The lowest triplet state of tetramethyl-1,3-cyclobutanedithione

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Material Information

Title:
The lowest triplet state of tetramethyl-1,3-cyclobutanedithione
Physical Description:
xiii, 273 leaves : ill. ; 28 cm.
Language:
English
Creator:
Baiardo, Joseph Peter, 1946-
Publication Date:

Subjects

Subjects / Keywords:
Tetramethyl cyclobutanedithione   ( lcsh )
Triplet state   ( lcsh )
Phosphorescence   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre:
bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1982.
Bibliography:
Bibliography: leaves 265-272.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Joseph Peter Baiardo.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 028535672
oclc - 08910825
System ID:
AA00022661:00001

Table of Contents
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
    List of Tables
        Page vii
        Page viii
    List of Figures
        Page ix
        Page x
        Page xi
    Abstract
        Page xii
        Page xiii
    Chapter 1. Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
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        Page 13
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    Chapter 2. Results of ab initio SCF calculations on carbonyl analogues
        Page 15
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    Chapter 3. The T 1 S0 electronic transition in crystalline tetramethyl-1, 3-cyclobutanedithione
        Page 40
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    Chapter 4. Spin-orbit coupling in tetramethyl-1, 3-cyclobutanedithione
        Page 90
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    Chapter 5. Zeeman spectroscopy of tetramethyl-1, 3-cyclobutanedithione
        Page 122
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    Chapter 6. Conclusions and suggestions
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    Appendix I
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    Appendix II
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    References
        Page 265
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    Biographical sketch
        Page 273
        Page 274
        Page 275
Full Text


















THE LOWEST TRIPLET STATE OF
TETRAMETHYL- 1, 3-CYCLOBUTANED ITHIONE














By

JOSEPH PETER BAIARDO

















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA 1982












r



In memoria di mio padre Ottavio Nino

e per la mia cara madre Gisella






and to my wife Nancy, whose love, encouragement and endless sacrifices kept my spirit alive and whose terrific menu did wonders for me;



to Joseph, your daily welcome home dash and embrace made everything bearable;



to Jonathan, your eagerness to help me was always my inspiration;



and Justin, your echoes and answering service has been the song in my mind.



To all of you who somehow managed to transform the daily valleys into peaks.


















ACKNOWLEDGEMENTS

I would like to express my deepest appreciation to Professor Martin T. Vala whose encouragement and optimism coupled with his sage advice and infinite patience over the years have been a source of inspiration without which this work would not have been possible.

I gratefully acknowledge Dr. Ib Trabjerg who spent countless hours recording the Zeeman spectra.

To my fellow students, past and present, thank you for sharing good times and bad and for giving an ear when it was needed the most.

To Drs. Jean Claude Rivoal, Ranajit Mukherjee and Marek

Kreglewski, I owe a great deal of thanks for the many stimulating discussions and timely advice which they shared with me.

Special thanks are due to the Northeast Regional Data Center

for making available the many hours of computer time over the years.

And of course to Ms. Joan Raudenbush, whose long hours of patient typing made possible the speedy completion of this work without sacrificing quality, I owe a great many thanks.

I wish to thank Professor William Weltner for helpful discussions on some parts of Chapter 5, and Professor M. Vala and our draftsman, Jeff Pate, for drafting most of the figures.

I am grateful to Professor Willis Person for his encouragement over the years.


iii

















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ----------------------------------------- iii

LIST OF TABLES ------------------------------------------- vii

LIST OF FIGURES ------------------------------------------ ix

ABSTRACT ------------------------------------------------ xii

CHAPTER

1. INTRODUCTION ---------------------------------------- 1

General Background ------------------------------- 1
Motivation and Direction ------------------------- 11

2. RESULTS OF ab initio SCF CALCULATIONS ON CARBONYL
ANALOGUES ------------------------------------------ 15

Computational Details ---------------------------- 24
Results and Discussion --------------------------- 25

Ionization Potentials -------------------------- 25
Excited nTr* States ---------------------------- 27

3. THE T -I- S 0 ELECTRONIC TRANSITION IN CRYSTALLINE
TET 6THYL-1,3-CYCLOBUTANEDITHIONE ---------------- 40

Introduction ------------------------------------- 40

Spectroscopic Technique ------------------------ 40
Crystal Symmetry ------------------------------- 41
Crystal States --------------------------------- 43
Effect of External Fields ---------------------- 44

