problem is given by p = (x '® -1;r) “1Jrr® -11jr (33> where is the block diagonal matrix composed of the individual variance-covariance matrices.

The variance-covariance matrix associated with the merged fit is given by

= a2M(XT~1X) -1 (34) where

(y - jgfi) r»-x(y - *P) (35) and fM is the number of degrees of freedom in the merged fit. In this case, fM is given by fM = 8 - 6 = 2.

E. Summary

In this introductory chapter, discussions of Fourier transform spectrometry, light collection optics and least-squares fitting have been presented. The remainder of this document will consist of two chapters which discuss spectroscopic experiments using a

Fourier transform spectrometer and computational techniques including least-squares fitting.

An additional chapter will discuss several experiments which were performed using photographic detection techniques and were intended to aid in the search for new spectral band systems. Several appendices are included which provide the experimental data 17 analyzed in these studies and also several computer programs which were used to aid in the analysis of the data. References

D.L. Albritton, A.L. Schmeltekopf and R. N. Zare, "An Introduction to the Least- Squares Fitting of Spectral Data", in Modern Spectroscopy. 2nd ed.. K.N. Rao ed., pp. 1-67, Academic Press, New York, (1976)

D.L. Albritton, A.L. Schmeltekopf and R.N. Zare, J. Molec. Spectrosc. 67 132-156 (1977)

F. C. Wyse and W. Gordy, J. Chem. Phys. 56, 2130-2136 (1972) CHAPTER II

Cyanuric Fluoride

A. Historical Background

The compound 1,3,5,-trifluoro-sym -triazine (cyanuric fluoride, C3N3F3) is of chemical interest as a starting material in many reactions involving fluorine. Cyanuric fluoride has also been the subject of several spectroscopic studies (1-5). Low resolution infrared and

Raman spectra were obtained and assigned by Long et al. (1) and by Griffiths and Irish (2).

In addition, normal coordinate calculations were carried out by Durig and Nagarajan (3).

These analyses provide strong evidence for a planar structure possessing D3h symmetry.

The only rotationally resolved spectrum was analyzed by Schlupf and Weber (4). Their rotational laser-Raman spectrum showed R- and S- branches with no resolved K structure; these branches were analyzed independently giving two different sets of rotational constants.

Schlupf and Weber also suggested that their observed rotational features are unresolved superpositions of the ground vibrational level and several vibrational "hot" bands. The present study of a vibrational transition provides the first observation of at least partial separation of these "hot" vibrational levels.

19 Figure 3. The structure of cyanuric fluoride optimized by semi-empirical calculation at the AM I level. 21

The photoelectron spectrum of cyanuric fluoride was reported by Brundle et al. (5).

This study indicates that substitution of hydrogen atoms by fluorine in planar aromatic ring molecules stabilizes o orbitals by approximately 2-3 eV while stabilizing it orbitals by an order of magnitude less. This suggests that the n -n ’ transition which is seen near 320 nm for the unsubstituted sym-triazine molecule (6) may be expected to be found in the vacuum ultraviolet for the fluorine substituted molecule, although these bands have not been observed. Examination of these transitions may be of considerable aid in deciphering the vibrational spectrum of the molecule due to vibronic interactions which lift the degeneracy of some of the vibrational modes.

B. Experimental Considerations

Cyanuric fluoride was prepared by the method of Tullock and Coffman (7).

Tetramethylensulfone (TMS), sodium fluoride (NaF) and cyanuric chloride (C3N3C13) were mixed in a round-bottom flask in the amounts shown in Table 1:

Table 1

Chemicals used in the Preparation of Cyanuric Fluoride

Compound Amount

Tetramethylensulfone 111.5 g

Sodium Fluoride 28.5 g

Cyanuric Chloride 31.6 g The flask was heated to approximately 200 °C using an electric heating mantle and the product, cyanuric fluoride (C3N3F3), was distilled out of the reaction mixture. The temperature at the distilling head was measured to be 68 °C. 18.0 grams of the product were collected in this manner corresponding to a 77.8% yield.

The liquid product was purified by vacuum distillation by the following method:

1) transfer under vacuum to a flask cooled to liquid nitrogen temperature

2) warm to room temperature

3) cool to dry ice/isopropanol temperature and pump on the sample for one hour

The final product was stored at room temperature. The vapor pressure was measured to be 108 Torr at 29.3 °C. This is in good agreement with the vapor pressure calculated at this temperature using the relationship (Eq. 36) determined by Seel and Balreich (8), indicating a reasonably pure sample.

4523 (24) K (36) T

Low-resolution infrared spectra of the vapor taken on a Mattson Polaris Fourier transform spectrometer yielded a spectrum identical to that reported by Griffiths and Irish (2).

The vu parallel band of cyanuric fluoride near 820 cm 1 was obtained in absorption at a spectral resolution of 0.01 cm'1 using a Bruker IFS 120 HR Fourier transform spectrometer. A mercury arc or a Globar light source provided the background radiation which was detected by a mercury-cadmium-tellurium (MCT) detector cooled to liquid nitrogen temperature. Spectra were taken at pressures of 3 Torr and 0.5 Torr in an 23 absorption cell fitted with sodium chloride windows and having an absorbing path length of

10 cm. The summing of 100 scans was used to improve the signal-to-noise ratio.

Wavenumber / cm'

Fig. 4. v,, band of cyanuric fluoride near 820 cm'1 taken at 3 Torr and 10 cm absorbing path length. The Q-branch shows total absorption.

The band, shown in Fig. 4, has the appearance of simple P-, Q- and R-branch structure.

The periodic intensity fluctuation in the baseline of the spectrum with a spacing of about

2 cm'1 results from interference fringes from the sodium chloride windows. This etalon pattern is characteristic of any spectrum taken under conditions using parallel surface windows. The etalon effect can be reduced by using wedged windows, but it did not interfere with the analysis of the spectrum.

The R-branch, which appears less complicated than the P-branch, shows a pattern of four features which is repeated approximately every 0.13 cm 1 as can be seen in Fig. 5. This pattern is inconsistent with the expected K structure for this type of band. The O-branch 24

R(J)

R(J) 45

825. 0 825. 5 826. 0 826. 5 827. 0 Wavenumber / cm

Fig. 5. A portion of the R-branch taken at 3 Torr and 10 cm absorbing path length, showing J assignments for the two strongest features. region also shows several features with a spacing of approximately 0.3 cm'1 which is too great to be interpreted as sub-band origin structure in light of the much smaller spacings in the

R-branch. These Q-branch features are interpreted as band origins of "hot" bands originating from excited vibrational levels and built upon the v,, fundamental band. This interpretation is consistent with the repeating pattern of lines in the R-branch. The satellite pattern is not as simple in the P-branch as it is in the R-branch due to a less regular pattern of overlapping of lines in this branch. 25

C. Spectral Interpretation and Analysis

i. Vibrational Interpretation

The vibrational energy of a polyatomic molecule with degenerate vibrations is given by

Eq. (37). If the anharmonicity constants x0 and g^ are not negligible, it is expected that

(37)

+ + • ■ iSj bands of the form v^-t-v-v, will appear as satellites to the band v,„ as has been reported in the infrared spectrum of sym-triazine (9).

Several vibrational "hot" bands may be observed if there is sufficient population in low- lying vibrational levels. These bands are expected to overlap strongly the fundamental band upon which they are built since the anharmonicities are expected to be small compared to the vibrational frequency of the band. The relative intensities of the satellite bands will be determined in part by the relative populations of the lower levels. A program for calculating vibrational populations of a polyatomic molecule is presented in Appendix A. This program uses the energies and degeneracies of the molecule’s normal vibrational modes in conjunction with the Maxwell-Boltzmann model to calculate a vibrational partition function and also the vibrational energy level populations. The results of this calculation are given in Table 2 for the five vibrational levels with highest occupancy at room temperature. The next most populated level, above those listed in the table, is v14 = 3 (at 678 cm 1 above the zero-point energy) which has five-fold degeneracy and a 3.77% occupancy calculated at 298

K. Fig. 6 shows the results of this calculation for four vibrational levels at several temperatures. The results in Fig. 3 suggest that at lower temperatures, the intensity of the 26 pure fundamental band relative to the hot bands will increase significantly. A 2:1 intensity ratio is expected for the v„ band relative to the v„ + vM-vM band at 195 K.

Table 2

Occupancy of Vibrational Levels of Cyanuric Fluoride

Level Energy (cm 1) Degeneracy % Occupation*

ground 0 1 19.89

v,4= l 226 2 13.36

v14 = 2 452 3 6.73

Vio= 1 379 2 6.38 >“ > II II © 605 4 4.29

"Calculation of relative populations of vibrational energy levels for cyanuric fluoride based on a temperature of 298 K and vibrational assignments given in Refs. (1-3)

ii. Rotational Analysis

The rotational energy levels of an oblate symmetric rotor are given to a good approximation by Eq. (38).

F ( J, K) = BJ (J l+ ) + (C-B)K2 (38) - DjJ2 (J+ l ) 2 - DjkJ (J+ l ) K2 - DkK*

Expressions for R- and P- branch lines are given in Eqs. (39) and (40). 27

100 n Vibrational Level ground 90 80 70 60

50 40 30

20

10

293 K273 K77 K 195 K K77 293 K273

Fig. 6. Percent occupancy of vibrational levels in cyanuric fluoride at various temperatures.

vp = v0 - 2 ABJ + A(C-B) K2 (40) + 4 ADjJ3 + 2ADjkJK2 - ADkK4

For a parallel band (AK = 0) which shows only slight degradation, indicating a very small change in B, the change in (C-B) is expected to be small provided the quantum defect is nearly zero due to planarity. In the limit that the constant (C-B) changes by a negligibly small amount, as is apparent in the present band, no K structure will be resolved and the resulting "lines" will be highly symmetric. The Doppler width for lines in this band is calculated to be approximately 1.4 x 10'5 cm 1 whereas the observed line widths are on the order of 0.02 cm1, further suggesting that the K structure is not resolved. Thus all 28 dependence on the K quantum number is excluded from the fitting of the data and only the

B and Dj constants are determined. This is similar to the analysis of Schlupf and Weber (4) for the rotational Raman spectrum. In the rotational Raman spectrum, however, the fit included the distortional constant Hj, with the caveat that this may not indeed be a true fourth-order centrifugal distortion constant. H; may be simply an empirical parameter made necessary to give a good fit due to the unresolved contributions of excited vibrational levels in the Raman spectrum. In the present study, the constant Hj was found to be undetermined and thus was excluded from the fitting procedure.

819. o 5 820. 0 820. 5819. 821. o Wavenumber / cm"1

Fig. 7. The Q-branch region of the v,, band of cyanuric fluoride, taken at 0.5 Torr and 10 cm absorbing path length. Maximum absorption is approximately 50%.

Fig. 4 shows a portion of the R-branch. The regular spacing between lines is extrapolated through the band origin to assign relative J quantum numbers to the P-branch lines. Absolute J numbering is determined by comparing the lower level combination 29 differences to the measured displacements in the rotational Raman spectrum (4). The lines were then subjected to a least-squares fitting procedure to determine rotational constants for the upper and lower levels and also a band origin. Comparison of the calculated band origin to the location of strong features in the Q-branch confirmed the absolute J assignments. The comparison of combination differences for the weaker satellites failed to give realistic assignments of absolute J’s for these bands since the corresponding band origins fell outside of the Q-branch region. Fig. 7 shows the locations of the assigned band origins. The assigned line wavenumbers for the strongest and second strongest R-branch features are given in Apendix A. Table 3 summarizes the rotational constants determined for these assignments.

Table 3

Rotational Constants for Cyanuric Fluoride

level B (cm 1) Dj (cm 1)

ground 0.065 608 4(36)' 3.88(34) x 10-9

v„ = l 0.065 590 1(35) 3.92(32) x lO'9

V,4=l 0.065 612 7(47) 4.44(60) x lO'9

v„ = l, V14= l 0.065 594 9(46) 4.54(57) x 10 9

‘Uncertainties shown are two standard deviations.

A value for a u of 1.83(50) x 105 cm 1 is calculated from the B values found in the analysis of the v„ band. Table 4 reports the band origins of the two analyzed bands. Vibrational 30 level assignments reported in both Table 3 and 4 are made based on predicted population of vibrational levels at room temperature and the relative intensities of the bands. The

Table 4

Band Origins for Cyanuric Fluoride near 820 cm '.

Band Origin (cm 1)

v„ 820.728 16(34)' v„ + vM-v14 820.428 44(44)

'Uncertainties shown arc two standard deviations. second strongest satellite shows some evidence of asymmetry in R-branch lines which may suggest that these lines are composites of lines from more than one satellite band.

D. Discussion and Conclusions

The distortional constant Dj is found to be larger than previously reported (4). This is partly due to the omission of the quartic distortional term, Hj, from the present fitting of the spectral data. One can estimate a reasonable value for the distortional constant, Dj, by using the approximation of Kratzer,

where o) is the frequency of the totally symmetric ring breathing mode. A value of Dj =

2.74 x 109 cm'1 is calculated based on the assignment of co = 642 cm 1 (1,2) for this mode. 31

This value of D, is slightly lower than the value determined by fitting the spectral data.

However, due to the large dependence on to, D; determined by this method requires a very precise determination of this vibrational frequency.

The band origins for the two sets of P- and R-branch data analyzed are shown in Fig.

7. The Q-branch features for these origins show sharp heads and slight degradation to lower energy. Other features in the Q-branch region show degradation to both higher and lower energies. Further work must be done to provide a better understanding of these satellite features and the P- and R-branches associated with them. In particular, the fundamental bands and hot bands should be studied for those levels which possess significant population at room temperature.

The relative J assignments for the weaker features in the P- and R-branches are straightforward as there is only slight degradation of the spacing between lines. However, absolute J assignments cannot be made by matching combination differences with those calculated from Raman data since forcing absolute J assignments in this way leads to a band origin which lies outside of the Q-branch region. It is therefore concluded that these bands must have significantly different lower level B values. Clearly, studies of other fundamental and hot bands would provide valuable information. Unfortunately, the overlapping hot- bands make resolution of perpendicular bands, such as those near 1100 cm'1 and 1420 cm'1, extremely difficult. These bands are not resolved in the present study but could perhaps be studied if the sample were cooled and a longer path length were used to compensate for the lower vapor pressure. Alternatively, a free-jet expansion probed with a diode laser might be employed for such a study. 32

i. Structural Considerations for Cyanuric Fluoride

For planar, oblate symmetric rotator molecules, the spectroscopic B value will be twice the value of C due to the constraints of an inertial defect (a measure of non-planarity) of zero. Subject to the assumption of a planar, D3h geometry, which is depicted in Fig. 8, three parameters are necessary to define the molecular structure. The parameters chosen are the C-N bond distance (rCN), the

C-F bond distance (rCF), and the CNC bond angle (ZCNC). Bauer et al. (10) used electron diffraction to determine these values to be rCN = 1.333 A, rCF = 1.310 A Fig. 8. D,h, planar structure of cyanuric fluoride. and ZCNC = 113°. These values yield a spectroscopic B value of B„, = 0.064 538 cm'1. This is lower than either of the B0 values reported by Schlupf and Weber (4) and also the one determined in the present study. While some difference between the spectroscopic B0 value and that calculated from an electron diffraction structure is expected (due to vibrational excitation of the molecule by electron impact), Schlupf and Weber note that the difference is larger for cyanuric fluoride than in the cases of similar molecules (4).

No unambiguous structural determination can be made from the present data since the

B0 value yields only one moment of inertia. However, several comments should be made about the constraints this one value places upon the structure. Given reasonable choices of the three structural parameters, ZCNC, rCF and rCN, a B value can be calculated using the program ABC which is included in Appendix C. The choices of the structural parameters 33 can be adjusted until the calculated B value matches that value determined from the spectrum.

Fig. 9 shows several values of ZCNC which were determined using various values for rCF.

120.0

▲ 115.0 —

o ▲ © ? 110.0 ~ ▲ < T> 1 A ” 105.0 _ O z o ▲ ▲ 100.0

95.0 I I I l 1.20 1.25 1.30 1.35 1.40

CF Bond Length (A)

Fig. 9. ZCNC calculated as a function of rCF based on rCN = 1.338 A (6), planar 03h structure (1- 4), and a rotational constant B = 0.065 608 cm'1.

The value of rCN = 1.338 A was fixed and taken from the unsubstituted molecule, sym- triazine (6). Choosing rCF = 1.354 A, as in fluorobenzene (11), a value of ZCNC = 103.0° is calculated based on B0 = 0.065 608 cm'1. This angle is significantly smaller than that found by Bauer et al. (10). Using the angle ZCNC determined by Bauer et al., a bond length of rCF = 1.2726 A is determined. Without a complete set of isotope substitution spectra, it is not possible to draw more definite conclusions on the structure of cyanuric fluoride based on spectroscopic data. 34

Schlupf and Weber recommend the set of constants found for the S-branch of the rotational Raman spectrum (4). It is found that the fit of the data in the present work matches the R-branch data of Schlupf and Weber better. It is recommended that the quartic distortional term, H,, be eliminated from the fit as it is undetermined at two standard deviations. Finally, both the accuracy and the precision of measurement of the band origin for the v„ band of cyanuric fluoride have been improved significantly (2). 35

References

1. D. A. Long, J. Y. H. Chau, and R. B. Gravenor, Tram. Faraday Soc., 58, 2316-2324 (1962)

2. J. E. Griffiths and D. E. Irish, Can. J. Phys., 42, 690-695 (1964)

3. J. R. Durig and G. Nagarajan, Acta Phys. Polon., 35, 867-874 (1969)

4. J. Schlupf and A. Weber, / Mol. Spectrosc., 54, 10-19 (1975)

5. C. R. Brundle, M. B. Robin, and N. A. Kuebler, J. Am . Cliem. Soc., 94, 1466-1475 (1971)

6. G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic Spectra of Polyatomic Molecules. Van Nostrand Reinhold, New York (1966) and references therein

7. C. W. Tullock and D. D. Coffman, / Org. Client., 25, 2016-2019 (1960)

8. F. Seel and K. Balreich, Chem. Ber., 92, 344-346 (1959)

9. J. E. Lancaster and N. B. Colthup, / Chem. Phys., 22, 1149 (1954)

10. S. H. Bauer, K. Katada, and K. Kimura, The Structures of C6, B3N3 and C3N3 Ring Compounds, in Structural Chemistry and Molecular Biology (A. Rich and N. Davidson Eds.), pp. 653-670, W. H. Freeman and Co., San Francisco, 1968 CHAPTER III

A Reanalysis of the A *11 - X 1S + Transition of AlBr

A. Introduction

Aluminum monobromide has been the subject of a number of spectroscopic investigations (1-14). Bredohl et al. (11) provided an extensive high-resolution band-by-band analysis of 28 bands of the A-X transition in the vibrational quantum number range 0 <; v"

£ 9 and 0 <; v’ <: 3. Rotational structure of each of the bands was assigned and fitted with lower state constants fixed to their microwave values. Rotational constants for the A 'II state determined in this manner agree with those reported in other studies.

Several accounts of the A ‘II - X '2 + system (7-11) indicate that the A 'II state is predissociative as no vibrational levels higher than v’ = 3 have been observed in any of the spectra. Ram (8) observed an intensity break-off in the emission spectrum at J’ = 93 in the v’ = 2 level and at J’ = 67 in the v’ = 3 level. Griffith and Mathews (9) reported a break- off in intensity of emission features at J’ = 97 for the v’ = 2 level and at J’ = 67 in the v’

= 3 level. Griffith and Mathews (9) also observed broadening of all features in the absorption spectrum of the 3-1 band from J’ = 75 to J’ = 90 at which point features become too weak and broad to be observed. These results are consistent with emission spectra, as

36 37 they are expected to depend on the stability of the exited state energy levels. Wolf and

Tiemann (10) recorded the laser excitation spectrum of the 0-1, 0-0, 1-1, 2-2, 2-1, 3-2 and

3-1 bands and reported break-offs at J ’ > 93 in the v’ = 2 level and J ’ > 64 for v’ = 3.

They also report observation by directly measuring laser absorption of several levels of higher J in both v’ = 2 and v’ = 3. These levels are broadened as in the spectra recorded by Griffith and Mathews (9). Wolf and Tiemann (10) used line positions, line widths

(including J dependance of the line width), and fluorescence intensities to determine the

RKR potential of the A 'II state and Frank-Condon factors for the A ‘II - X 'S ' transition.

Bredohl et al. (11) report no break-off in intensity in their emission spectra but rather a normal intensity distribution up to at least J = 76 in the v’ = 3 level (observed in the 3-8 band) and J - 100 in the v’ = 2 level (J’ = 101 is reported in the 2-3 band.) The present work was initiated with the intent of addressing the questions surrounding the predissociation of the A 'II state since the observations by Bredohl et al. would imply a predissociation of the A state which is dependant upon experimental conditions.

Unfortunately, temporary instrumental limitations have made these bands inaccessible at the present time.

Nevertheless, data have been collected which enable a re-examination of the results of Griffith and Mathews (9) and Bredohl et al. (11). The rotational assignments of the 1-0,

2-1, 3-2, 2-0, and 3-1 bands as reported by Griffith and Mathews (9) were used as a starting point. Rotational analyses of the 0-0, 1-1, 2-2, 0-1, and 1-2 bands have been added in the present study. Also, microwave measurements have been included at the merge level to provide the best set of constants for both electronic states. 38

B. Experimental Details

The emission spectrum of AlBr has been recorded in the region 2700 - 2900 A using a Bruker IFS 120 HR Fourier transform spectrometer equipped with a photomultiplier detector. An interference filter with a transmission maximum near 2800 A was used to eliminate problems due to aliasing in the Fourier transform spectrum. The emission source consists of a 100 W 2.45 GHz generator unit coupled to a discharge cavity through which

AlBr3 vapor is passed with helium as a carrier gas.

Spectra were recorded at unapodized resolutions of 4.0 and 0.03 cm'1 with the spectrometer operating at atmospheric pressure. Calibration was necessary as a systematic deviation of approximately 0.5 cm'1 was observed for all features in the spectrum. The spectra were calibrated using the emission spectrum of an iron/neon hollow cathode lamp taken under identical conditions. The calibration method was similar to that used by

Plummer et al. (15). The systematic deviation of the uncalibrated line positions from the calibrated positions resulted from taking the spectrum in air rather than under vacuum. The internal laser frequency was given in vacuum although the observation was made in air.

Thus, a deviation which is related to the ration of the index of refraction of the laser in air to that of the calibrated wavenumber in air is to be expected.

Peak intensities were determined using the algorithm developed by Brault for the program DECOMP (17) and implemented by Jensen in the program SPEAK (18). The uncertainty of line positions of strong, unblended lines is estimated to be 0.01 cm'1 at the higher resolution. This estimated uncertainty is similar to that obtained in the experiments by Griffith and Mathews (9) and Bredohl et. al (11) using photographic methods of detection. 39

The bands show P-, Q-, and R-branches and are degraded to longer wavelengths.

Each band appears to be doubled due to the naturally occurring isotopes of bromine (50.6%

Al^Br and 49.4% Al81Br.) The strongest sequence observed is Av = 0. No bands for which v’ > 3 are observed. The low-resolution spectrum is shown in Fig. 1. Intensity falls off on either side of the 2800 A center due to the transmission characteristics of the interference filter and also the Frank-Condon profile for this transition. Present limitations of the beamsplitter and filters have prevented us from obtaining high resolution spectra for which v’ = 3 at this time.

C. Isotopomer Identification

The earlier accounts of this system (2,7) take full advantage of the natural abundance of bromine isotopes in the samples used to produce the spectra. Shifts in band-origins which are approximated from Q-branch band-heads, were used to confirm the assignment of isotopomers. Assuming well behaved potential energy curves for both electronic states, band-origin shifts due to isotopic substitution can be calculated using the relationship

9 - = (1-p) Ci>e (v' + Vfe) - (1-p) G)e (v^ + Vfe) - (1-p2) G> eXg (v' + Vfe) 2 + (1-p2) 0 ) eXe (v^ + Vfe) 2 (42) + (1-p3) 0)eYe(V/ + 1/2) 3

(16) where p is given by

a JL (43) N and p is the reduced mass. The superscript i refers to the species containing the heavier isotope. Isotopic shift data are shown for several investigations in Table 5. Bredohl et al.’s

(11) reported band origin shifts agree with the calculated shifts in only 9 of the 28 bands 40 reported. Many of the bands show isotopic shifts which agree in magnitude but disagree in sign with the predicted value, indicating a mistaken assignment of isotopomers to the individual bands.