Features of Crystal Spectra ---------------------- 45

Crystal Vibrations ----------------------------- 45
Electronic Absorption -------------------------- 47






iv











Crystal Structure------------------------------------- 49

Crystal Growth------------------------------------- 53
Crystal Orientation-------------------------------- 54

Experimental Details---------------------------------- 55
Results----------------------------------------------- 5

Low Temperature----------------------------------- 5
Temperatures Above 10K----------------------------- 59

Vibrational Analysis of the T 1 S oTransition ---------61
The~~~~~~ o- ad------------------- 6
The 300 Ban------d----------------------------------61
The 300 cm-1 Band----------------------------------- 62
The 600 cmi1 Band----------------------------------- 65
Thearz970 cnr1 Bn-----------------------------------65
Polarzto -----c-------------------------------------65


Crystal Vibrations in TMCBDT-------------------------- 67
The Double Minimum Potentials------------------------- 70

Fitting Procedure and Results-----------------------70
The Calculated Spectra at 1.6K--------------------- 75
Temperature Dependence of Spectra------------------- 80
Physical Nature of DM2----------------------------- 80

Summary------------------------------------------------ 88

4. SPIN-ORBIT COUPLING IN TETRANETHYL-l, 3-CYCLOBUTANEDITHIONE-------------------------------------------------- 90

Introduction------------------------------------------- 90
T ~-S Crystal Transition Moment for TMCBDT -----------90
1o
Evaluation of Matrix Elements: and ---------- 98
so

Spin-orbit Hamiltonian ------------ ----------- 98
Choice of Wavefunction----------------------------- 98
Evaluation of < H so> With Respect to EHT Wavefunctions----------------------------------------- 102
Transition Moments With Respect to EHT Wavefunctions------------------------------------------ 107
Choice of Parameters Used in the Calculation ------111

Results----------------------------------------------- 111
Summay----------------------------------------------- 121

5. ZEEMAN SPECTROSCOPY OF TETRAMETHYL-l,3-CYCLOBUTANEDITHIONE----------------------------------------------- 122

Introduction------------------------------------------ 122
Theory------------------------------------------------ 125

v










Zeeman Intensity Ratio for an Arbitrary Field
Direction ------------------------------------------ 126
Polarized Zeeman Absorption ------------------------- 129
Unpolarized Zeeman Absorption ----------------------- 136
Zero-field Absorption (ZFA) ------------------------- 137

Effect of Zero-Field Splitting Parameters ------------- 138
Calculation of Zero-Field Splitting Parameters --------- 145

Influence of Triplet-State Perturbers --------------- 147
Localized and Delocalized Excitation ---------------- 152

Comment on Xanthione ----------------------------------- 153
Experimental Details ----------------------------------- 156

Apparatus ------------------------------------------- 156
Crystal Mounting ------------------------------------ 157

Experimental Results ----------------------------------- 163

Low Temperature Results: 1.6 K ---------------------- 163
Temperatures Above 4 K ------------------------------ 164
Measurement Errors ---------------------------------- 176

Discussion --------------------------------------------- 180

Temperatures above 4 K ------------------------------ 180
Zeeman Ratio as Function of R R and ----------- 187
Summary --------------------- ------------------- 201

Low Temperature and Field Dependent Results ------------ 202
Discrepancies ------------------------------------------ 213


R and g Tensor Consideration ------------------------ 213

Summary of Zeeman Absorption Experiments --------------- 222

6. CONCLUSIONS AND SUGGESTIONS ----------------------------- 224

APPENDIX I ------------------------------------------------- 230
APPENDIX II ------------------------------------------------- 248

REFERENCES -------------------------------------------------- 265

BIOGRAPHICAL SKETCH ----------------------------------------- 273










vi

















LIST OF TABLES

TABLE Page

2-1. ATOMIC COORDINATES FOR TMCBD AND CBD -----------------36

2-2. ORBITAL ENERGIES FOR CBD, TMCBD (ab initio, D 2h) 37

2-3. VERTICAL TRANSITION ENERGIES (ASCF) FOR THE 1'3n 7T*
STATES CALCULATED USING D2h WAVEFUNCTIONS ------------ 38

2-4. OMPARISON OF VERTICAL TRANSITION ENERGIES (ASCF) of
n 7* OF TMCBD STATES WITH OBSERVED AND SEMIEMPIRICAL
METHODS ----------------------------------------------39

3-1. VIBRATIONAL ANALYSIS OF T 4- S ABSORPTION OF CRYSTALLINE TMCBDT POLARIZED PER4ENDCULAR TO c ------------- 63

3-2. (STATIC) CORRELATION BETWEEN MOLECULAR (SITE) GROUP
AND FACTOR GROUP -------------------------------------66

3-3. DMP DESCRIPTION OF THE LOW FREQUENCY VIBRATIONS OBSERVED AT 1.6 K IN CRYSTALLINE TMCBDT SPECTRA -------- 72 3-4. CORRELATION TABLE FOR THE DISTORTED MOLECULAR EXCITED
STATE -----------------------------------78

4-1. PARAMETERS USED IN EHT CALCULATIONS ------------------112

4-2. CONTRIBUTIONS TO T S TRANSITION MOMENT FROM
SINGLET STATE PERTRBATIONS OF T nT *) ------------ 115
1+

4-3. CONTRIBUTIONS TO T + S TRANSITION MOMENT FROM
TRIPLET STATE PERTRBERS OF S -----------------------116
0

4-4. TRANSITION MOMENTS, OSCILLATOR STRENGTHS AND LIFETIMES
OF THE TRIPLET SUBLEVELS -----------------------------119

5-1. MOLECULAR AXES IN UNIT CELL FRAME AND THEIR DIRECTION
COSINES WITH RESPECT TO H ----------------------------133

5-2. OBSERVED RATIOS FOR THE ZEEMAN ABSORPTION (CRYSTAL B)
OF THE 5943 A BAND AT 16 K AS A FUNCTION OF POLARIZER
ANGLE ------------------------------------------------168





vii












5-3. OBSERVED RATIOS FOR THE ZEEMAN ABSORPTION (CRYSTAL
C) OF THE 5943 A BAND AT 5 K AS A FUNCTION OF
POLARIZER ANGLE---------------------------------------- 171

5-4. ZERO-FIELD ABSORPTION VS. POLARIZATION--------------- 184

5-5. OBSERVED A VALUES FROM FIELD DEPENDENT ABSORPTION
OF 5943 A BAND AND EMISSION OF 6003 A TRAP----------- 186

5-6. COMPARISON OF CALCULATED TO EXPERIMENTAL ZEEMAN
MEASUREMENTS AT 1.6 K---------------------------------- 206

5-7. POLARIZED ZEEMAN ABSORPTION INTENSITIES FOR CRYSTALS B AND C------------------------------------------- 210

5-8. INTENSITIES FOR CRYSTAL C CALCULATED USING X--+2,
Y=Z=-1 --- -------------------------------- 218












































viii
















LIST OF FIGURES

Figure Page

2-1. Through-space and through-bond interactions in TMCBD------------------------------------------- 18

2-2. Density and contour maps for the n +(b lu) and n_(b 3 ) molecular orbitals of CBD------------------ 20

2-3. Net orbital populations for CBD in C----------------31
S
2-4. Molecular orbitals and their one-electron energies for TMCBDT as calculated by Extended Hflckel
method--------------------------------------------- 34

3-1. Orientation of TMCBDT molecules within the tetragonal unit cell------------------------------- 50

3-2. Low temperature absorption spectrum of single crystal TMCBDT polarized perpendicular to c --- 58

3-3. Absorption spectrum of single crystal TMCBDT at 20 K and 47 K-------------------------------------- 60

3-4. Double minimum potential for ground state ----------73

3-5. Double minimum potential for triplet excited state- 74

3-6. Simulated absorption and emission spectra calculated using the DMP model as a function of temperature-- 82

3-7. Molecular displacements involved in the B 2glattice vibration -- - - -- - - 86

5-1. Coordinate system used in the derivation of Zeeman intensities for an arbitrary magnetic field
orientation in the Faraday configuration ----------131 5-2. Effect of zero-field-splitting parameters on the Zeeman spectra-------------------------------------- 141