The rotational assignments in this work agree in neither sign nor magnitude with those of Bredohl et. al (11) for the 1-1 band. Further, the current band-origin shift for the

1-1 band is in much better agreement with the calculated values than that reported by

Bredohl et. al (11). 41

AlBr A -X

2 - v" 4 3 2 1 1 - v" 3 2 l 0

0 - v" j . 2 ]. l 0

1 ! 1

34500 35000 35500 36000 36500 Wavenumber/crri

Figure 10. A -X Transition of AlBr near 2800 A. 42

AlBr A-X 0 - 0 Band

0 ( J )

Al Br

35804 35806 35808 35810 35812 Wavenumber/cm

Figure 11. A portion of the 0-0 band of the A-X transition of AlBr T able 5

Band origin shifts due to isotopic substitution (in cm'1)

v’ v" Ref(2) Ref(9) Calc. This Work

1 7 7.471 -7.172 2 8 9.437 -7.517 3 9 7.579 -8.010

1 6 5.860 -6.096 2 7 6.344 -6.458 3 8 6.587 -6.967

1 5 5.159 -5.004 2 6 5.995 -5.382 3 7 -5.8 5.779 -5.907

0 3 -3.4 3.379 -3.611 1 4 -3.8 3.452 -3.895 2 5 5.140 -4.289 3 6 -4.8 4.658 -4.831

0 2 -2.4 -2.336 -2.469 1 3 -2.6 -2.770 2 4 0.417 -3.181 3 5 -3.6 3.877 -3.739

0 1 -1.3 -1.259 -1.311 -1.329 1 2 -1.628 -1.670 2 3 -2.225 -2.055 3 4 -2.602 -2.630

0 0 -0.190 -0.137 -0.135 1 1 -0.5 1.159 -0.470 -0.441 2 2 -0.878 -0.914 -0.907 3 3 -1.495 -1.505

1 0 0.6 0.812 0.705 ( 0.753)° 2 1 -0.029 0.245 ( 0.223) 3 2 0.148 -0.363 (-0.448)

2 0 1.517 1.419 ( 1.415) 3 1 1.216 0.795 ( 0.915) aNumbers in parentheses indicate results for data taken from Ref. (9). 44

D. Rotational Analysis

J assignments in the 0-0 and 1-1 bands were made by extending those provided in references 2, 9, and 11. Assignments in the 0-1, 1-2, and 2-2 bands were made by comparing the experimentally observed spectrum to a calculated spectrum based on the 0-0, 1-1, 1-0, 2-1, 3-2, 2-0, and 3-1 bands (the latter five taken from ref. 9) and microwave data from Gordy and Wyse (12). The assignments for the 0-0, 1-1, 2-2,

0-1, and 1-2 bands are given in Appendix B. Data for the 1-0, 2-1, 3-2, 2-0, and 3-1 bands, taken from Griffith and Mathews (9), with slight modification of the 2-1 band for APBr, are also given in Appendix B for convenience.

Rotational line assignments have been extended to lower J values than in previous studies for the 1-2 and 0-0 bands. This extension accounts for approximately

10% of the lines assigned in the 0-0 band for Al81Br. This leads to more precise determinations of the band-origins. No combination defect has been observed at this resolution; consequently, A-type doubling is neglected in the Hamiltonian.

A portion of the 0-0 band is shown under high-resolution in Fig. 2. The assignments and measured energies for the 0-0 band agree with those of Griffith and

Mathews (9) and Bredohl et al. (11). The J assignments for the 1-1 band differ in some regions from those reported by Bredohl et al. (11).

The observations were first fitted band-by-band. In each case the lower state rotational constants were not constrained in order to minimize bias in the upper state rotational constants due to correlation. The problems associated with fixing lower state constants to their microwave values may account for the misidentification of 45 isotopomers in the paper by Bredohl et al. (11). We found, for example, that fitting the 0-3 band of Al^Br with the ground state constants fixed at those for Al81Br yielded upper state constants consistent with Al81Br. Thus, comparison of upper state rotational constants to confirm isotopomer assignment is not sufficient as the fitting method introduces excessive bias into the resultant constants.

The results of the band-by-band fits are shown in Table 6. The band-by-band fits were then merged (19) with the infrared measurement of Uehara et al. (14) and the microwave measurements of Gordy and Wyse (12) to provide the best possible set of constants for both the upper and lower states. The microwave data of Gordy and Wyse (12) were chosen over that of Wolf and Tiemann (13) as the Gordy and

Wyse data are more extensive in their coverage of both J and v. The rotational constants for each of the vibrational levels in the upper state are shown in Table 7.

Despite observation of only four vibrational levels in the upper electronic state, it is found that four constants (Tc, o>c, g>cx c, and oj,,) are needed to fit the data adequately. Further, it is observed that Wgy,. is two orders of magnitude larger in the upper state than in the lower state. Also, the distortion constants D and H do not change smoothly with increasing v (H is undetermined for v = 3.) Thus, fitting the data to the usual rotational constants Be, ae, ye, De, (3C, and Hc is not recommended.

Forcing the data to fit such a model not only compromises the quality of the fit, but it introduces unacceptable shifts in the vibrational constants due to strong correlation of c*>e and <*>exe with ae, Ye» and /?e. This is the major reason for the lack of agreement between references (9) and (11) in these constants. Table 6

Band-by-band results for Al^Br3

vo B’ D’ x 107 H’ x 1012 B" D" x 107 0 - 1 35 462.422(24) 0.153 95(14) 1.62(15) -1.08(37) 0.157 47(14) 1.00(14) 1 - 2 35 372.240(17) 0.152 02(15) 2.32(26) -2.05(62) 0.157 28(15) 1.49(25) 0 - 0 35 837.9229(55) 0.154 313 1(40) 1.686(33) -0.973 6(23) 0.158 678 4(39) 1.059(32) 1 - 1 35 745.151(16) 0.151 664(71) 1.869(65) -1.951(90) .157 796(69) 1.058(59) 2 - 2 35 637.693(17) 0.149 02(19) 2.09(31) -7.61(97) 0.157 41(18) 1.20(27) 1 - 0b 36 120.702(23) 0.151 764(83) 1.927(75) -1.844(96) 0.158 750(80) 1.103(68) 2 - l b 36 010.793(47) 0.148 650(78) 2.140(78) -4.89(21) 0.157 950(74) 1.161(62) 3 - 2b 35 881.900(12) 0.145 30(33) 4.4(11) ------0.157 36(33) 1.8(11) 2 - 0b 36 386.028(22) 0.148 59(11) 2.093(86) -4.63(16) 0.158 68(11) 1.029(80) 3 - l b 36 254.576(25) 0.145 19(19) 3.94(26) ------0.157 98(19) 1.18(26) aAll results are in units of cm'1. ‘These are fitting results for data taken from Reference (9). Table 6 (Continued)

Band-by-band results for Al81Bra

vo B’ D’ x 107 H’ x 1012 B" D" x 107 0 - 1 35 463.751(16) 0.153 247(98) 1.57(10) -1.63(23) 0.156 772(99) 1.05(10) 1 - 2 35 373.909(18) 0.150 62(14) 1.52(21) -3.55(57) 0.155 90(14) 0.87(20) 0 - 0 35 838.057 3(40) 0.153 423(37) 1.762(30) -0.947(20) 0.157 757(36) 1.141(29) 1 - 1 35 745.592(19) 0.151 147(78) 2.220(71) -1.480(98) 0.157 195(76) 1.344(65) 2 - 2 35 638.600(18) 0.147 35(21) 1.37(34) -5.83(94) 1.55 63(20) 0.35(30) 1 - 0b 36 119.949(21) 0.150 741(94) 1.853(78) -1.762(89) 0.157 651(90) 1.022(70) 2 - l b 36 010.570(25) 0.i47 49(95) 1.890(89) -5.07(13) 0.156 731(91) 0.978(78) 3 - 2b 35 882.348(18) 0.143 71(45) 2.2(16) ------0.155 74(46) -0.0(16) 2 - 0b 36 384.613(32) 0.147 92(13) 2.30(10) -4.06(20) 0.157 90(12) 1.194(94) 3 - l b 36 253.661(46) 0.144 07(29) 3.56(40) ------0.156 67(29) 0.75(38) aAll parameters are in units of cm'1. ‘These are fitting results for data taken from Reference (9). Table 7

Merged Constants for A 11I state3

Al^Br T (cm'1) B (cm'1) D x 107 (cm'1) H x 1012 (cm'1) 3 36 818.976(38) 0.145 009(33) 3.738(64) ------2 36 574.745(35) 0.148 725(24) 2.277(50) -4.114(31) 1 36 309.327(39) 0.151 811(23) 1.988(41) -1.699(21) 0 36 026.656(28) 0.154 395(16) 1.749(25) -0.978(11)

Al81Br T (cm'1) B (cm'1) D x 107 (cm*1) H x 1012 (cm'1) 3 36 816.443(53) 0.144 139(41) 3.663(71) ------2 36 572.784(51) 0.147 801(34) 2.239(68) -3.941(40) 1 36 308.042(52) 0.150 866(30) 1.956(54) -1.693(28) 0 36 026.195(32) 0.153 428(18) 1.721(30) -1.00(14) aUncertainties shown are one standard deviation. 49

Table 8

Equilibrium Constants (cm'1)3

A !n X *S+

Al^Br o c = 296.16(26) 378.106(22) o)cxc = 5.68(15) 1.307 4(78) g) ^ = -0.655(25) Tc = 35 880.01(11) Bc = * 0.159 197 066(71) a c x 104 = * 8.604 38(47) Yc x 106 = * 2.029 7(69) Dc x 107 = * 1.128 43(66) fic x 1010 = * 1.93(32)

Al81Br g>c = 295.14(35) 376.922(30) cocxc = 5.569(21) 1.301(10) (i>eye = -0.663(35) Tc = 35 880.10(14) B = * 0.158 195 64(11) a e x 10 = * 8.523 57(76) Ye x 106 = * 2.005(11) De x 107 = * 1.114 9(11) fic x 1010 = * 2.27(52)

‘This description of the A state is not recommended.

Uncertainties shown are one standard deviation. 50

E. Conclusions

Rotational assignments for AlBr have been extended to lower J values providing a more precise determination of the band-origins in the A *11 - X *£+ transition. Taking advantage of this improvement in band-origin data, the previous discrepancy in the reported vibrational constants in the A 1n state of aluminum monobromide (9,11) has been addressed. Rotational constants have been determined level by level (as opposed to the usual expansion in equilibrium constants) since the high correlation between the equilibrium rotational constants ac,

Yc, and /3C and the vibrational constants o>c, wcxc resulted in a large shift in the vibrational constants. Rotational constants determined in this study are in good agreement with those reported previously. The question of predissociation of the A

*11 state will be addressed separately. 51

References

1. F. H. Crawford and F. Folliot, Phys. Rev. 44, 953-954 (1933)

2. C. G. Jennergren, Arkiv Mat. Astron. FysikA 35, 1-29 (1948)

3. E. Miescher, Hev. Phys. Acta 8, 279-308 (1935); 9 693-706 (1936)

4. D. Sharma,Astrophys. J. 113, 219-221 (1951)

5. H. G. Howell, Proc. Roy. Soc. A148, 696-707 (1935)

6. P. C. Mahanti, Ind. J. Phys. 9, 435-449 (1976)

7. R. S. Ram, K. N. Upadhya, D. K. Ram, and J. Singh, Opt. Pura Apl. (Spain) 6, 38-63 (1973)

8. R. S. Ram, Spectrosc. Lett. 9, 435-449 (1976)

9. W. B. Griffith and C. W. Mathews, J. Molec. Spectrosc. 104, 347-352 (1983)

10. U. Wolf and E. Tiemann, Chem. Phys. 119, 407-418 (1988)

11. H. Bredohl, I. Dubois, E. Mahieu, and F. Mellen,/. Molec. Spectrosc. 145,12-17 (1991)

12. F. C. Wyse and W. Gordy, J. Chem. Phys. 56, 2130-2136 (1972)

13. T. Hoeft, T. Toerring, and E. Tiemann, Z. Naturforsch. A: Phys. Chem. K osm ophys. 28, 1066-1068 (1973) 52

14. H. Uehara, K. Horiai, Y. Ozaki and T. Kono, Chem. Phys. Lett. 214, 527-530 (1993)

15. G. M. Plummer, G. Winnewisser, M. Winnewisser, J. Hahn, and K Reinartz, J. Molec. Spectrosc. 126, 225-269 (1987)

16. G. Herzberg, Molecular Structure and Molecular Spectra. I. Spectra of Diatomic Molecules. Van Nostrand Reinholt, New York (1950)

17. M. C. Abrams and J. W. Brault, Computer program DECOMP, Paper TB1, Forty-Fourth Symposium on Molecular Spectroscopy, The Ohio State University, Columbus, Ohio, 1989

18. P. Jensen, "High Resolution FT-IR Spectroscopy with a PC: Processing Data . from a Bruker IFS 120 HR High-Resolution FT-IR Spectrometer Using a Personal Computer", Bruker Report 1/1989, pp. 3-9 (1989)

19. D. L. Albritton, A. L. Schmeltekopf, and R. N. Zare, J. Molec. Spectrosc. 67, 132-156 (1977) CHAPTER IV

Other Experiments

A. Searching for the Vacuum Ultraviolet Spectrum of FCN

Vacuum ultraviolet spectra of most of the cyanogen halides have been observed (24).

Cyanogen fluoride (FCN) is a candidate for study in the vacuum ultraviolet since no reports of an electronic transition of this molecule exist in the literature. This is quite likely due to the difficulty of obtaining a pure sample of the compound. While most of the cyanogen halides can be purchased commercially, cyanogen fluoride must be synthesized in the laboratory as was the case for the microwave studies of FCN (25).

The microwave spectrum of FCN was observed in the reaction of fluorine atoms with cyanamide (NH2CN) (26) during an attempt to produce the cyanamidyl radical (HNCN) by hydrogen abstraction from cyanamide (NH2CN). This observation was made while visiting the laboratory of Manfred Winnewisser at the Justus Leibig University in Giessen West

Germany. In the reaction, fluorine atoms were produced in a microwave discharge through either CF4 or SF6. These were then reacted with cyanamide by passing the nascent radicals over a sample of solid cyanamide. FCN lines appeared with greater intensity when no carrier gas was used in the microwave discharge. However, when a small amount of argon was introduced as a carrier gas, a pinkish glow appeared over the cyanamide sample which

53 54 may have been due to the red emission bands of CN. This same pinkish glow was observed in the reaction of fluorine atoms (produced in the same manner) with acetonitrile (CH3CN) vapor. It is presumed that the same physical observations of the reaction are indicative of similar chemistry. Hence, it was proposed that the reaction of fluorine atoms with acetonitrile would produce FCN. This may be a suitable method for producing the molecule under flowing conditions for examination in the vacuum ultraviolet region.

The spectra of the cyanogen halides show characteristics which have been observed in the spectrum of hydrogen cyanide. Microwave and infrared spectra have been observed for the cyanogen halides and all of them, including FCN, are known to be linear in their ground electronic states (25). Electronic transitions have been reported for ICN, BrCN and

C1CN (6). These molecules, like HCN, show spectra which indicate a bent geometry in their excited electronic states along with a well known linear geometry in their ground states.

This change of geometry leads to long progressions in the bending mode of the molecule.

The sub-band structure is simplified by the selection rules governing changes in the angular momentum about the molecule’s symmetry axis. Normally, the selection rule governing changes in this quantity is simply AK = K’-K" = 0 for transitions whose transition moments lie along the molecular symmetry axis (||-type bands) and AK = ± 1 for x-type bands. For linear molecules, the angular momentum about the molecular axis is the resultant of vibrational angular momentum (f) and orbital angular momentum (A) or K" = |J" ± A"|.

Thus, for closed shell linear molecules (A = 0) such as the cyanogen halides, K" simply becomes f" and a selection rule can be stated as

K’ - f" = 0 for parallel bands

K’ - f" = ±1 for perpendicular bands 55

Due to the electronic states involved, all of the molecules of the XCN class have perpendicular transitions.

i. Production of FCN

The synthesis of FCN by the method of Fawcett and Lipscomb (33) is a two step process involving the synthesis of a trimeric form, cyanuric fluoride, and then the pyrolysis of the trimer to form FCN. The synthesis of the trimer was accomplished by the method of Tolluck and Coffman (7) as discussed in Chapter II. Briefly, cyanuric chloride, purchased from the Aldrich company and used unpurified, was reacted with sodium fluoride in a high- boiling, polar solvent. Cyanuric fluoride was then distilled from the reaction mixture. The trimer was then purified by trap-to-trap distillation. The infrared spectrum of both the liquid and vapor phases confirmed the identity of the product (1-3).

FCN can be produced from the trimer by high-temperature pyrolysis (33). Attempts at this method failed to produce any observable amounts of FCN. Several impurities were observed by their infrared spectra including primarily C 02, H20 and HC1. Other attempts to break up the aromatic trimer included passing the trimer vapor through the positive column of an electrical discharge. This produced a sample containing several impurities as evidenced by the infrared spectrum. There may have been some peaks in the spectrum which were assignable to FCN, but they were not the dominant features in the spectrum of the sample. Cyanogen (NCCN) was conclusively observed in the mixture by its electronic spectrum near 2000 A. No other electronic bands were observed for the mixture in the region covered by the deuterium continuum lamp. 56

ii. Other Observations in the Laboratory

Fluorine atoms, produced in a microwave discharge, were reacted with cyanamide in an attempt to observe the vacuum ultraviolet spectrum of FCN. For this experiment, the fluorine atom source was a microwave discharge through sulfur hexafluoride (SF6). A series of absorption bands was observed in the region extending from 1870 A to 2175 A. The bands had sharply defined heads and were degraded to lower energies. The spacing between the bands was approximately 375 cm'1. The reaction was repeated using tetrafluoromethane (CF4) in the microwave discharge as a source of fluorine atoms. Under these conditions the bands were not observed. This result suggests that the bands are not in fact due to FCN but may contain at least one sulfur atom.

Table 9

Electronic States of SF2

Designation Term Value Method

4s ‘B, 54400 cm'1 2+1 REMPI

4p ‘B, 62000 cm'1 2+1 REMPI 3+1 REMPI

4p ‘A, 63800 cm'1 2+1 REMPI 3+1 REMPI

At first, it was proposed that the bands were due to a product of the discharge through SF6. SF2 had been reported as a product of such discharges by Johnson and

Hudgens (27) who made their observations using Resonance Enhanced Multiphoton

Ionization (REMP1) detecting SF) ion current as a function of laser frequency to record the 57 spectrum of the neutral. They reported three new electronic states of SF2 as summarized in the Table 1. For the 4s 'B, state, progressions in both v, (symmetric SF stretch) and v2

(bend) were observed with spacings of approximately 999 and 400 cm'1 respectively. As a check to see if we were in fact seeing absorption to the 4s 1B1 of SF2, an alternate method of producing SF2 was used. Glinski and Taylor (28) have reported an infrared emission due to SF2 in the afterglow of the reaction of molecular fluorine (F2) with carbon disulfide (CS2).

Due to the ease of setup, atomic fluorine produced in a discharge through CF4 was mixed with CS2 in an attempt to reproduce the band system. The bands were very strong in this experiment and persisted when the discharge was turned off. Based on this result and comparison to the literature, the bands were assigned to the A ‘B2 - X 'S* transition of CS2 which occurs in the region of 2200 - 1800 A (6). This system was recorded and found to be very strong; the cell was nearly opaque at pressures of CS2 well below its vapor pressure. Thus, only trace amounts were necessary for the original observations. Further, after exposure to CS2, it was necessary to remove the absorption cell and thoroughly clean it since CS2 is soluble in the black-wax (Apiezon W) used for some of the vacuum seals.

While no discrete electronic spectra of the trimeric form of FCN, cyanuric fluoride, have been reported, the photoelectron spectrum has been reported by Brundle et al. (5).

This study focused on the effects for fluorine atom substitution on the energies for molecular orbitals in planar aromatic rings. It suggested that fluorine atom substitution stabilized a orbitals by approximately 2-3 eV while stabilizing n orbitals by less than 0.5 eV.

If this pattern holds true for cyanogen fluoride, the n - n ' transition of hydrogen cyanide which is observed near 1900 A may be shifted to near 1400 A in cyanogen fluoride. This region was not accessible with our deuterium lamp due to absorption by the quartz envelope 58 of the lamp itself. A suitable light source for this region would be a medium pressure (200

Torr) krypton dimer lamp.

Two possibilities exist for the continuation of this project. First, the two-step synthesis of FCN should be pursued. The chief problems encountered with this synthesis involved the handling of the sample during and after the pyrolysis. A suitably packed pyrolysis tube must be used and a good vacuum must be maintained. Also, care must be taken to insure the purity of the surfaces within the pyrolysis tube. The alumina tube used in the pyrolysis was almost certainly the source of the impurities (HC1, H20 and C 02) found in the sample collected. Also, greater care must be employed during the vacuum line purification of the sample.

Second, the use of a fast flow reactor should be pursued as a source of FCN. This might use either the reaction of fluorine atoms with cyanamide or perhaps with acetonitrile.

In these experiments, a microwave discharge through CF4 should be used to avoid the introduction of CS2 which will almost certainly be prevalent if sulfur is present in the discharge afterglow. The range of wavelengths studied for this type of reaction spanned only those attainable with the deuterium continuum lamp and were limited by the quartz absorption cutoff. This range should be extended to include the ranges covered by the xenon and krypton dimer lamps (34), especially the region near 1400 A.

B. Production of CN Containing Radicals under Steady State Conditions

Molecules containing the CN fragment have been of considerable importance in the chemistry of interstellar clouds (29). Attempts were made to produce some of these radicals under steady-state conditions and observe them in emission. The experiments involved the reaction of nitrogen with methane in the high-energy environment of a microwave discharge. 59

HNCN has been observed in the products of a microwave discharge through nitrogen and methane when the products of such a discharge are trapped in a low-temperature matrix

(30). First, both nitrogen (N2) and methane (CH4) were mixed and passed through the electrodeless discharge. The emission spectrum from this system was recorded on Kodak

SA-1 film using a Bausch and Lomb 1.5 meter spectrograph. The spectrum was completely dominated by the C 3IIU - B 3ng system of N2 centered near 3371 A (31) and the B 2S + - X

2E + system of CN centered near 3880 A (31). Other fragments such as CH, NH and NCN may have been present, but their spectra were obscured by the other two very bright systems.

NCN has been observed in emission as a product of the reaction of atomic nitrogen with methane (32). This experiment was tried using the same Bausch and Lomb spectrograph. The production of atomic nitrogen in a microwave discharge is characterized by a yellow glow which extends some distance down the discharge tube from the center of the microwave discharge. The region of mixing of the two gasses included this yellow afterglow. The nascent molecules were monitored by their emission spectra. Only N2 was observed in this experiment.