5-3. Light-pipe and coils assembly used in the Zeeman experiments---------------------------------------- 158






ix










5-4. Zeeman absorption spectrum at 1.6 K of the
594 rn band of single crystal TMCBDT polarized Perpendicular to c----------------------- 160

5-5. Unpolarized Zeeman absorption spectrum at 1.6 K
of the 594 rn band of single crystal TMCBDT ------162

5-6. Polarized Zeeman absorption spectra of the
594 nm band at 16 K as a function of polarizer
orientation-------------------------------------- 166

5-7. Polarized Zeeman absorption spectra of the
594 nm. band at 5 K as a function of polarizer
orientation-------------------------------------- 170

5-8. Polarized zero-field absorption spectra of the
594 nm band at 5 K as a function of polarizer
orientation------------------------------------- 173

5-9. Unpolarized Zeeman absorption spectra of the
594 rn band at 5 K as a function of magnetic
field strength----------------------------------- 175

5-10. Unpolarized Zeeman emission spectra of the
600 nm trap at 5 K as a function of magnetic
field strength----------------------------------- 178

5-11. Effect of on the calculated Zeeman intensity
ratio for ~=5* and one spin-orbit route in the
absence of zero-field splitting------------------ 189

5-12. Effect of c on the calculated Zeeman intensity
ratio for 4 =20* and one spin-orbit route in the
absence of zero-field splitting------------------ 191

5-13. Effect of z spin-orbit route on the Zeeman intensity ratio in the absence of zero-field splitting---------------------------------------------- 193

5-14. Effect of x spin-orbit route on the Zeemnan intensity ratio in the absence of zero-field splitting---------------------------------------------- 195

5-15. Comparison of the calculated Zeeman ratio for the
y spin-orbit route with average experimental
ratios as a function of polarizer orientation--- 198

5-16. Comparison of the theoretical Zeeman ratio using
the transition moments determined from the EHTspin-orbit-coupling calculation ------------------200




x










5-17. Simulated Zeeman spectra of crystal A for the
two molecules in the unit cell and their sum --- 207

5-18. Simulated Zeeman spectra of crystal F for the
two molecules in the unit cell and their sum --- 209

5-19. Plot of calculated and experimental band positions as a function of magnetic field strength for D>O and spin axes coincident with molecular
symmetry axes --------------------------------- 214

5-20. Plot of calculated and experimental band positions as a function of magnetic field strength for D< 0 and spin axes coincident with molecular symmetry axes ---------------------------- 215

5-21. Plot of calculated and experimental band positions
as a function of magnetic field strength for the
case of non-coincident molecular symmetry and spin
axes ------------------------------------------ 217





































xi

















Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

THE LOWEST TRIPLET STATE OF
TETRAMETHYL-I,3-CYCLOBUTANEDITHIONE

By

Joseph Peter Baiardo

May, 1982

Chairman: Martin T. Vala
Major Department: Chemistry

The lowest energy band in the absorption spectrum of tetramethyl-l,3-cyclobutanedithione (TMCBDT) is determined to be due
3 1A
to A (n T*) A by Zeeman spectroscopy. The polarized single
u g

crystal absorption spectrum in zero field at 1.6 K consists of bands polarized exclusively perpendicular to c, with the 0-0 band at 594.3 nm. A model in which a double minimum potential (DMP) in both the ground and excited states, involving either a ring torsion mode or a lattice mode, is shown to account for the observed temperature dependence of the spectra. Vibrations observed
-i
in the triplet region are assigned to the C=S stretch at 970 cm ,
-i
skeletal vibrations at 309 and 600 cm and a C-C stretch or
-i
methyl bend at 913 cm

A detailed analysis of spin-orbit-coupling (SOC) in TMCBDT predicts that this transition should be polarized exclusively along the
3
C=S bonds, in agreement with experiment, and that two B 2g,nT*




xii










states significantly perturb the ground state and contribute 60% of the free molecule transition moment via T n T1 allowed transitions.
1 1 *
The most influential singlet state perturbing T1 is the B2u, 7rT state which adds 18% to the transition moment.

An expression for the Zeeman intensity for an arbitrary magnetic field orientation in the Faraday configuration, is derived. It is shown that the observed polarization dependence is due to field misalignment rather than multiple spin-orbit routes and that the observed Zeeman data is consistent with the SOC calculation results.