Further experimentation on these systems should include more permutations of running the discharge through nitrogen or methane and mixing the products in a manner suitable for both absorption and emission spectroscopy. These experiments would be very well suited to study using the Bruker IFS 120 HR spectrometer due to its high sensitivity, high resolution and flexibility in frequency coverage. 60

References

1. D. A. Long, J. Y. H. Chau, and R. B. Gravenor, Trans. Faraday Soc., 58, 2316-2324 (1962)

2. J. E. Griffiths and D. E. Irish, Can. J. Phys., 42, 690-695 (1964)

3. J. R. Durig and G. Nagarajan, A cta Phys. Polon., 35, 867-874 (1969)

4. J. Schlupf and A. Weber, / Mol. Spectrosc., 54, 10-19 (1975)

5. C. R. Brundle, M. B. Robin, and N. A. Kuebler, / Am. Chem. Soc. 94, 1466-1475 (1971)

6. G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic Spectra of Polyatomic Molecules. Van Nostrand Reinhold, New York (1966) and references therein

7. C. W. Tullock and D. D. Coffman, J. Org. Chem., 25, 2016-2019 (1960)

8. F. Seel and K. Balreich, Chem. Ber., 92, 344-346 (1959)

9. J. E. Lancaster and N. B. Colthup, / Chem. Phys., 22, 1149 (1954)

10. S. H. Bauer, K. Katada, and K. Kimura, The Structures of C6, B3N3 and C3N3 Ring Compounds, in Structural Chemistry and Molecular Biology (A. Rich and N. Davidson Eds.), pp. 653-670, W. H. Freeman and Co., San Francisco, 1968

11. L. Nygaard, I. Bojeson, T. Pedersen, and J. Rastrup-Andersen, J. Mol. Struct., 2209- , 215 (1968)

12. F. H. Crawford and F. Folliot, Phys. Rev. 44, 953-954 (1933)

13. C. G. Jennergen, Ark. Mat. Astern. Fys. A 35, 1-29 (1948)

14. E. Miescher, Helv. Phys. Acta 8, 279-308 (1935)

15. R. S. Ram, K. N. Upadhya, D. K. Ram, and J. Singh, Opt. PuraApl. 6, 38-63 (1973) 61

16. W. B. Griffith and C. W. Mathews, J. Mol. Spectrosc., 104, 347-352 (1984)

17. H. Bredohl, I. Dubois, E. Mahieu, and F. Mielen,/. Mol. Spectrosc. 145, 12-17 (1991)

18. D. Sharma, Astrophys. J. 113,219(1951)

19. A. Lakshiminurayana and P. B. V. Haranath, Curr. Sci. 39, 228-229 (1970)

20. F. C. Wyse and W. Gordy, /. Chem Phys. 56, 2130-2136 (1972)

21. T. Hoeft, T. Toerring, and T. Tiemann, Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 28, 1066-1068 (1973)

22. R. N. Zare, A. L. Schmeltekopf, W. J. Harrop, and D. L. Albritton, / Mol. Spectrosc. 46, 37 (1973); D. L. Albritton, A. L. Schmeltekopf, and R. N. Zare, Molecular Spectroscopy: Modern Research. Academic Press, New York (1976)

23. A. G. Worthington and J. Geffner, Treatment of Experimental Data. Wiley, New York (1943)

24. G. Herzberg, Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules. Van Nostrand Reinhold, New York (1945) and references therein

25. J. J. Ewing, H. L. Tigelaar and W. H. Flygare, /. Chem. Phys. 56, 1957-1966 (1972)

26. P. E. Fleming, Steady State Production of HNCN in the Gas Phase by Hydrogen Abstraction from Cyanamide. Thesis, The Ohio State University (1988)

27. R. D. Johnson and J. W. Hudgens, "SF2 Observed from 280 to 500 nm by Resonance Enhanced Multiphoton Ionization Spectroscopy", paper TH11 presented in the Forty-Fourth Symposium on Molecular Spectroscopy, The Ohio State University, Columbus, OH (1989)

28. R. J. Glinski and C. D. Taylor, "Effects of Isotopic Substitution on the Chemiiuminescence Spectra Obtained During the Reaction of F2 with CS2", paper MH3 presented in the Forty-Fourth Symposium on Molecular Spectrosccopy, The Ohio State University, Columbus, OH (1989)

29. B.R. Sweeting, Electronic Spectra of HNCN. Thesis, The Ohio State University (1986); B. R. Sweeting The Electronic Spectrum of the Free-Radical HCNN. Dissertation, The Ohio State University (1989)

30. M. Jacox, private communication 62

31. G. Herzberg, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules 2nd edition, Van Nostrand Reinhold, New York (1950) and references therein

32. G. Herzberg and D. N. Travis, Can. J. Phys., 42, 1658 (1964)

33. F. S. Fawcett and R. D. Lipscomb,/. Amer. Chem. Soc. 86, 2576-2585 (1964)

34. P.G. Wilkinson and E. T. Byran, Appl. Opt. 4, 581-588 (1965) CHAPTER V

Conclusions

A rotationally resolved vibrational spectrum (v„ - out of plane motion) of cyanuric fluoride was presented. This spectrum shows for the first time, the resolution of the

"satellite" structure of the hot bands prevalent in the system. Rotational constants determined in this study are in good agreement with those presented by Schlupf and Weber

(4) but are more reliable as the hot band structure is resolved in the current spectrum.

The A -X transition of aluminum monobromide has been re-examined. The isotopic assignments by Bredohl and co-workers (17) have been shown to not agree with simple models predicting band origin shifts due to isotopic substitution. Also, the rotational assignments in the 1-1 band have been revised. Rotational constants have been found by merging fits of ten separate bands in the A-X transition with microwave data (20). It is found that equilibrium rotational constants in the upper state have little meaning as the potential energy curve appears to change at high vibrational levels due to an interaction with another electronic state (which is probably also responsible for the predissociative nature of the A state.) meaningful vibrational constants can only be determined for the A state if the rotational constants are not constrained to fit models including equilibrium values. This study also extends J assignments to lower values than previous studies.

63 Bibliography

1. D. A. Long, J. Y. H. Chau, and R. B. Gravenor, Trans. Faraday Soc., 58, 2316-2324 (1962)

2. J. E. Griffiths and D. E. Irish, Can. J. Phys., 42, 690-695 (1964)

3. J. R. Durig and G. Nagarajan, Acta Phys. Polon., 35, 867-874 (1969)

4. J. Schlupf and A. Weber, / Mol. Spectrosc., 54, 10-19 (1975)

5. C. R. Brundle, M. B. Robin, and N. A. Kuebler, J. A m . Chem. Soc. 94, 1466-1475 (1971)

6. G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic Spectra of Polyatomic Molecules. Van Nostrand Reinhold, New York (1966) and references therein

7. C. W. Tullock and D. D. Coffman, / Org. Chem., 25, 2016-2019 (1960)

8. F. Seel and K. Balreich, Chem. Ber., 92, 344-346 (1959)

9. J. E. Lancaster and N. B. Colthup, / Chem. Phys., 22, 1149 (1954)

10. S. H. Bauer, K. Katada, and K. Kimura, The Structures of C6, B3N3 and C3N3 Ring Compounds, in Structural Chemistry and Molecular Biology (A. Rich and N. Davidson Eds.), pp. 653-670, W. H. Freeman and Co., San Francisco, 1968

11. L. Nygaard, I. Bojeson, T. Pedersen, and J. Rastrup-Andersen,/ Mol. Struct., 2, 209- 215 (1968)

12. F. H. Crawford and F. Folliot, Phys. Rev. 44, 953-954 (1933)

13. C. G. Jennergen, Ark. Mat. Astern. Fys. A 35, 1-29 (1948)

14. E. Miescher, Helv. Phys. Acta 8, 279-308 (1935)

15. R. S. Ram, K. N. Upadhya, D. K. Ram, and J. Singh, Opt. PuraApl. 6, 38-63 (1973)

64 65

16. W. B. Griffith and C. W. Mathews, / Mol. Spectrosc., 104, 347-352 (1984)

17. H. Bredohl, I. Dubois, E. Mahieu, and F. Mielen,/ Mol. Spectrosc. 145, 12-17 (1991)

18. D. Sharma, Astrophys. J. 113,219(1951)

19. A. Lakshiminurayana and P. B. V. Haranath, Curr. Sci. 39, 228-229 (1970)

20. F. C. Wyse and W. Gordy, /. Client Phys. 56, 2130-2136 (1972)

21. T. Hoeft, T. Toerring, and T. Tiemann, Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 28, 1066-1068 (1973)

22. R. N. Zare, A. L. Schmeltekopf, W. J. Harrop, and D. L. Albritton, / Mol. Spectrosc. 46, 37 (1973); D. L. Albritton, A. L. Schmeltekopf, and R. N. Zare, Molecular Spectroscopy: Modern Research Academic Press, New York (1976)

23. A. G. Worthington and J. Geffner, Treatment of Experimental Data. Wiley, New York (1943)

24. G. Herzberg, Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules. Van Nostrand Reinhold, New York (1945) and references therein

25. J. J. Ewing, H. L. Tigelaar and W. H. Flygare, / Chem. Phys. 56, 1957-1966 (1972)

26. P. E. Fleming, Steady State Production of HNCN in the Gas Phase by Hydrogen Abstraction from Cvanamide. Thesis, The Ohio State University (1988)

27. R. D. Johnson and J. W. Hudgens, "SF2 Observed from 280 to 500 nm by Resonance Enhanced Multiphoton Ionization Spectroscopy", paper TH ll presented in the Forty-Fourth Symposium on Molecular Spectroscopy, The Ohio State University, Columbus, OH (1989)

28. R. J. Glinski and C. D. Taylor, "Effects of Isotopic Substitution on the Chemiluminescence Spectra Obtained During the Reaction of F2 with CS2", paper MH3 presented in the Forty-Fourth Symposium on Molecular Spectrosccopy, The Ohio State University, Columbus, OH (1989)

29. B. R. Sweeting, Electronic Spectra of HNCN. Thesis, The Ohio State University (1986); B. R. Sweeting The Electronic Spectrum of the Free-Radical HCNN. Dissertation, The Ohio State University (1989)

30. M. Jacox, private communication 66

31. G. Herzberg, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules 2nd edition, Van Nostrand Reinhold, New York (1950) and references therein

32. G. Herzberg and D. N. Travis, Can. J. Phys., 42, 1658 (1964)

33. F. S. Fawcett and R. D. Lipscomb, / Amer. Chem. Soc. 86, 2576-2585 (1964)

34. P.G. Wilkinson and E. T. Byran, Appl. Opt. 4, 581-588 (1965) Appendix A

Line Positions and Assignments for the v„ and Vn + Vu-v,* Bands of Cyanuric Fluoride

67 68

Assignments* in the v„ Band of Cyanuric Fluoride

J r m ) Obs - Calcb PM) Obs - Calc

8 821.9045 -0.0029 9 822.0378 -0.0005 10 822.1682 -0.0009 11 822.2986 -0.0013 12 822.4305 -0.0001 13 822.5609 -0.0004 14 822.6913 -0.0007 • 15 822.8224 -0.0002 818.7554 -0.0007 16 822.9527 -0.0005 818.6233 -0.0010 17 823.0833 -0.0004 818.4916 -0.0010 18 823.2141 -0.0001 818.3594 -0.0014 19 823.3439 -0.0008 818.2270 -0.0019 20 823.4746 -0.0005 818.0964 -0.0006 21 823.6055 0.0001 817.9641 -0.0010 22 823.7366 0.0008 817.8324 -0.0007 23 823.8663 0.0002 817.7014 0.0003 24 823.9970 0.0006 817.5686 -0.0005 25 824.1269 0.0003 817.4361 -0.0009 26 824.2571 0.0003 817.3047 -0.0002 27 824.3873 0.0003 817.1722 -0.0006 28 824.5178 0.0007 817.0398 -0.0008 29 824.6478 0.0006 816.9087 0.0003 30 824.7775 0.0003 816.7763 0.0002 31 824.9076 0.0004 816.6439 0.0000 32 825.0376 0.0004 816.5127 0.0012 33 825.1680 0.0009 816.3787 -0.0005 34 825.2972 0.0002 816.2466 -0.0002 35 825.4275 0.0008 816.1155 0.0011 36 825.5574 0.0008 815.9822 0.0003 69

J R m Obs - Calc P(J) Obs - Calc

37 825.6878 0.0014 815.8491 -0.0004 38 825.8176 0.0016 815.7182 0.0012 39 825.9460 0.0003 815.5852 0.0008 40 826.0757 0.0004 815.4529 0.0011 41 826.2049 -0.0000 815.3179 -0.0014 42 826.3346 0.0001 815.1859 -0.0007 43 826.4646 0.0007 815.0542 0.0003 44 826.5943 0.0008 814.9215 0.0003 45 826.7229 0.0000 814.7887 0.0003 46 826.8528 0.0006 814.6578 0.0021 47 826.9811 -0.0005 814.5222 -0.0006 48 827.1117 0.0008 814.3917 0.0017 49 827.2402 0.0001 814.2539 -0.0032 50 827.3699 0.0005 814.1253 0.0011 51 827.4986 0.0001 813.9914 0.0001 52 827.6278 0.0002 813.8574 -0.0009 53 827.7570 0.0003 813.7261 0.0009 54 827.8857 -0.0001 813.5929 0.0007 55 828.0156 0.0009 813.4599 0.0008 56 828.1438 0.0001 813.3268 0.0008 57 828.2726 -0.0001 813.1917 -0.0011 58 828.4003 -0.0011 813.0577 -0.0020 59 828.5302 -0.0001 812.9263 -0.0002 60 828.6591 0.0001 812.7949 0.0017 61 828.7871 -0.0007 812.6592 -0.0008 62 828.9165 0.0000 812.5254 -0.0012 63 829.0444 -0.0008 812.3947 0.0014 64 829.1736 -0.0002 812.2599 -0.0000 65 829.3016 -0.0007 812.1266 0.0001 66 829.4298 -0.0010 811.9933 0.0002 67 829.5585 -0.0008 811.8592 -0.0004 68 829.6881 0.0004 811.7261 0.0001 69 829.8160 -0.0000 811.5893 -0.0033 70 829.9435 -0.0009 811.4575 -0.0014 71 830.0714 -0.0013 811.3239 -0.0014 72 830.1999 -0.0010 811.1913 -0.0004 73 830.3278 -0.0013 811.0567 -0.0013 74 830.4560 -0.0013 810.9228 -0.0016 75 830.5847 -0.0007 810.7916 0.0009 76 830.7130 -0.0004 810.6584 0.0016 77 830.8407 -0.0007 810.5217 -0.0014 78 830.9690 -0.0004 810.3898 0.0005 79 831.0956 -0.0017 810.2554 0.0000 80 831.2236 -0.0016 810.1211 -0.0004 81 831.3518 -0.0011 809.9892 0.0016 82 831.4796 -0.0012 809.8533 -0.0003 83 831.6074 -0.0010 809.7198 0.0002 84 831.7339 -0.0022 809.5838 -0.0018 85 831.8625 -0.0013 809.4507 -0.0008 70

Obs - Calc P L 2J___ Obs - Calc

86 831.9902 -0.0011 809.3152 -0.0023 87 832.1197 0.0008 809.1844 0.0010 88 832.2447 -0.0017 809.0470 - 0.0022 89 832.3723 -0.0015 90 832.5014 0.0002 91 832.6262 -0.0023 92 832.7567 0.0009 93 832.8823 -0.0008 94 833.0096 -0.0006 95 833.1373 -0.0001 96 833.2625 -0.0019 97 833.3921 0.0006 98 833.5212 0.0027 99 833.6456 0.0002 100 833.7709 -0.0014 101 833.8946 -0.0046 102 834.0262 0.0003 103 834.1520 -0.0007 104 834.2804 0.0011

*A11 line measurements are in units of cm'1. bNo. lines in fit = 170 Standard deviation of fit = 0.00100 cm'1 71

Assignments' in the v„ + v14-vu Band of Cyanuric Fluoride

J RM) Obs - Calcb P(J) Obs - Calc

12 818.8505 -0.0009 13 818.7196 -0.0002 14 818.5870 -0.0011 15 818.4570 0.0006 16 818.3265 0.0019 17 818.1927 -0.0002 18 818.0600 -0.0010 19 817.9279 -0.0013 20 817.7968 -0.0005 21 817.6646 -0.0008 22 817.5337 0.0003 23 823.5661 -0.0008 817.4021 0.0007 24 823.6960 -0.0012 817.2700 0.0006 25 823.8266 -0.0009 817.1377 0.0003 26 823.9582 0.0005 817.0052 -0.0000 27 824.0871 -0.0007 816.8742 0.0011 28 824.2183 0.0003 816.7401 -0.0009 29 824.3477 -0.0004 816.6074 -0.0014 30 824.4782 0.0001 816.4772 0.0006 31 824.6080 -0.0002 816.3441 -0.0002 32 824.7375 -0.0006 816.2118 -0.0003 33 824.8689 0.0008 816.0802 0.0005 34 824.9985 0.0005 815.9473 -0.0000 35 825.1285 0.0007 815.8150 -0.0000 36 825.2577 0.0001 815.6826 0.0000 37 825.3870 -0.0005 815.5495 -0.0006 38 825.5182 0.0010 815.4154 -0.0022 39 825.6469 0.0001 815.2876 0.0025 40 825.7764 -0.0001 815.1518 -0.0008 41 825.9055 -0.0006 815.0221 0.0021 72

J R m Obs - Calc P(J) Obs - Calc

42 826.0358 0.0001 814.8865 -0.0009 43 826.1655 0.0003 814.7556 0.0009 44 826.2961 0.0014 814.6205 -0.0015 45 826.4243 0.0002 814.4903 0.0010 46 826.5548 0.0013 814.3557 -0.0008 47 826.6821 -0.0008 814.2233 -0.0004 48 826.8141 0.0019 814.0927 0.0017 49 826.9413 -0.0002 813.9577 -0.0004 50 827.0725 0.0018 813.8244 -0.0008 51 827.1990 -0.0009 813.6920 -0.0003 52 827.3307 0.0017 813.5588 -0.0005 53 827.4573 -0.0008 813.4249 -0.0014 54 827.5877 0.0006 813.2950 0.0017 55 827.7169 0.0008 813.1591 -0.0012 56 827.8447 -0.0004 813.0263 -0.0009 57 827.9739 -0.0000 812.8948 0.0007 58 828.1018 -0.0010 812.7623 0.0014 59 828.2318 0.0002 812.6270 -0.0007 60 828.3600 -0.0004 812.4960 0.0015 61 828.4901 0.0010 812.3618 0.0005 62 828.6181 0.0003 812.2272 -0.0007 63 828.7470 0.0006 812.0980 0.0033 64 828.8742 -0.0008 811.9623 0.0010 65 829.0029 -0.0007 811.8281 0.0003 66 829.1321 0.0001 811.6945 0.0000 67 829.2611 0.0007 811.5628 0.0018 68 829.3884 -0.0005 811.4268 -0.0008 69 829.5165 -0.0007 811.2929 -0.0011 70 829.6443 -0.0012 811.1613 0.0009 71 829.7725 -0.0012 811.0280 0.0011 72 829.9007 -0.0012 810.8929 -0.0004 73 830.0289 -0.0011 810.7594 -0.0001 74 830.1579 -0.0003 810.6249 -0.0010 75 830.2848 -0.0014 810.4902 -0.0020 76 830.4134 -0.0007 77 830.5431 0.0010 78 830.6693 -0.0007 79 830.7974 -0.0004 80 830.9251 -0.0005 81 831.0533 -0.0001 82 831.1809 -0.0001 83 831.3107 0.0020 84 831.4368 0.0005 85 831.5632 -0.0006 86 831.6910 -0.0003 87 831.8193 0.0007 88 831.9437 -0.0023 89 832.0743 0.0010 90 832.2012 0.0007 J R( J) Obs - Calc

91 832.3274 -0.0003 92 832.4536 -0.0013 93 832.5823 0.0004 94 832.7097 0.0007 95 832.8374 0.0014 aAll line measurements are in units of cm'1 hNo. lines in fit = 136 Standard deviation of fit = 0.00097 cm'1 Appendix B

• Line listing for AlBr A-X

74 AlBr A - X for Bromine-79

0 - 1 Band 1 Band

R(J> Q(J) P(J) R(J) Q< J) P(J)

30 35458.992 72 35464.129 35441.904 31 35458.722 73 35463.793 35441.277 32 35458.448 74 35463.461 35440.689 33 35458.198 75 35463.154 35440.001 34 35457.981 76 35462.749 35439.324 35 35457.705 35447.009 77 35438.705 36 35457.465 78 35462.034 35438.004 37 35457.196 79 35461.615 35437.288 38 35456.878 35445.251 80 35461.181 35436.550 39 35456.681 35444.664 81 35460.746 35435.878 40 35456.382 35444.031 82 35435.130 41 35455.988 35443.417 83 35434.396 42 35455.682 35442.784 84 35433.662 43 35455.412 35442.227 85 35432.857 44 35455.064 35441.499 86 35432.058 45 35454.684 35440.919 87 35431.224 46 35454.337 35440.321 88 35430.425 47 35454.012 35439.632 89 35429.569 48 35453.665 35438.879 90 35428.741 49 35453.283 35438.226 91 35427.869 50 35452.893 35437.512 92 35427.002 51 35452.501 35436.849 93 35426.063 52 35452.077 35436.146 53 35451.629 35435.481 No. lin e s = 102 54 35451.247 35434.726 55 35450.854 35433.979 56 35450.400 35433.250 57 35449.939 35432.485 58 35449.503 35431.748 59 35449.041 35430.969 60 35448.507 35430.174 61 35448.022 35429.421 62 35447.505 35428.575 63 35446.963 35427.826 64 35446.420 35426.924 65 35445.975 35426.120 66 35445.428 67 35444.848 68 69 35443.737 70 35443.149 71 35464.442 35442.498 1 - 2 Band 2 Band

R(J> 0 (J ) P(J) R(J) Q(J) P(J>

23 35369.196 66 35347.009 24 35368.928 67 35346.217 25 35368.635 68 35345.388 26 35368.350 69 35344.467 27 35368.054 70 35343.613 28 35367.738 71 35342.752 29 35367.462 72 35341.804 30 35367.122 73 35340.919 31 35366.791 74 35339.955 32 35366.424 35356.678 75 35338.957 33 35366.048 76 35338.027 34 35365.713 77 35337.025 35 35365.354 78 35336.020 36 35364.897 35354.040 79 35335.008 37 35364.489 35353.314 80 35333.953 38 35364.144 35352.586 81 35332.871 39 35363.692 35351.869 40 35363.266 35351.110 No. lin e s = 102 41 35362.747 35350.356 42 35362.333 35349.590 43 35361.802 35348.813 44 35374.934 35361.360 35348.026 45 35374.705 35360.816 35347.167 46 35374.456 35360.313 47 35374.248 35359.753 35345.611 48 35374.020 35359.172 35344.774 49 35373.794 35358.678 35343.900 50 35373.475 35358.089 35343.023 51 35373.134 35357.512 35342.144 52 35356.913 35341.244 53 35372.537 35356.297 35340.342 54 35372.198 35355.679 35339.405 55 35371.898 35355.027 35338.515 56 35371.498 35354.406 35337.509 57 35371.167 35353.693 35336.562 58 35370.780 35353.032 35335.577 59 35369.960 35352.303 60 35351.619 35333.584 61 35369.536 35350.841 35332.534 62 35369.070 35350.155 63 35368.578 35349.408 64 35348.601 65 35347.839 0 - 0 Band 0 - 0 Band

R(J> Q(J) P(J) R(J> Q(J) P(J>

17 35836.465 60 35839.599 35820.922 35802.521 18 35836.246 61 35839.290 35820.323 35801.601 19 35836.073 62 35838.977 35819.703 35800.694 20 35835.895 63 35838.664 35819.087 35799.819 21 35835.704 64 35838.353 35818.481 35798.859 22 35835.565 65 35838.007 35817.806 35797.933 23 35835.328 66 35837.650 35817.140 35796.980 24 35835.121 67 35837.276 35816.477 35796.015 25 35834.912 68 35836.857 35815.799 35795.043 26 35834.700 69 35836.465 35815.113 35794.058 27 35834.421 70 35814.402 35793.075 28 35834.185 71 35813.656 35792.023 29 35833.893 72 35812.955 35790.976 30 35833.619 73 35812.214 35789.939 31 35833.349 74 35811.457 35788.897 32 35833.090 75 35810.660 35787.846 33 35832.776 76 35809.880 35786.753 34 35832.481 77 35809.074 35785.635 35 35832.152 35821.394 78 35808.247 35784.504 36 35831.827 35820.772 79 35807.423 35783.409 37 35831.488 35820.112 80 35806.584 35782.266 38 35831.169 35819.460 81 35805.730 35781.074 39 35830.801 35818.824 82 35804.842 35779.933 40 35830.437 35818.110 83 35803.939 35778.763 41 35830.064 35817.515 84 35803.064 35777.495 42 35829.689 35816.811 85 35802.123 35776.345 43 35829.299 35816.084 86 35801.162 35775.076 44 35828.866 35815.381 87 35800.210 35773.899 45 35842.584 35828.467 35814.622 88 35799.283 35772.608 46 35842.466 35828.033 35813.913 89 35798.259 35771.305 47 35842.354 35827.574 35813.163 90 35797.290 35770.019 48 35842.218 35827.152 35812.401 91 35796.253 35768.725 49 35842.016 35826.679 35811.647 92 35795.238 35767.418 50 35841.844 35826.222 35810.885 93 35794.161 35766.051 51 35841.662 35825.756 35810.101 94 35793.075 35764.683 52 35841.458 35825.225 35809.276 95 35792.023 35763.311 53 35841.297 35824.754 35808.491 96 35790.911 35761.892 54 35841.117 35824.232 35807.672 97 35789.782 35760.496 55 35840.868 35823.690 35806.858 98 35788.629 35759.015 56 35840.605 35823.192 35805.975 99 35787.474 35757.645 57 35840.352 35822.619 35805.191 100 35786.294 35756.166 58 35840.113 35822.069 35804.331 101 35785.070 35754.679 59 35839.857 35821.504 35803.446 102 35783.888 35753.198 0 - 0 Band

R (J) Q(J> P (J)

103 35782.608 35751.667 104 35781.372 35750.109 105 35780.058 106 35778.763 107 35777.440 108 35776.136 109 35774.753 110 35773.393 111 35771.936 112 35770.515 113 35769.058 114 35767.548 115 35766.051 116 35764.554 117 35763.011 118 35761.469 119 35759.801 120 35758.229 121 35756.561 122 35754.839 123 35753.151 124 35751.378 125 35749.662

No. lin e s = 204

—) 00 1 - 1 Band 1 - 1 Band

R(J) Q(J) P(J> R(J) Q(J) P(J>

36 35725.820 79 35702.545 35678.959 37 35725.046 80 35701.340 35677.486 38 35724.260 81 35700.127 35675.981 39 35723.462 82 35698.880 35674.458 40 35747.072 35722.618 83 35697.620 35672.941 41 35746.862 35721.782 84 35696.350 35671.448 42 35746.618 35720.953 85 35695.072 35669.865 43 35746.393 35733.091 35720.116 86 35693.765 35668.182 44 35746.128 35732.524 35719.299 87 35692.415 35666.549 45 35745.836 35731.924 88 35691.045 35664.889 46 35731.346 35717.453 89 35689.707 35663.252 47 35730.691 35716.569 90 35688.295 35661.546 48 35730.089 35715.632 91 35686.846 35659.856 49 35729.441 35714.667 92 35685.364 35658.163 50 35728.777 35713.753 93 35683.911 35656.375 51 35728.107 35712.789 94 35682.404 35654.658 52 35727.430 35711.760 95 35680.869 53 35726.747 35710.806 96 35679.292 54 35726.054 35709.733 97 35677.711 55 35725.281 35708.741 98 35676.032 56 35724.534 35707.641 99 35674.458 57 35723.758 35706.624 100 35672.781 58 35722.986 35705.558 101 35671.100 59 35722.202 35704.466 102 35669.394 60 35721.381 35703.358 103 35667.625 61 35720.559 35702.182 104 35665.815 62 35719.716 35701.067 105 35664.014 63 35718.853 35699.930 106 35662.146 64 35717.969 35698.737 107 35660.320 65 35717.052 35697.569 108 35658.408 66 35716.121 35696.350 109 35656.425 67 35715.220 35695.114 110 35654.523 68 35714.237 35693.874 69 35713.284 35692.601 No. lin e s = 132 70 35712.268 35691.329 71 35711.261 35689.990 72 35710.259 35688.749 73 35709.209 35687.379 74 35708.145 35685.976 75 35707.056 35684.677 76 35705.938 35683.228 77 35704.838 35681.840 -J 78 35703.674 35680.408 'O 2 -2 Band 2 -2 Band

RCJ) Q(J> P(J) RCJ) Q< J ) P(J>

19 35634.327 62 35602.956 20 35633.994 63 35620.580 35601.798 21 35633.639 64 35600.581 22 35633.259 65 35618.652 35599.343 23 35632.881 66 35617.704 35598.108 24 35632.495 67 35616.688 35596.764 25 35632.001 68 35615.655 35595.438 26 35631.597 35623.927 69 27 35631.116 70 35613.504 28 35630.652 35622.365 71 35612.370 29 35630.203 35621.594 72 35611.194 30 35629.690 35620.744 73 35610.028 31 35629.118 35619.953 74 35608.854 32 35628.559 35619.121 75 35607.663 33 35628.000 76 35606.305 34 35627.419 35617.375 77 35 35626.813 35616.408 78 35603.728 36 35626.174 35615.501 37 35625.559 35614.602 No. lin e s = 92 38 35624.893 35613.616 39 35624.193 35612.672 40 35623.565 35611.633 41 35622.838 35610.663 42 35622.071 35609.556 43 35621.311 44 35620.492 35607.464 45 35619.686 35606.394 46 35618.921 35605.249 47 35618.065 35604.118 48 35617.275 35602.956 49 35616.363 35601.906 50 35615.458 35600.643 51 35614.543 35599.465 52 35613.616 35598.232 53 35612.672 35596.979 54 35611.633 35595.701 55 35610.663 56 35609.611 57 35608.608 58 35607.502 59 35624.077 35606.437 60 35605.249 00 61 35622.365 35604.118 o 1 - 0 Band 1 - 0 Band

R(J) Q(J) P(J) R(J) Q(J) P(J)

40 36108.840 83 36067.222 36042.462 41 36108.244 84 36065.794 36040.775 42 36107.660 85 36064.384 36039.064 43 36107.035 86 36062.892 36037.328 44 36106.408 87 36061.406 36035.556 45 36105.723 88 36059.893 36033.773 46 36105.081 89 36058.314 36032.007 47 36104.333 90 36056.792 36030.120 48 36103.631 91 36055.236 36028.232 49 36102.897 92 36053.576 36026.368 50 36102.193 93 36051.921 36024.463 51 36101.392 94 36050.226 36022.528 52 36100.629 95 36048.568 53 36099.846 96 36046.841 54 36115.589 36099.025 97 36045.104 55 36115.033 36098.199 36081.640 98 36043.337 36014.413 56 36114.492 36097.356 36080.495 99 36041.538 57 36113.936 36096.492 36079.339 100 36039.705 58 36113.324 36095.603 36078.150 101 36037.849 59 36112.748 36094.709 36076.970 102 36035.958 60 36112.104 36093.794 36075.743 103 36034.039 61 36111.500 36092.867 36074.528 104 36032.101 62 36091.886 36073.272 105 36030.120 63 36090.923 36072.005 106 36028.054 64 36109.417 36089.933 36070.748 107 36025.972 65 36088.925 36069.428 108 36023.884 66 36107.982 36087.889 36068.093 109 36021.771 67 36086.848 36066.758 110 36019.605 68 36106.408 36085.776 36065.398 111 36017.415 69 36105.723 36084.693 36064.029 112 36015.171 70 36104.845 36062.686 71 36104.002 36082.441 36061.201 No. lin e s = 130 72 36103.087 36081.266 36059.735 73 36080.113 36058.314 74 36101.392 36078.934 36056.792 75 36077.735 36055.236 76 36076.505 36053.787 77 36098.504 36075.256 36052.238 78 36073.945 36050.663 79 36072.633 36049.054 80 36071.326 36047.463 81 36069.979 36045.831 00 82 36068.612 36044.149 2 - 1 Band 2 - 1 Band

R(J) Q(J> P(J) R(J) Q(J)P(J)

50 35986.182 93 35918.599 35891.853 51 35985.181 35970.153 94 35916.312 52 35984.152 35968.849 95 35913.977 35886.709 53 35983.105 96 35911.571 35884.056 54 35982.043 35966.157 97 35909.228 55 35980.942 35964.714 98 35906.720 56 35996.510 35979.814 35963.315 99 35904.227 57 35995.699 35978.682 35961.872 100 35901.668 58 35994.804 35977.517 35960.414 101 35899.081 59 35993.887 35976.329 35958.946 102 35896.534 60 35992.934 35975.120 35957.365 103 35893.750 61 35991.985 35973.801 35955.910 104 35890.999 62 35991.014 35972.501 35954.354 63 35989.976 35971.244 35952.744 No. lin e s = 123 64 35989.026 35969.907 35951.135 65 35987.904 35968.542 35949.533 66 35986.820 35967.183 35947.844 67 35985.708 35965.771 35946.147 68 35984.565 35964.347 35944.435 69 35983.388 35962.884 35942.703 70 35982.173 35961.414 35940.935 71 35980.942 35959.886 35939.144 72 35958.347 35937.301 73 35978.368 35956.771 74 35977.031 35955.170 35933.549 75 35975.687 35953.549 35931.667 76 35974.320 35951.891 35929.745 77 35972.854 35950.190 35927.775 78 35971.419 35948.474 35925.801 79 35969.907 35946.718 35923.706 80 35944.936 35921.696 81 35966.918 35943.092 35919.554 82 35965.349 35941.272 35917.482 83 35963.746 35939.417 35915.312 84 35937.460 35913.111 85 35910.896 86 35933.549 35908.632 87 35931.516 35906.364 88 35929.447 35904.020 89 35927.356 35901.668 90 35925.210 35899.251 91 35923.050 35896.833 oo 92 35920.852 35894.345 N) 3 - 2 Band

RCJ) Q(J) P(J)

14 35879.248 15 35878.855 16 35878.479 17 35878.057 18 35877.607 19 35877.115 20 35876.571 21 35876.086 22 35875.592 23 35875.025 24 25 35873.832 26 35873.136 27 35872.477 35864.652 28 35871.802 35863.710 29 35871.093 35862.695 30 35870.336 35861.643 31 35869.532 35860.606 32 35868.761 35859.486 33 35867.963 35858.370 34 35867.062 35857.235 35 35866.139 35856.063 36 35865.224 35854.864 37 35864.286 35853.647 38 35863.306 35852.380 39 35862.342 35851.085 40 35861.302 41 35860.215 35848.517 42 35859.153 35847.082 43 35858.042 35845.653 44 35856.919 35844.234 45 35855.709 46 35854.496 47 35853.278 48 35852.008 49 35850.702 50 35849.378 51 35848.007 52 35846.599 53 35845.184

No. lin e s = 56 u>00 2 - 0 Band 2 - 0 Band

R(J> Q(J) P(J) R(J) Q(J> PCJ)

31 36375.705 74 36325.824 36304.262 32 36375.066 75 36346.259 36324.057 36302.207 33 36374.425 76 36322.275 36300.150 34 36373.705 77 36343.207 36320.440 36298.137 35 36373.058 78 36341.588 36318.609 36295.920 36 79 36339.984 36316.743 37 36371.515 80 36338.338 36314.811 36291.538 38 36370.689 81 36336.668 36312.866 36289.324 39 36369.860 82 36334.853 36310.850 36287.008 40 36368.995 83 36333.207 36308.835 36284.769 41 36368.228 84 36331.351 36306.807 36282.441 42 36367.312 85 36329.607 36304.659 36280.071 43 36366.365 86 36302.545 36277.646 44 36365.444 87 36325.840 36300.378 36275.205 45 36364.538 88 36323.836 36298.137 36272.718 46 36363.556 89 36321.896 36295.920 36270.218 47 36362.550 90 36319.851 36293.660 36267.622 48 36361.524 91 36317.810 36291.310 36265.076 49 36360.408 92 36315.754 36288.941 36262.453 50 36359.366 93 36313.576 36286.535 51 36358.291 94 36311.329 36284.103 52 36357.187 95 36309.165 36281.571 53 36356.041 96 36279.057 54 36354.884 97 36276.482 55 36353.701 36337.447 98 36273.851 56 36352.512 36336.001 99 36271.174 57 36351.289 36334.449 100 36268.467 58 36350.021 36332.899 101 36265.641 59 36348.655 36331.351 102 36262.792 60 36347.336 103 36259.898 61 36345.998 36328.028 104 36257.047 62 36363.062 36344.648 36326.385 63 36361.953 36343.207 36324.669 No. lin e s = 138 64 36360.834 36341.738 36322.977 65 36359.656 36340.315 36321.219 66 36358.492 36338.822 36319.512 67 36357.187 36337.308 36317.647 68 36335.763 69 36354.643 36334.148 36314.035 70 36353.296 36332.545 36312.109 71 36351.954 36330.926 36310.166 72 36350.585 36329.262 36308.186 00 73 36349.174 36327.594 36306.334 3 - 1 Band

R(J) Q(J> P (J)

31 36241.490 32 36240.656 33 36239.765 34 36238.856 35 36237.871 36 36236.863 37 36235.836 38 36234.817 39 36233.768 40 36232.665 41 36231.581 42 36230.432 43 36229.227 36216.850 44 36227.978 36215.350 45 36213.834 46 36225.457 36212.299 47 36224.186 36210.707 48 36222.785 36209.096 49 36221.369 36207.411 50 36234.640 36219.991 36205.715 51 36233.429 36218.547 36203.950 52 36232.152 36217.064 53 36230.994 36215.541 36200.344 54 36229.712 36213.976 36198.549 55 36228.418 36212.379 36196.690 56 36227.062 36210.757 36194.807 57 36225.657 36209.096 36192.861 58 36224.186 36207.411 36190.871 59 36222.785 36205.715 36188.854 60 36221.239 36203.950 36186.834 61 36219.746 36202.102 36184.679 62 36218.148 36200.251 36182.575 63 36216.531 36180.449 64 36214.903 36178.257 65 36213.192 36194.452 36176.030 66 36211.439 36192.408 36173.761 67 36209.659 36190.366 36171.451 68 36207.788 36188.289 36169.108 69 36186.160

No. lin e s = 80

00 U l AlBr A - X for bromine-81

0 - 1 Band 0 - 1 Band

R(J) Q(J> P(J> R(J)Q(J) P(J)

29 35451.571 70 35466.099 35444.572 30 35460.266 35451.063 71 35465.825 35443.987 31 35460.069 35450.513 72 35465.508 35443.377 32 35459.862 35450.050 73 35465.187 35442.784 33 35459.582 74 35464.829 35442.140 34 35459.333 35448.906 75 35464.491 35441.499 35 35459.058 76 35440.846 36 35458.792 77 35463.793 35440.183 37 35458.504 78 35463.404 35439.542 38 35458.242 35446.655 79 35462.984 35438.832 39 35457.981 80 35462.528 35438.070 40 35457.641 35445.482 81 35462.119 35437.391 41 35457.408 35444.848 82 35436.636 42 35457.073 35444.270 83 35461.256 35435.934 43 35456.750 35443.598 84 35460.783 35435.178 44 35456.460 85 35434.359 45 35456.068 35442.329 86 35433.587 46 35455.730 35441.659 87 35432.799 47 35455.359 88 35431.982 48 35455.015 35440.388 89 35431.143 49 35454.583 35439.711 90 35430.314 50 35454.232 35438.972 91 35429.472 51 35453.846 35438.301 92 35428.575 52 35453.441 35437.561 93 35427.677 53 35453.060 35436.903 94 35426.726 54 35452.650 35436.146 95 35425.853 55 35452.183 35435.481 56 35451.772 35434.668 No. lin e s = 119 57 35451.329 35433.935 58 35450.854 35433.199 59 35450.400 60 35449.898 35431.686 61 35468.247 35449.430 35430.908 62 35468.030 35448.906 35430.109 63 35467.847 35448.424 35429.255 64 35467.616 35447.904 35428.456 65 35467.403 35447.369 35427.714 66 35467.190 35446.857 35426.795 67 35466.906 35446.277 35425.929 68 35466.684 35445.734 00 69 35466.353 35445.151 1 - 2 Band 1 - 2 Band

R(J) Q(J) PCJ) R(J) Q(J) P(J)

25 35370.331 68 35367.738 35347.223 26 35370.063 69 35346.355 27 35369.774 70 35345.508 28 35369.437 71 35344.623 29 35369.119 72 35343.700 30 35368.779 73 35342.794 31 35368.468 35359.092 74 35341.851 32 35368.114 35358.480 75 35340.919 33 35367.738 35357.825 76 35339.955 34 35367.367 35357.190 77 35338.957 35 35366.963 35356.486 78 35337.973 36 35366.603 35355.790 79 35336.897 37 35366.214 35355.125 80 35335.853 38 35365.759 35354.341 81 35334.798 39 35365.354 35353.641 82 35333.728 40 35364.897 35352.897 83 35332.585 41 35364.434 35352.114 42 35364.031 35351.414 No. lin e s = 103 43 35363.516 35350.646 44 35363.031 35349.830 45 35362.561 35348.997 46 35362.030 35348.203 47 35361.528 35347.394 48 35360.934 49 35360.402 50 35359.827 35344.903 51 35359.236 35343.999 52 35358.632 35343.111 53 35358.043 35342.224 54 35373.881 35357.387 35341.316 55 35373.581 35356.755 35340.342 56 35373.198 35356.143 35339.405 57 35355.438 35338.436 58 35372.473 35354.783 35337.454 59 35372.051 35354.090 35336.501 60 35371.586 35353.418 35335.479 61 35371.210 35352.685 35334.409 62 35370.737 35351.933 35333.454 63 35370.281 35351.179 64 35369.842 35350.402 65 35369.338 35349.634 66 35368.845 35348.813 00 67 35368.306 35348.026 -J 0 - 0 Band 0 - 0 Band

R(J)Q(J) P R(J) O(J) P(J>

9 35837.474 52 35841.618 35825.487 35809.594 10 35837.423 53 35841.458 35824.982 35808.820 11 35837.318 54 35841.242 35824.450 35808.008 12 35837.203 55 35841.013 35823.949 35807.180 13 35837.075 56 35840.793 35823.419 35806.356 14 35837.012 57 35840.537 35822.857 35805.501 15 35836.857 58 35840.262 35822.337 35804.668 16 35836.701 *9 35840.018 35821.760 35803.799 17 35836.563 60 35839.708 35821.166 35802.901 18 35836.411 61 35839.428 35820.572 35802.039 19 35836.246 62 35839.145 35819.975 35801.162 20 35836.073 63 35838.807 35819.366 35800.210 21 35835.895 64 35838.442 35818.761 35799.283 22 35835.704 65 35838.112 35818.110 35798.314 23 35835.514 66 35837.751 35817.452 35797.373 24 35835.293 67 35837.423 35816.767 35796.439 25 35835.063 68 35837.012 35816.117 35795.466 26 35834.850 69 35815.460 35794.463 27 35834.568 70 35814.713 35793.486 28 35834.340 71 35814.017 35792.492 29 35834.104 72 35813.276 35791.454 30 35833.814 35824.624 73 35812.524 35790.432 31 35833.533 35824.057 74 35811.794 35789.355 32 35833.272 35823.474 75 35811.014 35788.298 33 35832.974 35822.902 76 35810.230 35787.229 34 35832.650 35822.278 77 35809.436 35786.100 35 35832.337 35821.646 78 35808.618 35785.070 36 35832.017 35820.964 79 35807.772 35783.888 37 35831.667 35820.323 80 35806.972 35782.797 38 35831.337 35819.703 81 35806.109 35781.639 39 35830.994 35819.087 82 35805.191 35780.487 40 35830.632 35818.434 83 35804.331 35779.316 41 35830.259 35817.743 84 35803.446 35778.142 42 35829.877 35817.059 85 35802.521 35776.877 43 35829.461 35816.357 86 35801.640 35775.681 44 35829.080 35815.629 87 35800.694 35774.436 45 35828.675 35814.905 88 35799.705 35773.208 46 35828.242 35814.197 89 35798.728 35771.936 47 35842.412 35827.808 35813.470 90 35797.730 35770.646 48 35842.279 35827.374 35812.703 91 35796.722 35769.370 49 35842.130 35826.880 35811.948 92 35795.680 35768.052 50 35841.982 35826.453 35811.176 93 35794.651 35766.717 51 35841.801 35825.960 35810.393 94 35793.576 35765.324 0 - 0 Band

R(J)Q(J)P(J)

95 35792.492 35763.976 96 35791.410 35762.605 97 35790.323 35761.222 98 35789.165 35759.801 99 35787.983 35758.374 100 35786.828 35756.897 101 35785.635 35755.449 102 35784.451 35754.000 103 35783.181 35752.448 104 35781.950 35750.903 105 35780.693 106 35779.386 107 35778.092 108 35776.772 109 35775.371 110 35774.025 111 35772.608 112 35771.205 113 35769.752 114 35768.307 115 35766.777 116 35765.324 117 35763.758 118 35762.193 119 35760.592 120 35758.947 121 35757.359 122 35755.732 123 35754.000 124 35752.308 125 35750.551

No. lin e s = 214

\o00 1 - 1 Band 1 - 1 Band

R(J> Q(J) P(J> R(J)Q(J)P(J)

37 35725.649 80 35702.182 35678.470 38 35724.803 81 35700.989 35676.988 39 35724.023 82 35699.786 35675.483 40 35723.269 83 35698.514 35673.961 41 35722.431 84 35697.244 35672.477 42 35721.598 85 35695.985 35670.831 43 35746.967 35720.754 86 35694.708 35669.292 44 35746.667 35719.891 87 35693.370 35667.675 45 35746.332 35719.034 88 35691.961 35666.044 46 35746.041 35718.134 89 35690.616 35664.408 47 35745.742 35717.136 90 35689.223 35662.676 48 35716.317 91 35687.785 35661.033 49 35715.360 92 35686.366 50 35714.403 93 35684.867 35657.523 51 35713.444 94 35683.402 35655.788 52 35712.496 95 35681.889 53 35711.521 96 35680.350 54 35710.489 97 35678.784 55 35725.997 35709.471 98 35677.221 56 35725.197 35708.481 99 35675.535 57 35724.413 35707.360 100 35673.863 58 35723.664 35706.298 101 35672.243 59 35722.844 35705.223 102 35670.526 60 35722.038 35704.177 103 35668.780 61 35721.231 35703.001 104 35667.005 62 35720.372 35701.870 105 35665.231 63 35719.538 35700.740 106 35663.478 64 35718.642 35699.554 107 35661.546 65 35717.737 35698.369 108 35659.675 66 35716.830 35697.205 109 35657.794 67 35715.925 35695.946 110 35655.878 68 35715.001 35694.708 69 35714.031 35693.454 No. lin e s = 117 70 35713.041 71 35712.027 35690.884 72 35711.032 35689.621 73 35709.974 35688.256 74 35708.930 35686.971 75 35707.821 35685.573 76 35706.741 35684.207 77 35705.641 35682.836 78 35704.509 35681.363 VO 79 35703.358 35679.941 O 2 - 2 Band 2 - 2 Band

R(J) Q(J> P(J) RCJ) Q(J)

19 35635.314 62 35622.554 35604.204 20 35634.989 63 35621.669 35603.006 21 35634.606 64 35620.812 35601.798 22 65 35619.851 35600.534 23 35633.865 66 35618.882 35599.293 24 35633.420 67 35617.862 35598.033 25 35632.995 68 35616.849 35596.718 26 35632.600 69 35615.700 27 35632.094 35624.148 70 28 35631.648 35623.477 71 29 35631.159 72 35612.445 30 35630.652 73 35611.291 31 35630.127 74 35610.094 32 35629.608 75 35608.901 33 35628.998 76 35607.663 34 35628.444 77 35606.336 35 35627.827 78 35605.069 36 35627.231 35616.688 37 35626.601 35615.700 No. lin e s = 87 38 35625.917 35614.726 39 35625.210 35613.750 40 35624.594 35612.792 41 35623.835 35611.863 42 35623.124 35610.771 43 35622.322 35609.702 44 35621.594 35608.671 45 35620.812 35607.571 46 35620.021 35606.504 47 35619.183 35605.383 48 35618.344 35604.288 49 35617.441 35603.097 50 35616.595 35601.906 51 35615.655 35600.699 52 35614.687 35599.498 53 35613.750 35598.285 54 35612.792 35597.043 55 35611.863 35595.701 56 35610.771 57 35609.750 58 35608.671 59 35607.571 60 35606.503 VO 61 35623.477 35605.330 1 - 0 Band 1 - 0 Band