Field-strength-dependent Zeeman spectra demonstrate that the zero-field splitting (D) in single crystal TMCBDT is smaller than that found for xanthione by Burland. The SOC contributions to D are discussed in terms of localized vs. delocalized excited states and it is shown that both the extent of excitation-localization and the singlet-triplet splitting of perturbing states are important.

An orbital symmetry unrestricted calculation (double-) is

performed at the ab initio SCSCF level on the parent molecule cyclobutanedione. It is found that the localized description of the 1,3nTT* (and 2n) states gives a transition energy (and ionization potential) which is more in accord with experiment than that given by the delocalized solutions to the SCF equations. These results are used to qualitatively discuss the effect of localization on the SOC contributions to D.








xiii

















CHAPTER 1
INTRODUCTION

General Background

Within the framework of molecular orbital (MO) theory the

lowest energy electronic transition of a single carbonyl group is described as arising from the promotion of an electron in the highest occupied MO, the nonbonding lone pair of oxygen (n), to the lowest unoccupied MO, the antibonding carbonyl Tr orbital (iT*). This has come to be known as a T*- n (or n 1T*) transition and usually occurs in the near-ultraviolet region of the spectrum. This explanation was made by McMurry in 1941 in a spectroscopic study of aldehydes and ketones (1).

In a subsequent study of dicarbonyl compounds, McMurry (2) described the interaction of the carbonyl groups in terms of the simple LCAO-MO theory by taking symmetric and antisymmetric (+ and -) linear combinations of both the n orbitals and Tr* orbitals. He considered the n orbitals as strictly localized on the oxygen atoms and not interacting while he allowed for an interaction between the 7* orbitals thereby introducing a splitting between theTr* and7T* MO's (the latter being of higher energy due to an additional node). This was rationalized on the basis of the conjugative properties of ff orbitals and explained the observed splitting of the lowest n 7* carbonyl band in the dichromophoric compounds. In 1955 Sidman and




1





2




McClure (3) applied McMurry's approach in their study of the electronic spectra of the c-dicarbonyl biacetyl; they explained the split n r* band in this compound in terms of transitions from the degenerate n+ and n MO's to the split T* and T* MO's.

Tetramethyl-l,3-cyclobutanedione (TMCBD), a -dicarbonyl which has been studied recently by Vala and his coworkers (4-9), was first studied spectroscopically by LaLancette and Benson (10) in 1961 and in 1963 by Kosower (11). Kosower interpreted the solution spectrum of TMCBD in terms of two n 7T* transitions (in the region 225 nm to 375 nm) resulting from transannular interaction between the carbonyl TT* MO's, giving the split T* and 7T* linear combination. In 1970 Ballard and Park
+

(12) compared the solution spectra of TMCBD and TMCBDT and verified the observation of Kosower regarding the split n IT* band of TMCBD and concurred on the transannular interaction of the Tr* orbitals. In addition, however, they noted that if the n orbitals were also split, four symmetry forbidden n iT* transitions would then arise in TMCBD, twC of them A (n 7T* and n Tr*) and two B (n Tr* and n 7r*) as expressed
u +- + lg + +
in the D2h point group of the molecule. No indication of four nTT* transitions was reported by Ballard and Park, however.

For the corresponding dithione, on the other hand, Ballard and

Park (12) found that the solution spectrum contained a weak broad band in the region 400 to 625 nm having six poorly resolved maxima. These
-I
were assigned as vibrations because of the regularity of the 1460 cm spacing between the peaks and their approximate Gaussian distribution. Although Ballard and Park noted that the excited state frequency of
-l
the C=S stretch is expected to decrease from the %ii00 cm value in





3




the ground electronic state in response to the bond weakening due to
-i
the n r* transition, these authors nevertheless assigned the 1460 cm spacing to the C=S stretch. In addition they assigned a band at 294 nm as an n a* transition and another, very intense band, in which no splitting was observed, at 200 nm was assigned as ffff*. From these considerations Ballard and Park concluded that the n 1* band in TMCBDT is not split by a transannular Tr interaction as in the corresponding dione, and therefore suggested (12) that the transannular distance between the thiocarbonyl carbons must be greater in TMCBDT than in TMCBD.