R(J)Q(J) P(J) R(J) Q(J) P(J)

39 36108.840 82 36068.352 36044.149 40 36108.244 83 36066.979 36042.462 41 36107.660 84 36065.571 36040.775 42 36107.035 85 36064.128 36039.064 43 36106.408 86 36062.686 36037.328 44 36105.723 87 36061.201 36035.556 45 36105.081 88 36059.735 36033.773 46 36104.439 89 36058.209 36032.007 47 36103.765 90 36056.633 36030.120 48 36103.087 91 36055.119 36028.232 49 36102.341 92 36053.491 36026.368 50 36101.624 93 36051.921 36024.463 51 36100.870 94 36050.226 36022.528 52 36100.113 95 36048.568 36020.569 53 36099.330 96 36046.841 36018.606 54 36098.504 97 36045.104 36016.617 55 36097.655 98 36043.337 36014.586 56 36096.826 36080.113 99 36041.538 57 36095.996 36078.935 100 36039.705 58 36095.084 36077.735 101 36037.849 59 36094.224 102 36035.958 60 36093.311 103 36034.039 61 36092.381 36074.152 104 36032.101 62 36110.238 36091.436 36072.928 105 36030.120 63 36090.470 36071.675 106 36028.232 64 36108.840 36089.505 36070.403 107 36026.120 65 36088.459 36069.100 108 36024.057 66 36107.445 36087.481 36067.795 109 36021.949 67 36106.693 36086.416 36066.453 110 36019.831 68 36105.902 36085.361 36065.108 111 36017.663 69 36084.287 36063.741 112 36015.488 70 36104.333 36083.179 36062.346 113 36013.213 71 36103.504 36082.072 36060.941 72 36102.614 36080.906 36059.478 No. lin e s = 131 73 36101.764 36079.763 36058.066 74 36100.870 36078.580 36056.633 75 36077.378 36055.119 76 36099.025 36076.146 36053.576 77 36097.982 36074.913 36052.034 78 36097.086 36073.636 36050.524 79 36095.996 36048.943 80 36095.084 36071.032 36047.365 VO 81 36094.007 36069.709 36045.753 N) 2 - 1 Band 2 - 1 Band

RCJ) Q(J) PC J) RCJ) Q(J) P (J)

41 35994.203 84 35937.930 35913.723 42 35993.394 85 35935.981 35911.570 43 35992.567 86 35934.019 35909.227 44 35991.713 87 35932.060 35907.020 45 35990.844 88 35929.997 35904.723 46 35989.976 89 35927.909 35902.363 47 35989.026 90 35925.801 35899.988 48 35988.106 91 35923.706 35897.594 49 35987.160 92 35921.480 50 35986.182 93 35919.248 35892.664 51 35985.181 94 35917.000 52 35984.152 95 35914.703 53 35983.105 96 35912.355 54 35982.043 97 35909.975 55 98 35907.540 56 35979.812 35963.432 99 35905.056 57 35978.682 35962.033 100 35902.542 58 35977.516 35960.545 101 35899.988 59 35976.328 35959.077 102 35897.360 60 35975.121 35957.598 103 35894.699 61 35973.902 35956.094 104 35891.978 62 35991.014 35972.641 35954.586 105 35889.258 63 35989.976 35952.980 106 35886.427 64 35989.026 35970.012 35951.426 65 35987.902 35968.707 35949.766 No. lin e s = 116 66 35986.820 35967.328 35948.109 67 35985.707 35965.941 35946.437 68 35984.566 35964.523 35944.762 69 35983.387 35963.074 70 35982.172 35961.609 35941.273 71 35980.941 35960.113 72 35979.812 35958.617 35937.680 73 35978.449 35957.020 35935.840 74 35977.164 35955.457 35934.020 75 35975.852 35953.820 35932.059 76 35974.488 35952.191 35930.176 77 35973.086 35950.516 35928.223 78 35948.820 35926.254 79 35970.153 35947.086 35924.223 80 35945.305 35922.207 81 35943.527 35920.090 82 35941.684 35918.027 83 35939.828 35915.883 u> 3 - 2 Band

R(J> Q(J> P(J)

17 35878.479 18 35878.057 19 35877.607 20 35877.115 21 35876.571 22 35876.086 23 35875.592 24 25 35874.318 26 35873.621 27 35872.921 35865.224 28 35872.302 35864.286 29 35871.553 35863.306 30 35870.813 35862.209 31 35870.045 35861.149 32 35869.247 35860.057 33 35859.039 34 35867.583 35857.783 35 35866.657 35856.643 36 35865.750 35855.468 37 35864.841 35854.306 38 35863.908 35852.999 39 35862.902 35851.684 40 35861.857 35850.424 41 35860.828 35849.099 42 35859.759 35847.747 43 35858.649 35846.388 44 35857.524 45 35856.376 46 35855.140 47 35853.940 48 35852.682 49 35851.394 50 35850.097 51 35848.716 52 35847.334 53 35845.935 54 35844.491

No. lin e s = 53

v© 2 - 0 Band 2 - 0 Band

RCJ) Q(J) PCJ) RCJ) QCJ) PCJ)

37 36370.182 80 36337.447 36314.036 36290.855 38 36369.306 81 36335.763 36312.109 36288.745 39 36368.601 82 36334.148 36310.166 36286.535 40 36367.759 83 36332.357 36308.186 41 36366.962 84 36330.579 36306.147 36281.908 42 36366.087 85 36328.765 36304.051 36279.561 43 36365.169 86 36326.917 36301.931 36277.183 44 36364.212 87 36325.002 36299.786 36274.776 45 36363.327 88 36323.226 36297.590 36272.315 46 36362.354 89 36321.219 36295.344 47 36361.385 90 36319.197 36293.113 36267.312 48 36360.408 91 36317.145 36290.855 36264.734 49 36359.366 92 36315.047 36288.477 36262.125 50 36358.291 93 36312.886 36286.092 51 36357.187 94 36310.856 36283.679 52 36356.041 95 36281.227 53 36354.884 96 36278.675 54 36353.701 97 36276.158 55 36352.512 98 36273.544 56 36351.289 99 36270.917 57 36333.419 100 36268.226 58 36331.905 101 36265.489 59 36347.582 36330.316 102 36262.792 60 36346.259 36328.765 103 36259.898 61 36363.062 36344.918 36327.100 104 36257.047 62 36361.953 36343.573 36325.432 63 36360.834 36342.196 36323.836 No. tin e s = 127 64 36359.656 36340.739 65 36358.540 36339.322 66 36337.842 36318.609 67 36336.342 36316.743 68 36334.853 36315.047 69 36333.207 36313.164 70 36331.616 36311.329 71 36350.937 36330.003 36309.385 72 36349.563 36328.376 36307.464 73 36348.171 36326.693 36305.509 74 36346.737 36325.002 36303.512 75 36345.268 36323.220 36301.545 76 36343.761 36321.466 36299.387 77 36342.196 36319.653 36297.354 78 36340.739 36317.810 36295.344 vO 79 36339.052 36315.938 36293.113 3 - 1 Band

RCJ) Q(J) PCJ)

32 36239.959 33 36239.074 34 36238.187 35 36237.273 36 36236.269 37 36235.235 38 36234.177 39 36233.198 40 36232.152 41 36230.994 42 36229.822 36217.851 43 36228.675 36216.306 44 36227.485 36214.903 45 36239.359 36226.249 36213.374 46 36238.363 36224.962 36211.859 47 36237.410 36223.687 36210.297 48 36236.269 36222.359 36208.786 49 36235.236 36220.956 36207.100 50 36234.177 36219.545 36205.392 51 36218.145 36203.654 52 36231.581 36216.639 36201.911 53 36230.433 36215.167 36200.061 54 36229.227 36213.630 36198.275 55 36227.978 36212.056 36196.418 56 36226.693 36210.431 36194.452 57 36225.247 36208.786 36192.408 58 36223.868 36207.100 59 36205.392 36188.770 60 36203.654 36186.830 61 36219.369 36201.911 36184.680 62 36217.851 36200.061 36182.575 63 36198.275 36180.449 64 36214.610 36196.291 36178.257 65 36212.940 36194.453 36176.030 66 36211.224 36192.412 36173.761 67 36209.490 36190.368 36171.451 68 36188.290 36169.113 69 36186.159 36166.727 70 36183.994 36164.286 71 36181.777 36161.816 72 36179.512 36159.350 73 36177.210 36156.759 VO No. lin e s = 92 Ov Appendix C

VIB-DIST.BAS

A program to find vibrational population distributions from vibrational energy level data.

97 98

The files included in this appendix include:

VIB-DIST.BAS - QuickBASIC program to calculate vibrational partition function and populations for Maxwell-Boltzman distribution

POPULATE - Calculated populations for all vibrational levels less than lOkT for T = 298 K.

The program VIB-DIST.BAS can calculate energy levels. However, this takes a great deal of time for a molecule with 14 vibrational modes (something on the order of 5.5 to 8 hours on a 6 MHz IBM PC/AT.) So after it has done this once, it is preferable to read the energy levels from a disk file. This file is called ELEVELS. The partition function will be calculated for a temperature specified in the subroutine Temperature. So long as this temperature is less than the one used to calculate the energy levels listed in ELEVELS, there is no need to recalculate these energy levels. The subroutine for calculating energy levels is remarked out in the source code provided. I find it just as easy to run the program from the QuickBASIC environment as to compile it - especially if several temperatures are to be calculated. VIB-DIST.BAS

DEFINT I-J, V DECLARE FUNCTION degen (nmodes, v(), d()) DECLARE FUNCTION Energy (nmodes, omega(), v(), d()) DIM E(1000), Ievel$(1000), deg(lOOO), pop(lOOO)

VIB-DIST.BAS Patrick Fleming 1991

This program calculates the vibrational energy levels of a molecule which lie below lOkT. This inforamtion, along with the degenerqcies of the levels, is used to calculate a vibrational partition function. Using the partition function, thermal vibrational populations can be calculated using the Maxwell-Boltzman model.

NOTE: Since calculating the enrgy leels is very time consuming (about 5-8 hours on a 6MHz AT class machine for cyanuric fluoride) the energy levels are written to a file named ELEVELS.VIB. Once this file has been formed (at it should be calculated at the highest temperature) it can be read by the program from the disk rather than calvulating the data each time. To do this, remark out the GOSUB statement in the MainProgram for CalculateEnergyLevels and instead use GOSUB ReadEnergyLevels.

Variables:

nmodes - number of vibrational modes of the molecule omega(i) - frequency of the i-th mode v(i) - vibrational quanta in the i-th mode d(i) - degeneracy of the i-th mode T - tempreature (Defined in subroutine Temperature) kT - value of kT at the temperature T (in cm-1) nelevels - number of energy levels wiht energy less than lOkT E(j) - Energy of the j-th level (in cm-1) level$(j) - vibrational quantum numbers (in a string) of j-th level deg(j) - degeneracy of the j-th level Qvib - vibrational partition function 100

’ pop(j) - percent population of j-th level 9 f

MainProgram: CLS GOSUB DefineMolecularParameters GOSUB Temperature GOSUB ReadEnergyLevels ’GOSUB CalculateEnergyLevels GOSUB CalculatePartitionFunction GOSUB CalculatePopulations GOSUB SortByPopulation GOSUB WriteResultsToAFile END

DefineMolecularParameters:

Define each vibrational mode here. These are for cyanuric fluoride.

Values taken from Griffiths and Irish, Can. J. Chem., 42, 690 (1964) Long, Chau and Gravenor, Trans. Faraday Soc., 58, 2316 (1962)

nmodes = 14 DIM omega(nmodes), d(nmodes), v(nmodes) om ega(l) = 1496: d (l) = 1: ’ A l’: sym C-F str omega(2) = 999: d(2) = 1: ’ A l’: Ring Breathing (C,N out of phase) omega(3) = 642: d(3) = 1: ’ A l’: Ring Breathing (all atoms in phase) omega(4) = 1579: d(4) = 1: ’ A2’: C atom twist against N omega(5) = 713: d(5) = 1: ’ A2’: F atom twist against ring omega(6) = 1617: d(6) = 2: ’ E’ : Ring Stretching omega(7) = 1424: d(7) = 2: ’ E’ : Ring Stretching omega(8) = 1087: d(8) = 2: ’ E’ : C-F stretching omega(9) = 578: d(9) = 2: ’ E’ : Ring angle bend omega(lO) = 379: d(10) = 2 ’ E’ : C-F Rocking omega(ll) = 817: d(ll) = 1 ’ A2": Out of plane Ring mode (C, N out of phase) omega(12) = 436: d(12) = 1 ’ A : C-F wagging (F in phase) omega(13) = 743: d(13) = 2 ’ E" : C-F wagging omega(14) = 226: d(14) = 2 ’ E" : Out of plane ring mode RETURN

Temperature: T = 298 koverhc! = 207.22 / 298.15 kT! = koverhc! * T: ’ kT is now in cm-1 RETURN 101

CalculateEnergy Levels: OPEN "elevels.vib" FO R OUTPU T AS #1 FOR i = 1 TO nmodes v(i) = 0 NEXT i E0 = Energy(nmodes, omegaQ, v(), d()) j = -1 FO R v l = 0 TO 1 v(l) = vl FOR v2 = 0 TO 1 v(2) = v2 FO R v3 = 0 TO 2 v(3) = v3 FOR v4 = 0 TO 1 v(4) = v4 FO R v5 = 0 TO 2 v(5) = v5 FOR v6 = 0 TO 1 v(6) = v6 FOR v7 = 0 TO 1 v(7) = v7 FOR v8 = 0 TO 1 v(8) = v8 FOR v9 = 0 TO 2 v(9) = v9 FOR vlO = 0 TO 4 v(10) = vlO FOR vll = OTO 2 v(l 1) = v ll FO R vl2 = 0 TO 4 v(12) = vl2 FOR vl3 = 0 TO 2 v(13) = vl3 FO R vl4 = 0 TO 9 v(14) = vl4 IF Energy(nmodes, omega(), v(), d()) - E0 < 10 * kT! THEN j = j + 1 E(j) = Energy(nmodes, omega(), v(), d()) - E0 deg(j) = 1 FOR i = 1 TO nmodes level$ (j) = level$G) + STR$(v(i)) IF v(i) < > 0 AND d(i) < > 1 THEN degG) = degen(nmodes, v(), d()) NEXT i PRINT #1, USING " #### j; PRINT #1, level$G);" PRINT #1, USING " #### ###"; EG); degG) PRINT USING " #### j; 102

PRINT level$(j); " PRINT USING " #### ###"; E(j); degG) END IF NEXT vl4, vl3, vl2, v ll, vlO, v9, v8, v7, v6, v5, v4, v3, v2, vl nelevels = j CLOSE #1 RETURN

CalculatePartitionFunction: Qvib = 0 FOR j = 0 TO nelevels Qvib = Qvib + deg(j) * EXP(-E(j) / kT) NEXT j RETURN

CalculatePopulations: FOR j = 0 TO nelevels popG) = ((degG) * EXP(-EG) / kT)) / Qvib) * 100 sum = sum + pop(j): ’just to check that the total over pop(j) = 100% NEXT j PRINT : PRINT "Sum of all populations = sum; RETURN

SortByPopulation: flag$ = "up" WHILE flag$ = "up" flag$ = "down" FOR j = 0 TO nelevels - 1 IF pop(j) < pop(j + 1) THEN SWAP popG), popG + 1) SWAP EG), E(j + 1) SWAP level$G), level$G + 1) SWAP degG), degG + 1) flag$ = "up" END IF NEXT j WEND RETURN

WriteResultsToAFile: OPEN "populate" FOR OUTPUT AS #1 PRINT #1, "Calculation of relative populations of vibrational energy levels" PRINT #1, "for cyanuric flouride at T; "Kelvin." PRINT #1, "" PRINT #1, " vib. quantum numbers Energy Degeneracy %Population" FOR j = 0 TO nelevels PRINT #1, USING " #### "; j; PRINT #1, level$G); " "; 103

PRINT #1, USING " ### # ###"; E(j); degG); PRINT #1, USING " ###.##"; popG) NEXT j CLOSE #1 RETURN

ReadEnergy Levels: OPEN "elevels.vib" FOR INPUT AS #1 j = 0 DO INPUT #1, x, v( 1), v(2), v(3), v(4), v(5), v(6), v(7), v(8), v(9), v(10), v(ll), v(12), v(13), v(14), EG), degG) FO R i = 1 TO 14 level$ G) = level$ G) + STR$(v(i)) NEXT i PRINT USING " #### j; PRINT levelSG);" PRINT USING " #### ###"; EG); degG) j = j + 1 LOOP UNTIL EOF(l) = -1 nelevels = j - 1 CLOSE #1 RETURN

FUNCTION degen (nmodes, v(), d()) degeneracy = 1 FOR i = 1 TO nmodes IF v(i) < > 0 AND d(i) < > 1 THEN IF v(i) = 1 THEN degeneracy = degeneracy * d(i) ELSE degeneracy = degeneracy * (d(i) * (v(i) - 1) + 1) END IF NEXT i degen = degeneracy END FUNCTION

FUNCTION Energy (nmodes, omega(), v(), d()) E = 0 FOR i = 1 TO nmodes E = E + omega(i) * (v(i) + d(i) / 2) NEXT i Energy = E END FUNCTION 104

These pages the caclulated populations for all vibrational levels of 1,3,5-trifluoro-sym- triazine determined with the program VIB-DIST.BAS.

Calculation of relative populations of vibrational energy levels for cyanuric flouride at 298 Kelvin. All energies are expressed in cm'1. The vibrational quantum numbers are listed in order (v„ v2, .. ., v14). vibrational quantum numbers Energy Peg. % Occupation 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 9 .8 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 22 6 2 1 3 .3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 2 452 3 6 .7 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 379 2 6 . 38 0 0 0 0 0 0 0 0 0 1 0 0 0 1 6 05 4 4 .2 9 0 0 0 0 0 0 0 0 0 0 0 0 0 3 678 5 3 .7 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0 578 2 2 .4 4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 3 6 1 2 .4 2 0 0 0 0 0 0 0 0 0 1 0 0 0 2 8 3 1 6 2 . 16 0 0 0 0 0 0 0 0 0 0 0 0 0 4 904 7 1 .7 7 0 0 0 0 0 0 0 0 1 0 0 0 0 1 804 4 1 . 64 0 0 0 0 0 0 0 0 0 0 0 1 0 1 662 2 1 . 63 0 0 0 0 0 0 0 0 0 2 0 0 0 0 758 3 1 . 54 0 0 0 0 0 0 0 0 0 1 0 0 0 3 1 0 5 7 10 1 .2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 743 2 1 .1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 984 6 1 . 03 0 0 1 0 0 0 0 0 0 0 0 0 0 0 642 1 0 .9 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 3 0 6 0 .8 3 0 0 0 0 0 0 0 0 0 0 0 1 0 2 888 3 0 .8 2 0 0 0 0 0 0 0 0 1 1 0 0 0 0 957 4 0 .7 8 0 0 0 0 0 0 0 0 0 1 0 1 0 0 8 1 5 2 0 .7 8 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 1 3 0 9 0 .7 6 0 0 0 0 0 0 0 0 0 0 0 0 1 1 969 4 0 .7 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 713 1 0 .6 4 0 0 1 0 0 0 0 0 0 0 0 0 0 1 868 2 0 . 60 0 0 0 0 0 0 0 0 0 1 0 0 0 4 1283 14 0 .5 7 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1183 8 0 .5 3 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 4 1 4 0 .5 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 1 2 1 0 9 0 .5 2 0 0 0 0 0 0 0 0 1 0 0 0 0 3 1 2 5 6 10 0 .4 6 0 0 0 0 0 0 0 0 0 0 0 1 0 3 1114 5 0 .4 6 0 0 0 0 1 0 0 0 0 0 0 0 0 1 939 2 0 .4 3 0 0 0 0 0 0 0 0030000 1137 5 0 .4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 817 1 0 . 39 0 0 0 0 0 0 0 0000012 1195 6 0 . 37 0 0 0 0 0 0 00010010 1122 4 0 .3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1 3 5 6 11 0 .3 1 0 0 1 0 0 0 00000002 1094 3 0 .3 0 0 0 0 0 0 0 0 0100100 1014 2 0 .3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 872 1 0 .3 0 0 0 0 0 0 0 0 0 0 2 0 0 0 3 1 4 3 6 15 0 .2 9 105

quantum numbers Energy Peg. % Occupation 0 0 0 0 1 0 0 0 0 1 0 2 1 2 0 .2 9 0 0 0 0 3 0 0 0 1 1363 10 0 .2 8 0 0 0 1 1 0 0 0 2 1 4 0 9 12 0 .2 7 0 0 0 0 1 0 1 0 2 1267 6 0 .2 6 0 0 0 0 0 1 0 0 1 1043 2 0 .2 6 0 0 0 0 1 0 0 0 5 1509 18 0 .2 5 0 0 0 0 1 0 0 1 1 1 3 4 8 8 0 .2 4 0 0 0 2 0 0 0 0 0 1 1 5 6 3 0 .2 2 0 0 0 1 0 0 0 0 4 1482 14 0 .2 2 0 0 0 0 0 0 1 0 4 1 3 4 0 7 0 .2 2 0 0 0 0 0 0 0 0 2 1 1 6 5 3 0 .2 2 0 0 1 0 0 0 0 0 0 1 0 8 7 2 0 .2 1 0 0 0 0 0 0 0 1 3 1 4 2 1 10 0 .2 1 0 0 0 0 1 0 0 0 0 1092 2 0 .2 0 0 0 0 1 0 0 1 0 1 1 2 4 0 4 0 .2 0 0 0 0 0 0 0 2 0 1 1 0 9 8 2 0 .2 0 0 0 0 0 1 0 0 0 1 1247 4 0 .1 9 0 0 0 1 2 0 0 0 0 1 3 3 6 6 0 .1 9 0 0 0 0 2 0 1 0 0 1194 3 0 .1 9 0 0 0 0 0 0 0 0 3 1 3 2 0 5 0 .1 7 0 0 0 0 0 0 0 0 0 999 1 0 .1 6 0 0 0 2 0 0 0 0 1 1382 6 0 .1 5 0 0 0 1 1 0 0 0 3 1 6 3 5 20 0 .1 5 0 0 0 0 1 0 1 0 3 1493 10 0 . 15 0 0 1 0 0 0 0 0 1 1313 4 0 .1 4 0 0 0 0 3 0 0 0 2 1 5 8 9 15 0 . 14 0 0 0 0 1 0 0 0 1 1318 4 0 .1 4 0 0 0 0 2 0 0 0 4 1662 21 0 .1 4 0 0 0 1 0 0 0 1 0 1 3 2 1 4 0 .1 4 0 0 0 0 0 0 1 1 0 1179 2 0 .1 3 0 0 0 0 0 1 0 0 2 1 2 6 9 3 0 .1 3 0 0 0 1 2 0 0 0 1 1562 12 0 . 13 0 0 0 0 2 0 1 0 1 1 4 2 0 6 0 . 13 0 0 0 0 0 0 0 0 7 1582 13 0 .1 2 0 0 0 0 1 1 0 0 .0 1 1 9 6 2 0 .1 2 0 0 0 0 0 0 0 0 3 1 3 9 1 5 0 .1 2 0 0 0 0 1 0 0 1 2 1574 12 0 .1 2 0 0 0 1 0 0 0 0 0 1 2 2 0 2 0 .1 1 0 0 0 0 0 0 1 0 0 1078 1 0 .1 1 0 0 0 0 0 0 0 0 1 1 2 2 5 2 0 .1 1 0 0 0 0 1 0 0 0 6 1 7 3 5 22 0 . 10 0 0 0 1 0 0 1 0 2 1 4 6 6 6 0 . 10 0 0 0 0 0 0 2 0 2 1324 3 0 .1 0 0 0 0 0 0 0 0 1 4 1647 14 0 .1 0 0 0 0 0 1 0 0 0 2 1473 6 0 .1 0 0 0 0 1 1 0 1 0 0 1393 4 0 .1 0 0 0 0 0 1 0 2 0 0 1 2 5 1 2 0 . 09 0 0 0 1 0 0 0 0 5 1708 18 0 . 09 0 0 0 0 0 0 1 0 5 1 5 6 6 9 0 . 09 0 0 0 0 4 0 0 0 0 1 5 1 6 7 0 . 09 106

quantum numbers Energy Peg. % Occupation 0 0 0 1 0 0 0 1 1 1547 8 0 .0 9 0 0 0 0 0 0 1 1 1 1 4 0 5 4 0 .0 9 0 0 0 0 2 0 0 1 0 1 5 0 1 6 0 .0 8 0 0 0 0 1 1 0 0 1 1422 4 0 . 08 0 0 0 0 0 0 0 0 4 1 5 4 6 7 0 . 08 0 0 0 1 0 0 0 0 0 1 2 9 1 2 0 . 08 0 0 0 0 3 0 0 0 3 1 8 1 5 25 0 .0 8 0 0 0 0 0 0 1 0 0 1 1 4 9 1 0 . 08 0 0 0 2 0 0 0 0 2 1 6 0 8 9 0 . 08 0 0 0 1 0 0 0 0 1 1 4 4 6 4 0 . 07 0 0 0 0 0 0 1 0 1 1304 2 0 . 07 0 0 0 0 0 1 0 0 3 1 4 9 5 5 0 . 07 0 0 0 2 1 0 0 0 0 1 5 3 5 6 0 . 07 0 0 1 0 0 0 0 0 2 1 5 3 9 6 0 . 07 0 0 0 1 1 0 0 0 4 1 8 6 1 28 0 . 07 0 0 0 0 1 0 1 0 4 1 7 1 9 14 0 . 07 0 0 0 0 2 0 0 0 0 1 4 0 0 3 0 .0 7 0 0 0 0 1 0 0 0 2 1544 6 0 . 07 0 0 1 0 1 0 0 0 0 1 4 6 6 4 0 . 07 0 0 0 0 1 0 0 1 3 1 8 0 0 20 0 . 07 0 0 0 1 1 0 1 0 1 1 6 1 9 8 0 . 06 0 0 0 1 2 0 0 0 2 1788 18 0 . 06 0 0 0 0 1 0 2 0 1 1 4 7 7 4 0 . 06 0 0 0 0 2 0 1 0 2 1 6 4 6 9 0 . 06 0 0 0 0 4 0 0 0 1 1742 14 0 . 06 0 0 0 0 2 0 0 0 5 1888 27 0 . 06 0 0 0 0 2 0 0 1 1 1727 12 0 . 06 0 0 0 0 0 0 0 0 4 1617 7 0 . 06 0 0 0 1 0 0 1 0 3 1692 10 0 . 06 0 0 0 0 0 0 2 0 3 1 5 5 0 5 0 . 06 0 0 0 0 1 0 0 0 3 1699 10 0 . 05 0 0 0 0 0 0 0 0 2 1 4 5 1 3 0 . 05 0 0 0 1 0 0 0 0 1 1 517 4 0 . 05 0 0 0 0 0 0 1 0 1 1 3 7 5 2 0 . 05 0 0 0 0 1 0 0 0 0 1 3 7 8 2 0 . 05 0 0 0 1 3 0 0 0 0 1 7 1 5 10 0 . 05 0 0 0 0 3 0 1 0 0 1573 5 0 . 05 0 0 0 0 0 0 0 1 0 1 3 8 5 2 0 . 05 0 0 0 0 2 0 0 0 0 1 4 7 1 3 0 . 05 0 0 0 2 1 0 0 0 1 1 7 6 1 12 0 . 05 0 0 0 0 0 0 0 0 8 1 8 0 8 15 0 . 05 0 0 0 1 0 1 0 0 0 1 3 9 5 2 0 . 05 0 0 0 0 0 1 1 0 0 1253 1 0 . 05 0 0 0 0 2 0 0 0 1 1 6 2 6 6 0 . 05 0 0 0 1 0 0 0 1 2 1773 12 0 . 05 0 0 0 0 0 0 0 2 0 1 4 8 6 3 0 . 05 0 0 0 0 0 0 1 1 2 1 6 3 1 6 0 . 05 0 0 1 0 1 0 0 0 1 1692 8 0 . 05 0 0 0 1 1 0 0 1 0 1 7 0 0 8 0 . 04 0 0 0 0 1 0 1 1 0 1558 4 0 . 04 107

Q u an tu m numbers Enerav D eq . % O cc 0 0 0 2 0 0 0 0 3 1 8 3 4 15 0 . 04 0 0 0 0 0 0 0 1 5 1873 18 0 . 04 0 0 0 0 1 1 0 0 2 1 6 4 8 6 0 . 04 0 1 0 0 0 0 0 0 0 1 4 2 4 2 0.04 0 0 0 0 0 0 0 0 0 1 284 1 0.04 0 0 0 0 1 0 0 0 7 1 9 6 1 26 0.04 0 0 1 0 0 0 0 0 3 1 7 6 5 10 0.04 0 0 0 0 1 0 0 0 3 1 7 7 0 10 0.04 0 0 0 1 0 0 0 0 6 1 934 22 0.04 0 0 0 0 0 0 1 0 6 1 7 9 2 11 0.04 0 0 0 1 0 0 0 0 2 1 672 6 0.04 0 0 0 0 0 0 1 0 2 1 5 3 0 3 0.04 0 0 0 0 3 0 0 0 4 2041 35 0.04 0 0 0 1 0 0 2 0 0 1 4 5 0 2 0.04 0 0 0 0 0 0 3 0 0 1 3 0 8 1 0 . 04 0 0 0 1 2 0 0 0 3 2 0 1 4 30 0.04 0 0 0 0 2 0 1 0 3 1 872 15 0 . 04 0 0 0 1 1 0 0 0 0 1 5 9 9 4 0 . 04 0 0 0 0 0 0 0 1 0 1 4 5 6 2 0 . 04 0 0 0 0 1 0 1 0 0 1457 2 0 . 04 0 0 0 0 1 0 0 0 1 1604 4 0 . 03 0 0 0 0 0 0 0 0 5 1772 9 0.03 0 0 0 0 0 1 0 0 4 1 7 2 1 7 0.03 0 0 0 1 3 0 0 0 1 1 9 4 1 20 0.03 0 0 0 0 3 0 1 0 1 1 7 9 9 10 0 . 03 0 0 0 0 0 0 0 1 1 1 6 1 1 4 0.03 0 0 0 0 2 0 0 0 1 1697 6 0 . 03 0 0 0 1 1 0 1 0 2 1 8 4 5 12 0.03 0 0 0 0 1 0 2 0 2 1703 6 0.03 0 0 0 1 0 1 0 0 1 1 6 2 1 4 0.03 0 0 0 0 0 1 1 0 1 1 4 7 9 2 0.03 0 0 0 0 1 0 0 1 4 2026 28 0.03 0 0 0 0 4 0 0 0 2 1 9 6 8 21 0.03 0 0 0 0 0 0 0 2 1 1712 6 0.03 0 0 0 0 0 0 0 0 3 1 6 7 7 5 0.03 0 0 0 0 1 0 1 0 5 1 9 4 5 18 0.03 0 0 0 0 2 1 0 0 0 1 5 7 5 3 0.03 0 0 0 1 1 0 0 1 1 1 9 2 6 16 0.03 0 0 0 0 1 0 1 1 1 1784 8 0.03 0 0 0 0 2 0 0 1 2 1953 18 0.03 0 0 0 0 0 0 0 0 0 1 3 5 5 1 0.03 0 1 0 0 0 0 0 0 1 1 6 5 0 4 0.03 0 0 0 2 0 0 1 0 0 1592 3 0.03 0 0 0 0 0 0 0 0 1 1 5 1 0 2 0.03 0 0 0 1 0 0 1 0 4 1918 14 0 . 03 0 0 0 1 0 0 0 0 2 1743 6 0.03 0 0 0 0 0 0 2 0 4 1 7 7 6 7 0.03 0 0 0 0 0 0 1 0 2 1 6 0 1 3 0 . 03 0 0 1 1 0 0 0 0 0 1 6 6 5 4 0.03 0 0 0 J 1 0 0 0 4 1 9 2 5 14 0.03 quantum numbers Energy Peg. % Occupation 0 0 0 1 0 0 0 1 3 1 9 9 9 20 0.03 0 0 1 0 0 0 1 0 0 1523 2 0.03 0 0 0 0 0 0 1 1 3 1857 10 0.03 0 0 0 1 1 0 0 0 0 1 6 7 0 4 0.03 0 0 0 0 1 0 1 0 0 1 5 2 8 2 0.02 0 0 0 0 0 0 0 0 5 1 843 9 0.02 0 0 0 2 1 0 0 0 2 1 9 8 7 18 0.02 0 0 0 1 0 0 2 0 1 1 6 7 6 4 0.02 0 0 0 0 0 0 3 0 1 1 534 2 0.02 0 0 0 1 1 0 0 0 1 1 8 2 5 8 0.02 0 0 0 0 0 0 0 1 1 1 682 4 0.02 0 0 0 0 1 0 1 0 1 1 683 4 0.02 0 0 0 0 2 0 0 0 2 1 852 9 0.02 0 0 0 0 1 1 0 0 3 1 874 10 0 . 02 0 0 0 1 2 0 1 0 0 1 772 6 0.02 0 0 0 0 2 0 2 0 0 1 6 3 0 3 0 . 02 0 0 0 0 3 0 0 1 0 1 8 8 0 10 0.02 0 0 1 0 1 0 0 0 2 1 918 12 0.02 0 0 0 0 0 1 0 1 0 1 5 6 0 2 0.02 0 0 0 1 0 0 0 0 3 1 8 9 8 10 0 . 02 0 0 0 0 0 0 1 0 3 1 7 5 6 5 0 . 02 0 0 0 0 0 0 0 0 0 1426 1 0.02 0 0 0 2 0 0 0 0 4 2060 21 0.02 0 0 0 0 2 1 0 0 1 1 8 0 1 6 0 . 02 0 0 0 1 0 0 0 0 0 1 577 2 0.02 0 0 0 0 0 0 1 0 0 1 4 3 5 1 0.02 0 0 0 0 0 0 0 0 1 1 5 8 1 2 0 . 02 0 0 1 0 0 0 0 0 4 1 9 9 1 14 0.02 0 0 0 0 3 0 0 0 0 1 7 7 9 5 0.02 0 0 0 2 0 0 1 0 1 1818 6 0.02 0 0 0 0 0 0 0 0 9 2034 17 0.02 0 0 0 0 1 0 0 0 4 1 9 9 6 14 0.02 0 0 0 1 1 0 1 0 3 2071 20 0.02 0 0 0 0 1 0 2 0 3 1929 10 0.02 0 0 0 0 1 0 0 0 2 1 8 3 0 6 0.02 0 0 0 2 2 0 0 0 0 1914 9 0.02 0 0 0 0 0 1 0 0 0 1459 1 0.02 0 0 1 1 0 0 0 0 1 1 8 9 1 8 0 . 02 0 0 1 0 0 0 1 0 1 1 7 4 9 4 0.02 0 0 0 0 3 0 1 0 2 2025 15 0.02 0 0 0 1 1 0 0 0 1 1 8 9 6 8 0.02 0 0 0 0 0 0 0 1 2 1837 6 0.02 0 0 0 0 1 0 1 0 1 1754 4 0.02 0 0 0 0 2 0 0 0 2 1923 9 0 . 02 0 0 0 1 0 0 1 1 0 1757 4 0 . 02 0 0 0 0 0 0 2 1 0 1 6 1 5 2 0 . 02 1 0 0 0 0 0 0 0 0 1617 2 0.02 0 0 1 0 2 0 0 0 0 1 8 4 5 6 0 . 02 0 0 0 1 0 1 0 0 2 1847 6 0.02 0 0 0 0 1 0 0 1 0 1764 4 0 . 02 o O O o O O O O o o o o o o o o o o o o o o o o o o ooOOOOoooool->OooooooOOo o o Lj.< o O O o o O O o o o o o o o o o o o o o H* oooHooHOoooooo t-> oOOooooooOoooo O' nw o M o o o O O o o o o o H I-*o o H o o o O H o to o H o O o HH to o o H* o o O o o o o o o o o o o o o itrf o O o o o O O o o o o o O o o o o o o o O O o ooOoooOOooooo o O o o o o o o o o o o o o H- Clrt o o to H o O o o o O o H o o o o O o I-1o o HOO o o o O H o o O O o o o o o O o o M o o o o o o o o rtl3 o O o o O o O o o o o o o ooooooOOoooooooOOooooooOoooOooo o o o o o 1-1 o O o O o O o O o o o o o o o o o o o o OOooooooI-1OOoot-1oooOoooOooo o o o o o Q 1-if- o O M O o o o O o o H oooooooooOOoo o o o o o O O o o o o o o O o o o O o o o o o o o o 0) H1J HOOO o l->o O o o o t-1o o o o H> o H> o OO to ooooH->oOI-1ooooooOooo oo H o o o o ft to H* to O o o 4v l->o M o o H o o M o o o to CO o h->o to CO O H>O O o o o o o o O M (->o O o l->M o to to o o 3 o O O o o o O O o o o o I-1o o o O o o l->O o o o o o o O O O oo o o o o I-1O o o o O H* I-1o o o o l-> 3 o O O o to h-1h-“O to CO o to o I-1o I-1O CO to oooooH>ooOO to h->o o o o o o o K-*o o o t—>o M to l-»o I—* 3 J-r"C3 M t->O o l-> O I-*o o 1-*o o o I-*t->o o o o o o M o o o o o O o o o o o o o M o M to o o o o o o o O to o (D nw O (-*H* M 1—*l->O O CJ1o o o M to to 4v. to to to o o M o o I-1CO o M O o o to l-> to OV 4* I-* o to o CO CO Ul o o ■O I-1t-> to to 01 to H> to H H t-> H H to H H» H H (-*I-1to to HHH to t->H H to HHHH HHHHHH HH to H> H H l-» H H to H H H I-* W o VO o 03 CD VO VO 00 o ov 00 03 ov VO VO o o -0 vo Ul O 03 ov OV o 03 00 03 U1 OV 'J ov 00 vo VO 4v. O 03 00 VO VO OV -O o 00 VO VO 3 -J VO ■o 4* 4v 00 Ul CO o 03 CO to 00 o o 00 Ul OV o CO Ul o VO ov ov 'J Ul O O H U1 CO Ul 'J vo O 00 CO H OV to 0V 4v CO H Ul VO CO o (D vo O I-1CO CO to Ul to -o o VO Ul VO 03 CO l->o to o ~0 Ul vo CO I-100 o CO CO 4v Ov ov to ov oo CO OV OV O Ul 'J VO —J to 4>.00 OV 00 00 Ul t-l Q <

a M H I-1l-> 1—* I-1 M I-* I-* I-1 l-> to to CO to 4v 4* 03 4* VO to 4^ 4» to OV ov 4V. to CO OV H CO o OV to to

<#> o o o o O O o o O o O O o o O O O O O O OOOO O O OOOoOOOOOOO o OO O O O O o o o o o o ••••••••••••••• •• • ■ • • • • • • • • ••••••••••••• •••••••••• o oooooooooooooo o o o o o o o o o o o o o o o o o o o o o o o ooooooooooooo o I-1I-1I-1H H I-1I-1H I-*H HHHHHHHHHHHH M H 1-*H H H H H H* I-* H HHHHH to to to to to to to o c 0 0) rt H- o 3 o VO vibrational quantum numbers Energy Pea. % Occupation 0 0 0 0 0 0 0 0. 0 2 0 1 1 0 1937 6 0.01 0 0 0 0 0 0 0 0 1 1 1 0 0 1 2 0 0 0 8 0.01 0 0 1 0 0 0 0 0 2 0 0 0 0 0 1 7 9 8 3 0.01 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 8 5 8 4 0.01 0 0 0 0 0 0 0 0 0 2 1 0 0 2 2027 9 0.01 0 0 0 0 1 0 0 0 0 0 0 0 0 6 2 0 6 9 11 0.01 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1722 2 0.01 0 0 1 0 0 0 0 0 0 0 0 1 0 4 1982 7 0.01 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 5 7 9 1 0.01 0 1 0 0 0 0 0 0 0 1 0 0 0 3 2056 10 0.01 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1807 3 0.01 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1727 2 0 . 01 0 0 0 0 1 0 0 0 0 0 0 2 0 0 1 5 8 5 1 0.01 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1729 2 0 . 01 0 0 1 0 0 0 0 0 0 0 0 0 1 3 2063 10 0. 01 0 0 0 0 0 0 0 0 2 0 0 1 0 2 2044 9 0.01 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 734 2 0.01 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 882 4 0.01 0 0 0 0 0 0 0 0 1 0 1 0 0 3 2073 10 0.01 0 0 1 0 0 0 0 0 0 0 0 2 0 1 1 7 4 0 2 0.01 0 0 0 0 0 0 0 0 0 0 1 1 0 3 1 9 3 1 5 0.01 0 0 0 0 0 0 1 0 0 1 0 0 0 1 2029 8 0.01 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1742 2 0.01 0 0 0 0 1 0 0 0 0 3 0 0 0 1 2076 10 0.01 0 0 0 0 0 0 0 0 2 1 0 1 0 0 1 9 7 1 6 0 . 01 0 0 2 0 0 0 0 0 0 1 0 0 0 1 1 8 8 9 4 0.01 0 0 0 0 0 0 0 1 0 0 0 1 0 2 1 9 7 5 6 0.01 0 0 1 0 0 0 0 0 1 2 0 0 0 0 1 978 6 0.01 0 0 1 0 0 0 0 0 0 2 0 1 0 0 1 8 3 6 3 0.01 0 0 0 0 1 0 0 0 0 1 0 1 0 2 1 9 8 0 6 0.01 0 1 0 0 0 0 0 0 0 2 0 0 0 1 1983 6 0.01 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 7 5 6 2 0.01 0 0 0 0 0 0 0 1 1 1 0 0 0 0 2044 8 0.01 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1902 4 0.01 0 0 0 0 0 0 0 0 0 3 1 0 0 0 1954 5 0 . 01 0 0 0 0 0 0 0 0 1 1 0 2 0 1 2 0 5 5 8 0 . 01 0 0 0 0 0 0 0 1 0 0 0 0 1 1 2056 8 0. 01 0 0 0 0 0 0 0 0 0 1 0 3 0 1 1913 4 0.01 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2082 9 0.01 0 0 2 0 0 0 0 0 0 0 0 0 0 3 1962 5 0.01 0 0 0 0 1 0 0 0 0 1 0 0 1 1 2 0 6 1 8 0.01 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1634 1 0.01 0 0 0 0 0 0 0 0 0 0 1 0 1 2 2 012 6 0 . 01 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1641 1 0. 01 0 0 0 0 1 0 0 0 2 0 0 0 0 0 1869 3 0.01 0 0 0 0 1 0 0 0 0 0 0 1 0 4 2053 7 0.01 0 0 0 0 2 0 0 0 0 0 0 0 0 2 1878 3 0.01 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1939 4 0.01 0 0 0 0 0 0 0 0 0 0 0 3 0 3 1 9 8 6 5 0 . 01 0 0 1 0 0 0 0 0 2 0 0 0 0 1 2024 6 0.01 vibrational quantum numbers Energy Peg. % Occupation 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 8 0 0 2 0 . 01 0 1 0 0 0 0 0 0 1 0 0 0 0 2 2029 6 0.01 0 1 0 0 0 0 0 0 0 0 0 1 0 2 1 8 8 7 3 0.01 0 0 0 0 2 0 0 0 0 1 0 0 0 0 1 8 0 5 2 0.01 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 8 0 5 2 0 . 01 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1953 4 0 . 01 0 0 0 0 1 0 0 0 0 0 0 2 0 1 1 8 1 1 2 0.01 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 9 5 5 4 0.01 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 9 5 6 4 0.01 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 814 2 0.01 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 9 6 0 4 0.01 0 0 0 0 0 0 0 0 0 3 0 2 0 0 2009 5 0.01 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 9 6 3 4 0 . 01 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 8 2 1 2 0 . 01 0 0 0 0 1 0 0 0 1 2 0 0 0 0 2049 6 0. 01 0 0 0 0 1 0 0 0 0 2 0 1 0 0 1 9 0 7 3 0 . 01 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 9 6 8 4 0.01 0 0 1 0 0 0 0 0 0 0 1 0 0 2 1 9 1 1 3 0 . 01 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 8 3 1 2 0.01 0 0 0 0 0 0 0 0 0 0 1 2 0 0 1 6 8 9 1 0.01 0 0 1 0 0 0 0 0 0 2 0 1 0 1 2062 6 0. 01 0 0 0 0 0 0 0 0 1 0 0 0 2 0 2064 6 0. 01 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 8 3 8 2 0 . 01 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1922 3 0 . 01 0 0 0 0 0 0 0 0 0 0 0 2 1 2 2067 6 0.01 0 0 0 0 0 1 0 0 0 0 0 0 0 2 2069 6 0.01 0 0 1 0 1 0 0 0 0 0 0 0 0 3 2033 5 0.01 0 0 0 0 0 0 0 0 0 1 0 2 1 0 1994 4 0 . 01 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 9 9 6 4 0 . 01 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 7 1 2 1 0 . 01 0 0 0 0 0 0 0 0 0 1 1 1 0 2 2084 6 0. 01 0 0 0 0 0 0 1 0 1 0 0 0 0 0 2002 4 0. 01 0 0 0 0 0 0 0 0 0 0 2 0 0 1 1 8 6 0 2 0 . 01 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 8 6 0 2 0 . 01 0 0 2 0 0 0 0 0 1 0 0 0 0 0 1862 2 0.00 0 0 2 0 0 0 0 0 0 0 0 1 0 0 1 7 2 0 1 0 . 00 1 0 0 0 0 0 0 0 0 0 0 0 0 2 1 9 4 8 3 0 . 00 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1867 2 0 . 00 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 8 7 5 2 0 . 00 0 0 1 0 0 0 0 0 0 0 0 2 0 2 1 9 6 6 3 0.00 0 0 0 0 1 0 0 1 0 0 0 0 0 1 2026 4 0.00 0 0 0 0 0 0 0 0 1 0 0 3 0 0 1 8 8 6 2 0 . 00 0 0 0 0 2 0 0 0 0 1 0 0 0 1 2031 4 0. 00 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1744 1 0. 00 0 0 0 0 0 0 0 0 2 0 1 0 0 0 1973 3 0. 00 0 0 0 0 1 0 0 0 1 0 0 0 1 0 2034 4 0. 00 0 0 1 0 0 0 0 0 1 1 0 1 0 0 2035 4 0. 00 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1892 2 0 . 00 0 0 1 0 0 0 0 0 0 1 0 2 0 0 1893 2 0 . 00 0 1 0 0 0 0 0 0 0 1 0 1 0 1 2040 4 0. 00 quantum numbers Energy Peg. % Occupation 0 0 0 0 0 1 0 0 2 1982 3 0 . 00 0 0 0 0 0 0 1 1 1 2047 4 0.00 0 0 1 0 0 1 0 0 0 1904 2 0.00 0 0 0 0 1 1 0 0 0 1909 2 0.00 0 0 0 1 0 1 1 0 1 2 0 5 7 4 0.00 0 0 0 0 0 1 2 0 1 1 9 1 5 2 0.00 0 0 0 0 1 1 0 0 1 2064 4 0.00 0 0 0 0 2 1 1 0 0 2 0 1 1 3 0.00 0 0 0 1 0 0 0 0 0 1933 2 0.00 0 0 0 0 0 0 1 0 0 1 7 9 1 1 0 . 00 0 0 0 0 0 0 0 0 1 1938 2 0 . 00 0 0 0 2 0 0 2 0 0 2028 3 0. 00 0 0 0 0 0 0 1 0 1 1 9 4 6 2 0 . 00 0 0 0 0 0 0 0 0 2 2031 3 0. 00 0 0 0 0 0 0 2 0 2 2037 3 0. 00 0 0 0 0 1 0 0 0 0 1958 2 0 . 00 0 0 0 0 2 0 0 0 0 2042 3 0. 00 0 0 1 0 0 0 2 0 0 1959 2 0 . 00 0 0 0 0 0 1 0 0 0 1 8 1 6 1 0 . 00 0 0 0 0 1 0 2 0 0 1964 2 0 . 00 0 0 0 0 0 0 4 0 1 1 9 7 0 2 0 . 00 0 0 0 0 2 0 3 0 0 2066 3 0. 00 0 0 0 0 0 1 1 1 0 1 9 9 6 2 0 . 00 0 0 0 1 0 0 0 0 0 2004 2 0. 00 0 0 0 0 0 0 1 0 0 1862 1 0 . 00 0 0 0 0 1 2 0 0 0 2013 2 0 . 00 0 0 0 1 0 0 1 0 0 2013 2 0 . 00 0 0 0 0 0 0 2 0 0 1 8 7 1 1 0 . 00 0 0 0 0 0 0 1 0 1 2 0 1 7 2 0.00 0 0 0 0 1 0 0 0 0 2020 2 0.00 0 0 0 0 0 0 0 1 0 2027 2 0.00 0 0 0 1 0 1 0 0 0 2037 2 0.00 0 0 0 0 0 1 1 0 0 1 8 9 5 1 0 . 00 0 0 0 0 0 1 0 0 1 2042 2 0. 00 0 0 0 0 0 0 3 1 0 2 0 5 1 2 0 . 00 1 0 0 0 0 0 1 0 0 2 0 5 3 2 0.00 0 1 0 0 0 0 0 0 0 2066 2 0.00 0 0 0 0 1 1 2 0 0 2068 2 0. 00 0 0 0 1 0 0 0 0 0 2074 2 0. 00 0 0 0 0 0 0 1 0 0 1932 1 0.00 0 0 0 0 0 0 3 0 0 1 9 5 0 1 0 . 00 0 0 0 0 0 1 1 0 0 1 9 6 6 1 0.00 0 0 0 0 0 0 0 0 0 1997 1 0 . 00 0 0 0 0 0 0 1 0 0 2 0 1 5 1 0.00 0 0 0 0 0 0 3 0 0 2021 1 0. 00 0 0 0 0 0 0 0 0 0 2068 1 0. 00 0 0 0 0 0 2 1 0 0 2070 1 0. 00 0 0 0 0 0 0 1 0 0 2077 1 0.00 Appendix D

ABC.BAS MATRIX.BAS TRIAZINE.BAS

Programs to find spectroscopic constants from molecular structure.

113 114

The following program is written in Microsoft QuickBASIC 4.5. It uses several routines contained in the module MATRIX.BAS which is included after ABC.BAS. To compile the program, include a small ASCII file named ABC.MAK with the lines

ABC.BAS MATRIX.BAS and issue the command

QB ABC from the command line to enter the QuickBASIC development environment. The program can then be compiled by selecting "Make .EXE" from the Run menu.

An Alternative method is to compile the MATRIX module and create a quick-library (usable from within the development environment) and a linkable library (for creating compiled .EXE files from QuickBASIC source code requiring the library routines.) The prpoer command then becomes

QB ABC /L MATRIX and a compiled .EXE file can be created in the same way as above.

ABC.BAS

DECLARE SUB ZcroElement (n%, a#(), epsilon#) DECLARE SUB Jacobi (n%, h #(), a#(), r#()) DECLARE SUB Matlnv (n%, c#()) DECLARE SUB MatMull (m%, n%, 1%, a#(), b#(), c#()) DEFINT I-N DEFDBL A-H, O-Z DIM m(100), x(100), y(100), z(100), xyz(3, 3), r(3, 3), abc(3, 3), rabc(3, 1)

ABCXYZ Patrick Fleming 1989

This program will take data on the structure of a molecule and compute the principle axies, principle moments of inertia and rotational constants of the molecule.

The data is taken by the program in the form of an ASCII file with the following format:

Comment line #1 Comment line #2 N m(l) x(l) y(l) z(l) m(2) x(2) y(2) z(2) m(N) x(N) y(N) z(N) where

N - is the number of atoms in the molecule m(i) - is the mass of the ith atom x(i) - is the x coordinate of the ith atom (in an arbitrary Cartesian axis system) y(i) - is the y coordinate of the ith atom z(i) - is the z coordinate of the ith atom

The first two lines are for literal comments which will be sent dirrectly to the output file.

The program will find the center of mass for the piolecule and then find the principle axis system such that the rotational inertia tensor is diagonalized.

Variables:

N - number of atoms in the molecule m(i) - mass of the ith atom x(i) - x coordinate of ith atom in original coordinate system y(i) - y coordinate of ith atom in original coordinate system z(i) - z coordinate of ith atom in original coordinate system xcm - x coordinate of the center of mass in original coordinate system yem - y coordinate of the center of mass in original coordinate system zem - z coordinate of the center of mass in original coordinate system xc(i) - x coordinate of ith atom relative to the center of mass as the origin yc(i) - y coordinate of ith atom relative to the center of mass as the origin zc(i) - z coordinate of ith atom relative to the center of mass as the origin XYZ(ij) - undiagonalized rotational inertia tensor ABC(ij) - diagoanlized rotational inertia tensor A,B,C - rotational constants of the molecule I,J - looping variables F$ - input data file name SMX - sum of mass weighted x coordinates SMY - sum of mass weighted y coordinates SMZ - sum of mass weighted z coordinates 116

References:

W. S. Struve, Fundimentals of Molecular Spectroscopy, John Wiley and Sons, New York, 1989

J. D. Graybeal, Molecular Spectroscopy, McGraw-Hill, New York, 1988

J. Kraitchman, Am. J. Phys. 21, 17 (1953)

D. M. Young and R. T. Gregory, A Survey of Numerical Mathematics, Dover, New York, 1973

CLS PRINT : PRINT GOSUB GetData GOSUB CenterOfMass GOSUB BuildTcnsor GOSUB Eigenvalues GOSUB RotationalConstants GOSUB XYZtoABC GOSUB SymmetricTop GOSUB OulputFile ’GOSUB PrintResults ’GOSUB HardCopy GOSUB WriteResultsForFCN3 END

GetData:

’ This routine is for the input of data. It prompts for the name of ’ the input data file and also the name of the output data file.

f$ = COMMANDS IF PS = THEN PRINT : PRINT : PRINT 'Use ? for a list of files. ": PRINT INPUT "input data file name (.ABC extention will be added) = = > ", f$ END IF IF IS = "" OR VAL(fS) < > 0 THEN GOTO GetData IF LEFT$(1S, 1) = "?" OR LEFT$(f$, 1) = THEN PRINT : PRINT : FILES "*.abc" PRINT : PRINT GOTO GetData END IF IF LEN(fS) > 12 THEN IS = LEFT$(1S, 12) FOR i = 1 TO LEN(IS) IF MID$(1S, i, 1) = OR MID$(1S, i, 1) = " " THEN : f$ = LEFT$(f$, i - 1): i = LEN(fS) 117

+ 5 NEXT i f$ = f$ + ".ABC" OPEN f$ FOR INPUT AS #1 INPUT #1, commentl$ INPUT #1, comment2$ INPUT #1, n FOR i = 1 TO n INPUT #1, m(i), x(i), y(i), z(i) NEXT i CLOSE #1 ’INPUT "output data Tile name = = > ", fout$ RETURN

CenterOfMass:

This routine simply finds the center of mass using the relationship:

n .SIGMA. m(i)*x(i) = 0 i= 1

FOR i = 1 TO n sm = sm + m(i) smx = smx + x(i) * m(i) smy = smy + y(i) * m(i) smz = smz + z(i) * m(i) NEXT i xcm = INT(smx / sm * 1000000! + .5) / 1000000! yem = INT(smy / sm * 1000000! + .5) / 1000000! zem = INT(smz / sm * 1000000! + .5) / 1000000! FOR i = 1 TO n xc(i) = x(i) - xcm yc(i) = y(i) - yem zc(i) = z(i) - zem NEXT i RETURN

BuildTensor:

This rountine builds the rotational inertia tensor using Kraitchman’s equations which can be found in Graybeal or in Kraitchman’s original paper (see references.) Note that these equations do not use the center of mass determination from the previous subroutine, but are good for any arbitrary set of cartesian coordinates.

FOR i = 1 TO n xyz(l, 1) = xyz(l, 1) + m(i) * (y(i)"2 + z(i) ~ 2) xyz(2, 2) = xyz(2, 2) + m(i) * (x(i) A 2 + z(i) ~ 2) 118

xyz(3, 3) = xyz(3, 3) + m(i) * (x(i) A 2 + y(i) A 2) xyz(l, 2) = xyz(l, 2) - m(i) * x(i) * y(i) xyz(l, 3) = xyz(l, 3) - m(i) * x(i) * z(i) xyz(2,3) = xyz(2, 3) - m(i) * y(i) * z(i) NEXT i xyz(l, 1) = xyz(l, 1) - (smy A 2 + smz A 2) / sm xyz(2, 2) = xyz(2, 2) - (smx A 2 + smz A 2)/ sm xyz(3, 3) = xyz(3, 3) - (smx A 2 + smy A 2) / sm xyz(l, 2) = xyz(l, 2) + smx * smy / sm xyz(l, 3) = xyz(l, 3) + smx * smz / sm xyz(2, 3) = xyz(2, 3) + smy * smz / sm xyz(2, 1) = xyz(l, 2) xyz(3, 1) = xyz(l, 3) xyz(3, 2) = xyz(2, 3) CALL ZcroElcment(3, xyz(), .000001) RETURN

Eigenvalues: CALL Jacobi(3, xyz(), abc(), r()) ’ Jacobi will diagonalize the rotational inertia tensor RETURN

RotationalConstants: flag$ = "up" WHILE flag$ = "up" flag$ = "down” FOR i = 2 TO 3 IF abc(i - 1, i - 1) > abc(i, i) THEN SWAP abc(i - 1, i - 1), abc(i, i) FOR j = 1 TO 3 SWAP r(i - 1, j), r(i, j) NEXT j flag$ = "up" END IF NEXT i WEND IF abc(l, 1) < > 0 THEN a = 16.85763143# / abc(l, 1) IF abc(2, 2) < > 0 THEN b = 16.85763143# / abc(2, 2) IF abc(3, 3) < > 0 THEN c = 16.85763143# / abc(3, 3) RETURN

SymmetricTop:

’ This sub routine is intended to sugest the possibility that a ’ molecule may be a symmetric or even a spherical top. Recall that ’ a molecule is a prolate symmetric top if B = C and an oblate ’ symmetric top if A = B. It is a spherical top if A = B = C. Note ’ that a linear molecule is a prolate symmetric top. The program will ’ only look to see if the constants are nearly equal (to say a part ’ in 10A5). Group theory is left up to the user (i.e. to determine ’ the rotator is symmetrical by symmetry or by accident.) Ray’s ’ assymmetry parameter (kappa) is also calculated by 119

2B - A - C kappa = ...... A - C

Note that this parameter is undefined in the case of a spherical to molecule since A = C. It is also important to note that in the case of a symmetric or spherical top, the choice of principle axes is not unique.

IF INT(a * 100000! + .5) = INT(b * 100000! + .5) THEN oblate$ = "yes" IF INT(b * 100000! + .5) = INT(c * 100000! + .5) THEN prolate$ = "yes" IF oblateS = "yes" AND prolate$ = "yes” THEN sphcrical$ = "yes" IF spherical$ < > "yes" THEN kappa# = (2 * b - a - c) / (a - c) ELSE kappa# = 2 RETURN

XYZtoABC:

’ This routine does the linear transformation of coordinates from ’ the original cartesian system to the cartesian system defined by ’ the molecule’s principle axes. R is inverse of the matrix whose ’ columns are the unit vectors which give the directions of the ’ principle axes. The transformation is then given by

X’ = RX

’ Where X’ is the position vector of an atom relative to the center ’ of mass in the new coordinates and X is the position vector in the ’ old coordinate system.

FOR i = 1 TO 3 FOR j = 1 TO 3 rinv(i, j) = r(i, j) NEXT j, i CALL Matlnv(3, rinv()) FOR i = 1 TO n rxyz(l, 1) = xc(i) rxyz(2, 1) = yc(i) rxyz(3, 1) = zc(i) CALL MatMult(3, 3, 1, rinv(), rxyz(), rabc()) ac(i) = rabc(l, 1) bc(i) = rabc(2, 1) cc(i) = rabc(3, 1) NEXT i RETURN

OutputFile: > ’ This routine simply writes the calculated data to a file whose ’ name can be specified by the user, (with minimal code changes)

fout$ = "abcout.dat" 120

OPEN fout$ FOR OUTPUT AS #1 PRINT #1, commentl$ PRINT #1, comment2$ PRINT #1, " " PRINT #1, " " PRINT #1, "The structure of the molecule was given by:" PRINT #1, " " PRINT #1, " mass x y z" PRINT #1, ...... " " FOR i = 1 TO n PRINT #1, USING ”##.####~w' ##.####------##.####~'~' m(i); x(i); y(i); z(i) NEXT i PRINT #1, " PRINT #1, " " PRINT #1, "center of mass (in original coordinates):" PRINT #1, " " PRINT #1, USING "##.####----- # # . # #------# # # # .# # # # ~ '~ " ; xcm; yem; zem PRINT #1, " " PRINT #1, " " PRINT #1, "The structure of the molecule (in center of mass coords.):" PRINT #1, " " PRINT #1, " mass x y z" PRINT #1, ...... " " FOR i = 1 TO n PRINT #1, USING "##.####"— ##.####~~ ##.####/~~ m(i); xc(i); yc(i); zc(i) NEXT i PRINT #1, " " PRINT #1, " " PRINT #1, "The principal axes (in original coordinates) are given by:": PRINT #1, " PRINT #1, " " PRINT #1, " a b c" PRINT #1, ...... " " FOR i = 1 TO 3 FOR j = 1 TO 3 PRINT #1, USING "##.####------"; r(i, j); NEXT j PRINT #1, " " NEXT i PRINT #1, " ": PRINT #1, " " PRINT #1, "The positions of the atoms relative to the center of mass in" PRINT #1, "the diagonalized coordinate system are:" PRINT #1, " " PRINT #1," mass a(i) b(i) c(i)" PRINT #1, ...... " " FOR i = 1 TO n PRINT #1, USING ”##.####~~' ##.####/v/^ ##.####~w' ##.####------"; m(i); ac(i); bc(i); cc(i) NEXT i PRINT #1, " ": PRINT #1, " ": PRINT #1, " " PRINT #1, "The rotational constants are:" PRINT #1, " ": PRINT #1, " " 121

IF a < > 0 THEN PRINT #1, "A = a, IF b < > 0 THEN PRINT #1, "B = b, IF c < > 0 THEN PRINT #1, "C = c PRINT #1, " PRINT #1, " " IF sphericalS = "yes" THEN PRINT #1, 'The molecule may be a spherical top." ELSEIF a = 0 THEN PRINT #1, "The molecule must be linear." ELSEIF prolateS = "yes” THEN PRINT #1, "The molecule may be a prolate symmetric lop." ELSEIF oblatcS = "yes” THEN PRINT #1, "The molecule may be an oblate symmetric top." END IF IF sphericalS < > "yes" THEN PRINT #1, "Ray’s asymmetry parameter (kappa) = kappa# CLOSE #1 RETURN

WriteResuItsForFCN3: PRINT : PRINT PRINT commentlS PRINT commcnt2$ PRINT "The rotational constants arc:" PRINT" " IF a < > 0 THEN PRINT USING "A = #.#######"; a IF b < > 0 THEN PRINT USING "B = #.#######"; b IF c < > 0 THEN PRINT USING "C = #.#######"; c RETURN

PrintRcsults: OPEN fout$ FOR INPUT AS #1 i = 1 WHILE NOT EOF(l) INPUT #1, dump$ PRINT dump$ i = i + 1 IF i = 23 THEN INPUT "Paused . . .", r$ i = 1 END IF WEND CLOSE #1 RETURN

HardCopy: PRINT : PRINT : PRINT INPUT "Do you want a hard copy of this data"; r$ r$ = UCASE$(LEFT$(r$, 1)) IF r$ = "Y" THEN OPEN foutS FOR INPUT AS #1 i = 1 WHILE NOT EOF(l) INPUT #1, dumpS LPRINT dump$ i = i + 1 IF i = 60 THEN LPRINT CHR$(12) i = 1 END IF WEND LPRINT CHR$(12) END IF CLOSE #1 RETURN MATRIX.BAS

DECLARE SUB SumOffDiagonalsSquarcd (n%, a#(), sods#) DECLARE SUB ZcroElemcnt (n%, a#(), epsilon#) DECLARE SUB MatMult (m%, n%, 1%, a#(), b#(), c#()) DEFINT I-N DEFDBL A-H, O-Z

SUB Jacobi (n, h(), a(), r())

This routine finds the eigenvalues and eigenvectors of a symetric square matrix by Jacobi’s Method as outlined in

D. M. Young and R. T. Gregory, A Survey of Numerical Mathematics, Dover, New York, 1973

Variables:

n - dimension of the matrix h(ij) - original symetric matrix specified by user a(ij) - matrix returned by routine the diagonal elemnts are the eigenvalues of the original matrix r(ij) - matrix returned by routine the columns of this matrix are the eigenvectors of the original matrix

DIM rm(n, n), rml(n, n) FOR i = 1 TO n FOR j = 1 TO n a(>, j) = h(i, j) IF i = j THEN r(i, j) = 1 ELSE r(i, j) = 0 NEXT j, i epsilon = .000001 CALL SumOffDiagonalsSquared(3, h(), sods) DO WHILE sods > epsilon FOR q% = 1 TO n FOR p% = q% + 1 TO n beta = ABS(a(q%, q%) - a(p%, p%)) alpha = 2 * a(p%, q%) * SGN(a(q%, q%) - a(p%, p%)) IF a(q%, q%) = a(p%, p%) THEN ctheta = 0 stheta = 1 GOTO 110 END IF ctheta = SQR((1 + beta / SQR(alpha * 2 + beta ~ 2 )) / 2 ) stheta = alpha / (2 * ctheta * SQR(alpha ~ 2 + beta ~ 2 )) 110 FOR i = 1 TO n 124

FOR j = 1 TO n IF i = j THEN rm(i, j) = 1 ELSE rm(i, j) = 0 NEXT j, i rm(q%, q%) = ctheta rm(q%, p%) = -stheta rm(p%, q%) = stheta rm(p%, p%) = ctheta FOR i = 1 TO n IF i = p% OR i = q% THEN 120 a(q%, i) = a(q%, i) * ctheta + a(p%, i) * stheta a(p%, i) = -a(q%, i) * stheta + a(p%, i) * ctheta a(i, q%) = a(i, q%) * ctheta + a(i, p%) * stheta a(i, p%) = -a(i, q%) * stheta + a(i, p%) * ctheta 120 NEXT i a(q%, q%) = a(q%, q%) * ctheta " 2 + 2 * a(q%, p%) * stheta * ctheta + a(p%, p%) * stheta ~ 2 a(p%, p%) = a(q%, q%) * stheta ~ 2 - 2 * a(p%, q%) * stheta * ctheta + a(p%, p%) * ctheta ~ 2 a(q%, p%) = 0 a(p%, q%) = 0 CALL ZeroElcment(3, a(), .000001) IF stheta ~ 2 + ctheta ~ 2 - 1 > epsilon THEN PRINT PRINT PRINT "What the hell you gonna do now ???" PRINT "The Jacobi sub-program is failing numerically." PRINT INPUT "Paused . . r$ END IF CALL MatMuIt(3, 3, 3, r(), rm(), rml()) CALL ZeroElement(3, rml(), .000001) FOR i = 1 TO n FOR j = 1 TO n r(i,j) = rml(i.j) NEXT j, i NEXT p% NEXT q% CALL SumOffDiagonalsSquared(3, a(), sods) LOOP END SUB

SUB Matlnv (n, c())

This routine will invert an n x n sqaure matrix using Guass-Jordon elimination. This procedure is described in

R. W. Hornbeck, Numerical Methods, Prentice-Hall/Quantum Englewood Cliffs, New Jersey, 1975

DIM e(n, n) » 125

’set idcntitiy matrix

FOR i = 1 TO n FOR j = 1 TO n IF i = j THEN e(i, j) = 1 ELSE c(i, j) = 0 NEXT j, i FOR k = 1 TO n

’ check for non zero pivot

IF c(k, k) = 0 THEN GOSUB SwapRows

’ divide row by pivot

x = c(k, k) FOR j = 1 TO n c(k,j) = c(k,j) / x e(k,j) = c(k,j) / x NEXT j

’ zero elements in pivot column

FOR i = 1 TO n IF i = k THEN 10 x = c(i, k) FOR j = 1 TO n c(i, j) = c(i, j) - c(k, j) * x e(i> j) = e(i, j) - e(k, j) * x NEXT j 10 : NEXT i NEXT k

’ set matrix to be returned

FOR i = 1 TO n FOR j = 1 TO n c(i. j) = e(i, j) NEXT j, i GOTO 20 SwapRows: m = k + 1 15 : IF c(m, k) = 0 AND m < = n THEN m = m + 1: GOTO 15 IF m > n THEN PRINT : PRINT : PRINT "The matrix is singular - bummer.": STOP FOR j = 1 TO n SWAP c(k, j), c(m, j) SWAP e(k, j), e(m, j) NEXT j RETURN 20 : END SUB 126

SUB MatMult (m, n, I, a(), b(), c())

This routine will multiply two matrices as follows:

A is an mxl matrix B is an nxl matrix C = AB is an mxr matrix whose elements c(i,j) are

n c(i,j) = .SIGMA. a(i,k)*b(k,j) k = 1

FOR i = 1 TO m FOR j = 1 TO 1 c(i, j) = 0 NEXT j, i FOR i = 1 TO m FOR j = 1 TO 1 FOR k = 1 TO n c(i> j) = c(i, j) + a(i, k) * b(k, j) NEXT k, j, i

END SUB

SUB PrintMat (n, c()) FOR i = 1 TO n FOR j = 1 TO n PRINT c(i, j), NEXT j PRINT NEXT i END SUB

SUB SumOffDiagonalsSquared (n, a(), sods)

This routine is used to find the sum of the squares of the off diagonal elements of square matrix of rank n. it is useful as a test criterion in the Jacobi method of finding eigenvalues and eigenvectors.

sods = 0 FOR i = 1 TO n FOR j = 1 TO n IF j < > i THEN sods = sods + a(i, j) ~ 2 NEXT j, i END SUB

SUB ZeroElement (n, a(), epsilon)

’ This routine is included to try to minimize numerical errors ’ which are generally due to round off. Here, a value in a matrix ’ is taken to be 0 if it is several orders of magnitude less than ’ the root-mcan-sqaurc of all the values in the matrix. The limit ’ is set by the value of epsilon.

rms = 0 FOR i = 1 TO n FOR j = 1 TO n rms = rms + a(i, j) ~ 2 NEXT j, i rms = rms / n A 4 FOR i = 1 TO n FOR j = 1 TO n IF ABS(a(i, j) / rms) < epsilon THEN a(i, j) = 0 NEXT j, i END SUB TRIAZINE.BAS

This program will produce a data file which is readable by ABC.BAS for the molecule 1,3,5- trifiuoro-sym-triazine based on the internal coordinates rCN, rCF and ZCNC. The assumption made that the molecule possesses D,h symmetry and is planar.

DEFDBL A-H, O-Z

This program is intended to produce a .ABC data file for the program ABC. It is specific for the molecule 1,3,5- trifluoro-sym-triazinc. The assumptions made are D3h symmetry and planarity. Only one spectrscopic value can be used in the determination of the structure, but three molecular parameters are needed to specify the structure completely. As used by Schlupf and Weber, those parameters arc the CN bond length, the CF bond length and the CNC bond angle. The first two will be taken from the literature (from 1,3,5-sym-triazine and fluorobcnzenc respectively) and the last will be varricd until a good match to the measured B value is obtained.

Variables: pi - 3.1415926537 rcn - the CN bond length ref - the CF bond length rnn - the NN distance alpha - 1/2 of the CNC bond angle delta - 1/2 of the NCN bond angle x?? - x coordinate of ? atom number ? y?? - y coordinate of ? atom number ?

MainProgram: GOSUB InputData GOSUB CalculateCoordinates GOSUB WriteDataFile END

InputData: CLS pi = 4 * ATN(l) PRINT : PRINT : ’INPUT "C=N bond distance : rcn’ C=N bond length INPUT "C-F bond distance : ref ’ C-F bond length INPUT "CNC bond angle : alpha alpha = alpha / 2 129

alpha = alpha * pi / 180

rcn = 1.338 ’Herzberg, Polyatomics ’ref = 1.354 ’Nery.Rousy, Compt. Rend., 203, 27813 (1974) RETURN

CalculateCoordinates: Calculatelntermcdiates: beta = 2 * alpha - pi / 3 delta = (pi - beta) / 2: del = delta * 180 / pi rnn = 2 * rcn * SIN(delta)

xnl = 0 xn2 = rnn / 2 xn3 = -rnn / 2 ynl = rcn * COS(alpha) yn2 = rcn * COS(alpha) - rnn * COS(pi / 6) yn3 = yn2 xcl = rcn * SIN(alpha) xc2 = 0 xc3 = -rcn * SIN(alpha) ycl = 0 yc2 = rcn * COS(alpha) - rnn * COS(pi / 6) - rcn * COS(dclta) yc3 = 0

costheta = ((xn3 - xcl) * (xc3 - xcl) + (yn3 - ycl) * (yc3 - ycl)) costheta = costheta / ((xn3 - xcl) ~ 2 + (yn3 - ycl) ~ 2) ~ .5 costheta = costheta / ((xc3 - xcl) * 2 + (yc3 - ycl) ~ 2) ~ .5 sintheta = (1 - costheta ~ 2) A .5

xfl = xcl + ref* costheta xf2 = 0 xf3 = -xfl yfl = ref * sintheta yf2 = yc2 - ref yf3 = yfl

RETURN

WriteDataFile: OPEN "fcn3.abc" FOR OUTPUT AS #1 PRINT #1, "1.3.5-trifluoro-sym-triazine; CNC bond angle = 360 * alpha / pi PRINT #1, "assume D3h symmetry; C = N bond length = rcn; "; C-F bond length = "; ref PRINT #1, 9 PRINT #1, 18.998403#, xfl, yfl, 0 PRINT #1, 18.998403#, xf2, yf2, 0 PRINT #1, 18.998403#, xf3, yC3, 0 PRINT #1, 14.0067, xnl, ynl, 0 PRINT #1, 14.0067, xn2, yn2, 0 PRINT #1, 14.0067, xn3, yn3, 0 PRINT #1, 12.011, xcl, ycl, 0 PRINT #1, 12.011, xc2, yc2, 0 130

PRINT #1, 12.011, xc3, yc3, 0 CLOSE #1 RETURN Appendix E

CHEW.BAS CHEW-MER.BAS

Lcast-Squarcs Filling Programs to find spectroscopic constants from molecular spectra.

131 132

CHEW.BAS

This program is a generic linear least-squarcs fitting program. In the form shown here, this program was used to perform band-by-band fitting of the data for AlBr. It is easily modified for other applications by changing the number of and names of the adjustable parameters in the subroutine SetParms and the dependance of the variables in the Function x.

DECLARE FUNCTION x# (i%, vu%, vl%, ibranch%, J%, iflag%) DECLARE SUB MatEquals (m%, n%, a#(), b#()) DECLARE SUB Matlnv (n%, c#()) DECLARE SUB MatMult (m%, n%, 1%, a#(), b#(), c#()) DEFDBL A-H, O-Z DEFINT I-N

This program uses the MATRIX library

use qb chew /I matrix

CLS GOSUB SetParms GOSUB OpenFile GOSUB ReadFile GOSUB FitTheThing GOSUB CalcDeviation GOSUB PrintFit DadGummitBlah: PRINT : PRINT "All Done! " END

SetParms: m = 6 fileoutS = "chew.out" DIM a(m, m), b(m, m), h(m, 1), c(m, 1) DIM parmname$(m) parmname$(l) = " nuzero" parmname$(2) = " B’" parmname$(3) = '' D’" parmname$(4) = " H’" parmname$(5) = " B”" parmname$(6) = " D”" RETURN

OpenFile: IF LEN(COMMANDS) = 0 THEN BeReasonable: INPUT "File name ? ", filenames br = 0 133

FOR i = 1 TO LEN(filenamc$) IF MID$(filenamc$, i, 1) = " " THEN br = 1 PRINT : PRINT "Try again. Say a different name." PRINT "And be reasonable." END IF NEXT i IF br = 1 THEN GOTO BcRcasonable OPEN filenames FOR INPUT AS #1 ELSE br = 0 FOR i = 1 TO LEN(COMMANDS) IF MID$(COMMAND$, i, 1) = "" THEN PRINT "Be reasonable.": br = 1 NEXT i IF br = 1 THEN PRINT "Be Reasonable. Say a different name.": STOP filenames = COMMANDS OPEN filenames FOR INPUT AS #1 END IF RETURN

ReadFile: PRINT "Reading file . . ." INPUT #1, n PRINT "There arc"; n ;" observations." FOR k = 1 TO n INPUT #1, vu%, vl%, ibranch, Jl, wavcnumbcr, iflag FOR i = 1 TO m FOR J = 1 TO m a(i, J) = a(i, J) + x(i, vu%, vl%, ibranch, Jl, iflag) * x(J, vu%, vl%, ibranch, Jl, iflag) NEXT J h(i, 1) = h(i, 1) + x(i, vu%, vl%, ibranch, Jl, iflag) * wavcnumbcr NEXT i IF k / 10 = INT(k / 10) THEN PRINT k, NEXT k CLOSE #1 PRINT RETURN

FitTheThing: PRINT "Fitting Data . . ." CALL MatEquals(m, m, a(), b()) CALL Matlnv(m, b()) CALL MatMult(m, m, 1, b(), h(), c()) RETURN

CalcDeviation: PRINT "Calculating deviations . . ." stddev = 0 OPEN filenames FOR INPUT AS #1 INPUT #1, n FOR k = 1 TO n INPUT #1, vu%, vl%, ibranch, J, wavenumber, iflag 134

calc = 0 FOR i = 1 TO m calc = calc + x(i, vu%, vl%, ibranch, J, iflag) * c(i, 1) NEXT i stddcv = stddcv + (wavcnumbcr - calc) ~ 2 NEXT k CLOSE #1 stddev = (stddcv / (n - m)) * .5 RETURN

PrintFit: PRINT "Saving results . . OPEN filenames FOR INPUT AS #1 OPEN fileoutS FOR OUTPUT AS #2 INPUT #1, n PRINT #2, " obs. calc. obs.-calc." PRINT # 2 ," ...... " FOR k = 1 TO n INPUT #1, vu%, vl%, ibranch, J, wavenumbcr, iflag calc = 0 FOR i = 1 TO m calc = calc + x(i, vu%, vl%, ibranch, J, iflag) * c(i, 1) NEXT i IF iflag = 2 THEN PRINT #2, USING " MW # # vl%; IF iflag = 1 THEN PRINT #2, USING " IR # # vl%; IF iflag = 0 THEN PRINT #2, USING " # # # # vu%; vl%; IF ibranch = 1 THEN PRINT #2, USING " R ( # # # .# ) # # # # # . # # # # # # # # # . # # # # # # # # # .# # # # " ; J; wavcnumbcr; calc; wavenumber - calc; IF ibranch = 0 THEN PRINT #2, USING " Q (# # # .# ) # # # # # . # # # # # # # # # . # # # # # # # # # .# # # # " ; J; wavenumber; calc; wavcnumbcr - calc; IF ibranch = -1 THEN PRINT #2, USING " P(###.#) # # # # # .# # # # # # # # # . # # # # # # # # # .# # # # " ; J; wavcnumbcr; calc; wavenumber - calc; IF ABS(wavenumber - calc) > 2 * stddcv THEN PRINT #2, " < — dev. > 2 sigma" ELSE PRINT #2, "" NEXT k PRINT #2, " PRINT #2, " ": PRINT #2, "Number of observations = "; n PRINT #2, USING "Standard Deviation = # # .# # # # # ~ '~ " ; stddev PRINT #2, " ” FOR i = 1 TO m PRINT #2, USING " \ \ = ##.###########~~( + parmnameS(i); c(i, 1); b(i, i) ~ .5 * stddev; IF ABS(c(i, 1)) < 2 * b(i, i) ~ .5 * stddev THEN PRINT #2, " < - WARNING!!" ELSE PRINT #2, "" END IF NEXT i PRINT #2, " PRINT #2, " " PRINT #2, "Correlation matrix:" PRINT #2, " "; FOR i = 1 TO m 135

PRINT #2, parmname$(i); NEXT i PRINT #2,"" PRINT #2, " FOR i = 1 TO m PRINT #2, ...... " NEXT i PRINT #2, " " FOR i = 1 TO m PRINT #2, parmname$(i); FOR J = 1 TO i PRINT #2, USING " # # .# # # " ; b(i, J) / (b(i, i) * b(J, J)) " .5; NEXT J PRINT #2, " " NEXT i PRINT #2, " " PRINT #2, " PRINT #2, " " PRINT #2, "Varriance-covarriancc matrix:" PRINT #2, " FOR i = 1 TO m PRINT #2, parmname$(i); " NEXT i PRINT #2, " " PRINT #2, " FOR i = 1 TO m PRINT #2, ...... " NEXT i PRINT #2, " " FOR i = 1 TO m PRINT #2, parmname$(i); FOR J = 1 TO i PRINT #2, USING " # # .# # # # ~ '~ " ; b(i, J) * stddcv * 2; NEXT J PRINT #2, * " NEXT i PRINT #2, ” " PRINT #2, CHR$(12) CLOSE #2 RETURN

FUNCTION x (i, vu%, vl%, ibranch, J, iflag) xf = 0 IF iflag = 0 THEN J2u = (ibranch + J) * (ibranch + J + 1) - 1 J21 = J * (J + 1) IF i = 1 THEN xf = 1 IF i = 2 THEN xf= J2u IF i = 3 THEN xf =-J2u ~ 2 IF i = 4 THEN xf =J 2u ~ 3 IF i = 5 THEN xf =-J21 IF i = 6 THEN xf =J21 ~ 2 END IF 136

IF iflag = 2 THEN IF i = 13 THEN xf = (2 * (J + 1)) IF i = 14 THEN xf = -(vl% + .5) * (2 * (J + 1)) IF i = 15 THEN xf = (vl% + .5) ~ 2 * (2 * (J + 1)) IF i = 16 THEN xf = -4 * (J + 1) ~ 3 IF i = 17 THEN xf = (vl% + .5) * (4 * (J + 1) A 3) END IF x = xf END FUNCTION 137

CHEW-MER.BAS

This program was used to merge ultraviolet data with microwave data to provide the constants reported for AlBr. It follows the equations set forth in the paper by Allbritton, Schmeltekopf and Zare.

DEFDBL A-H, O-Z DEFINT I-N

This program uses the MATRIX library

use qb chew /I matrix

CLS fout$ = "mcrgc.out" GOSUB OpenFile GOSUB FoolTheComputer DIM x(nn, 11), xtrans(ll, nn), phiinv(nn, nn), y(nn, 1), beta(ll, 1) DIM templ(ll, nn), temp2(ll, 11), tcmp3(ll, 1) DIM temp4(l, 11), temp5(ll, 1), sigma2(l, 1) DIM parmname$(ll) GOSUB RcadFile

’ Here is the merging part

PRINT "inverting . . CALL Matlnv(nn, phiinv()) PRINT "multiplying . . CALL MatMult(ll, nn, nn, xtrans(), phiinv(), templ()) PRINT "multiplying . . CALL MatMult(Il, nn, 11, templ(), x(), temp2()) PRINT "inverting . . CALL Matlnv(ll, temp2()) PRINT "multiplying . . CALL MatMult(ll, nn, 1, templ(), y(), temp3()) PRINT "multiplying . . CALL MatMult(ll, 11, 1, temp2(), temp3(), beta())

’ And now for the uncertainties

PRINT "finding uncertainties . . CALL MatMult(nn, 11, 1, x(), beta(), temp3()) FOR i = 1 TO 11 temp3(i, 1) = y(i, 1) - temp3(i, 1) NEXT i CALL MalTrans(ll, 1, temp3(), temp4()) CALL MatMult(ll, 11, 1, phiinvQ, temp3(), temp5()) CALL MatMult(l, 11, 1, tcmp4(), temp5(), sigma2()) sigma2(l, 1) = sigma2(l, 1) / (nn - 11) GOSUB PrintResults END

OpenFile: IF LEN(COMMANDS) = 0 THEN BeReasonablc: INPUT "File name ? ", filenames br = 0 FOR i = 1 TO LEN(filcnamc$) IF MID$(filename$, i,I) = " " THEN br = 1 PRINT : PRINT "Try again. Say a different name." PRINT "And be reasonable." END IF NEXT i IF br ^ 1 THEN GOTO BeReasonablc OPEN filenames FOR INPUT AS #1 ELSE br = 0 FOR i = 1 TO LEN(COMMANDS) IF MID$(COMMAND$, i, 1) = " " THEN PRINT "Be reasonable.": br NEXT i IF br = 1 THEN PRINT "Be Reasonable. Say a different name.": STOP filenames = COMMANDS OPEN filenames FOR INPUT AS #1 END IF RETURN

FoolTheComputcr: INPUT #1, 11, mm, nn PRINT "You arc finding"; 11; "merged constants" PRINT "from"; mm; "separate fits" PRINT "consisting o f; nn; "measured constants." PRINT RETURN

ReadFile: PRINT : PRINT nconst(O) = 0 FOR i = 1 TO mm INPUT #1, nconst(i) PRINT "Fit #"; i ; " contains"; nconst(i); "constants." NEXT i INPUT "Press < return > to continue . . .", r$ FOR i = 1 TO 11 INPUT #1, parmnameS(i) PRINT "Parameter #"; i; "is caled "; parmnameS(i); NEXT i INPUT "Press < return > to continue . . .", r$ PRINT : PRINT 139

FOR i = 1 TO nn FOR j = 1 TO 11 INPUT #1, x(i, j) xtrans(j, i) = x(i, j) PRINT x(i, j); NEXT j PRINT NEXT i INPUT "Press < return > to continue . . r$ PRINT : PRINT count% = 0 FOR k = 1 TO mm count% = count% + nconst(k - 1) FOR i = 1 TO nconst(k) FOR j = 1 TO i INPUT #1, x phiinv(i + count%, j + count%) = x phiinv(j + count%, i + count%) = x NEXT j, i, k OPEN "tmp-phi" FOR OUTPUT AS #2 FOR i = 1 TO nn FOR j = 1 TO nn PRINT #2, USING " # # .# # # # ~ '~ " ; phiinv(i, j); NEXT j PRINT #2, " " NEXT i CLOSE # 2 PRINT "You don’t really want to see the phi matrix . . PRINT "But you can find it in the file tmp-phi." INPUT "Press < return > to continue . . r$ PRINT : PRINT FOR i = 1 TO nn INPUT #1, y(i, 1) PRINT "Measured constant #"; i; "has the value"; y(i, 1); NEXT i INPUT "Press < return > to continue . . r$ CLOSE #1 RETURN

PrintResults: OPEN fout$ FOR OUTPUT AS #2 FOR i = 1 TO 11 PRINT #2, USING " \ \ = ##.########------( + / - # # .# # # ~ ~ 7 ' ; parmname$(i); beta(i, 1); (temp2(i, i) * sigma2(l, 1)) ~ .5; IF ABS(beta(i, 1)) < 2 * (temp2(i, i) * sigma2(l, 1)) ~ .5 THEN PRINT #2, " < -WARNING!!" ELSE PRINT #2, " " END IF NEXT i PRINT #2, " PRINT #2, " " PRINT #2, "Sigma = sigma2(l, 1) 140

PRINT #2, " * PRINT #2,"" PRINT #2, "Varriance-covarriance matrix:" PRINT #2," " PRINT #2, FOR i = 1 TO II PRINT #2, USING " \ \ ”; parmname$(i); NEXT i PRINT #2, " " PRINT #2, FOR i = 1 TO 11 PRINT #2,"...... NEXT i PRINT #2, " " FOR i = 1 TO 11 PRINT #2, USING "\ \ |parmnamc$(i); FOR j = 1 TO i PRINT #2, USING " # # .# # # # ~ ~ " ; tcmp2(i, j) * sigma2(l, 1); NEXT j PRINT #2, " " NEXT i PRINT #2, CHR$(12) CLOSE # 2 OPEN fout$ FOR INPUT AS #1 DO INPUT #1, dump$ IF dump$ < > CHR$(12) THEN PRINT LEFT$(dump$, 78) LOOP UNTIL dump$ = CHR$(12) CLOSE #1 RETURN A ppendix F

SIM.BAS CONV.FOR

Programs for the simulation of spectra and conversion into Bruker format.

141 142

S1M.BAS

This program will take a list of spectral lines and intensities and provide a lineshape and thus simulate a spectrum.

DECLARE FUNCTION RotDist# (B#, j%, T#) DECLARE FUNCTION Gaussian# (x#, mu#, sigma#) DEFDBL A-H, O-Z DEFINT I-N

CLS Main: GOSUB GetFileName GOSUB SetParams GOSUB SimSpectrum ’GOSUB Result GOSUB Makefile END

GetFileName: IF LEN(COMMANDS) = 0 THEN INPUT "File name? ", filenames ELSE filenames = COMMANDS END IF RETURN

SetParams: OPEN filenames FOR INPUT AS #1 INPUT #1, simrcs INPUT #1, hwhm INPUT #1, wavehigh INPUT #1, wavelow DIM total(INT((wavehigh - wavelow) / simres)) INPUT #1, nlines RETURN

SimSpectrum: FOR i = 1 TO nlines INPUT #1, waveline, area, restS front = INT(((waveline - 6 * hwhm) / simres) + .5) * simres back = INT(((waveline + 6 * hwhm) / simres) + .5) * simres FOR x = front TO back STEP simres j = INT((x - wavelow) / simres) lotal(j) = total(j) + Gaussian(x, waveline, hwhm) * area NEXT x PRINT nlines - i NEXT i CLOSE #1 RETURN

Result: FOR j = 1 TO INT((wavchigh - wavelow) / simres) PRINT j, j * simres + wavelow, total(j) NEXT j RETURN

MakeFile: OPEN "sim.out" FOR OUTPUT AS #1 PRINT #1, INT((wavehigh - wavelow) / simres) FOR j = 1 TO INT((wavehigh - wavelow) / simres) PRINT #1, j * simres + wavelow, totalCj) NEXT j CLOSE #1 RETURN

FUNCTION Gaussian (x, mu#, sigma) pi = 3.1414526536# prob = EXP(-.5 * ((x - mu#) / sigma) A 2) prob = prob / (sigma * (2 * pi) A .5) Gaussian = prob END FUNCTION 144

CONV.FOR

This program will convcr a file of x,y ASCII data into a format similar to that used by Bruker and readable by pprograms such as SPEAK (by Per Jensen) and GhostPlot (by Georg Wagner.) For a description of this format, sec the documentation of SPECON2 (by Per Jensen) and source code of SPEAK.

C PROGRAM conv LOGICAL LFILE

DOUBLE PRECISION XORD(20000),XFRQ(20000) double precision simres,XHI DIMENSION IOUT(256),ROUT(256) integer*2 i,p,x,dummy,middle CHARACTER*30 FILOUT,FILEIN,filctmp character*8 bitey.FNAM character*4 fnaml,fnam2 character* 1 Imp C C C SECTION 1 INPUT DATA FILE C WRITE(*,1140) 1140 FORMAT(lX,’Enter input file name: \ \ ) 1 READ(*,1020)FILEIN INQUIRE(FILE = FILEIN,EXIST = LFILE) IF(.NOT.LFILE)THEN WRITE(*,*)’FILE DOES NOT EXIST REENTER FILE NAME’ GOTO 1 ENDIF OPEN(3,FILE = FILEIN,STATUS = ’OLD’) C C SECTION 2 C READ # OF DATA POINTS C READ(3,*)INPT READ(3,*)(XFRQ(I),XORD(I), I = l.INPT) middle = inpt/2 simres=(XFRQ(2)-XFRQ(1)) simres= simres + XFRQ(middle + l)-XFRQ(middle) simres=simres+XFRQ(INPT)-XFRQ(INPT-l) simres = simres/3 XHI = XFRQ(INPT) + simres 355 WRITE(*,1010) 1010 FORMAT(lX,’Enter the name of the output file: ’,\) READ(*,1020)FILOUT filetmp = FILOUT 1020 FORMAT(A30) INQUIRE(FILE = FILOUT,EXIST = LFILE) IF(LFILE)THEN WRITE(*,*)’THIS FILE ALREADY EXISTS’ GOTO 355 ENDIF call left(FILOUT,bitcy,8,x) do 10 i = 1,8 call mid(bitcy,tmp,i,l,x) if (tmp.eq.7) p = i-l 10 continue call left(bitey,FNAM,p,x) call mid(FNAM,fnaml,1,4,dummy) call mid(FNAM,fnam2,5,4,dummy) 1025 OPEN(4,FILE = filetmp,STATUS = ’NEW’,ACCESS = ’DIRECT’, + FORM = ’UNFORMATTED’,RECL= 1024) WRITE(*,1021) 1021 FORMAT(lX,’Enter scale factor exponent:’,\) READ(*,1022)ISCL 1022 FORMAT(I4) C XFRQ(l) = (XFRQ(1)-1.7866756244)/.99993277919 C XFRQ(INPT) = (XFRQ(INPT)-1.7866756244)/.99993277919 C C ZERO OUT ARRAY AND WRITE 1ST RECORD C DO 1030 KK= 1,256 IOUT(KK) = 0 1030 CONTINUE IOUT(2) = fnaml IOUT(3) = fnam2 IOUT(4) = ’sim’ IOUT(65) = 2 IOUT(66) = INPT IOUT(69) = ISCL IOUT(70) = INT(XFRQ(1)) IOUT(71) = INT((XFRQ(1)-INT(XFRQ(1)))*1.6777216D + 07) IOUT(72) = INT(XHI) IOUT(73) = INT((XHI-INT(XHI))*1.6777216D+07) IOUT(74)=63*64*64 + 64+16 IOUT(75) = 2*64 + 58 + 4096 WRITE(4,REC=l)IOUT C C ZERO OUT ARRAY AND WRITE DATA C DO 1040 KK=1,256 ROUT(KK)=0 1040 CONTINUE C C THE DATA POINTS NEED TO START AT ITEM 65 OF REC C THEREFORE 192 DATA POINTS WILL FIT IN REC = 2 C C IBUFS= # OF FULL RECORDS NEEDED C 146

IBUFS=0 IF (INPT.GT.448) THEN BUFS = DBLE(INPT-192) /2.56D+02 IBUFS = INT(BUFS) ENDIF C C NCOUNT KEEPS TRACK OF THE POINT WE ARE AT IN THE INTERPOLATED C ORDINATE ARRAY C NCOUNT=0 C C WRITE DATA INTO REC = 2 C IEND = MIN0 (INPT.192) DO 1050 KK=1,IEND ROUT(KK + 64) = XORD(KK) 1050 CONTINUE WRITE(4,REC = 2)ROUT NCOUNT=NCOUNT+IEND C IREC=3 y IF (IEND .LT. 192) GOTO 2000 IF (IBUFS .EQ. 0) GOTO 1070 DO 1060 LL= 1,IBUFS C DO 1055 KK= 1,256 ROUT(KK) = XORD(KK + NCOUNT) 1055 CONTINUE WRITE(4,REC = IREC)ROUT IREC = 1 + IREC NCOUNT=NCOUNT+256 1060 CONTINUE C C NOW PROCESS DATA WHICH DOES NOT FILL A REC. C 1070 LEFTOV = INPT-256*IBUFS-192 IF (LEFTOV.LE.O) GOTO 2000 DO 1080 KK= 1,LEFTOV ROUT(KK)=XORD(KK + NCOUNT) 1080 CONTINUE NCOUNT=NCOUNT+LEFTOV DO 1090 KK=LEFTOV+1,256 ROUT(KK)=0 1090 CONTINUE WRITE(4,REC=IREC)ROUT 2000 CLOSE(3) CLOSE(4) CLOSE(ll) WRITE(*,*)’*** MISSION COMPLETED ***’ END