At about this time the theoretical interpretation of interacting

chromophoric groups was revolutionized by Hoffman and coworkers (13-15) who, in a series of Extended Hdckel Theory (EHT) (16) and CNDO/2 (17) calculations, demostrated that the non-bonding orbitals in a molecule containing two or more symmetry related heteroatoms can interact by two different mechanisms and therby split. These mechanisms were termed through-space and through-bond interactions. Through-space interaction between two orbitals na and n for example, occurs when their spatial overlap Sab is significant. The transannular interaction mechanism invoked by Kosower and Ballard and Park, for example, is of this type. If Sab is small, however, the two orbitals na and nb may still interact indirectly via the a framework orbitals as follows. The linear combinations n+ and n- formed from na and nb are still degenerate; however, these now transform as two different irreducible representations of the molecular point group. If there is significant overlap between one or both of these linear combinations with a framework MO of the





4




same symmetry, usually lower in energy, then the n + and n -combinations will interact differently with the framework orbitals thereby splitting. Normally through-space interaction above is considered to produce the n- combination at higher energy, than the n + while the through-bond mechanism may destabilize the n + orbital more than the n and could result in n + lying above n -.

In 1971 Cowan et al. (13) using molecular photoelectron spectroscopy (PES) (19) determined experimentally the order and splitting of the n orbitals in TMCBD and several other dicarbonyl molecules. They found that in TMCBD the through-bond interaction causes n + to lie

0.7 ev higher in energy than n-. This was a significant result because it directly confirmed the prediction of Swenson and Hoffman (14) and suggested that Ballard and Park's (12) observation of the possibility of four n ir* transitions in TMCBD may be observable.

Using the powerful technique of low temperature single crystal

polarized absorption spectroscopy, Spafford et al. (7) later demonstrated that each of the two nWT* transitions previously observed (11,12) are further split into two n 7r* bands. Based on the polarization of bands, vibrational assignments, and crystal and site symmetries (discussed in Chapter 3) they were able to assign four singlet-singlet n ff* bands in the order A u < B 2g < B2g < A u (in D 2h ) by invoking a distorted geometry in each of the four excited states: C 2vin the first and third and C 2hin the second and fourth. The other important interpretations advanced in this work are the additional verification of the throughbond mechanism (Vide suPra ) and the introduction of a circumannular interaction whereby the 7T* orbitals are split because of a preferential destabilization of the Tr* orbital by the bonding a C(ring)-C(methyl)





5




orbitals; this is another manifestation of the through-bond interaction mechanism.

A theoretical analysis advanced by Baiardo et al. (8) compared

three semiempirical MO methods in their ability to correctly predict the four n ff* transitions in cyclobutane-l,3-dione (CBD) and TMCBD. It was found that the EHT method was more accurate and reasons were advanced for this; the mechanisms of through-bond interactions active in both the n-orbital and iT*-orbital splittings were said to outweigh the through-space mechanisms, in accord with the previously observed PES (19) results regarding the n orbital ordering and splitting.

Working independently Gordon et al. (20) simultaneously reported a very similar result for the n7T* transitions of TMCBD. The band positions agreed with those of Spafford et al. (7) but a different vibrational and electronic state assignment was given resulting in different excited state distortions and only three n f* bands. The fourth was assigned as a CH stretch vibronic origin based on comparison with d12 isotope spectra.

These are the first published reports of direct experimental

evidence for more than two nTT* transitions in a dicarbonyl molecule, thus providing additional experimental evidence for the n orbital and 7T* orbital splitting in these molecules.

Investigation of n orbital splittings has been intensely pursued in the azabenzenes and azanaphthalenes using PES by Heilbronner and his coworkers (21-23) and in the dicarbonyl compounds also using PES by Cowan et al. (19), Dougherty and McGlynn (24) and Dougherty et al.

(25).





6



Unlike their dicarbonyl analogues dithiocarbonyls have received very little attention spectroscopically over the years. The same comparison is true for the monochromophoric compounds, but to a lesser extent.

Thiophosgene has been studied by Brand et al. (26), Oka et al.

(27) and Okabe (28); thiobenzophenone by Gupta et al. (29) and a number of monothiones by Blackwell et al. (30). An important result of the work of Blackwell et al. (30) is the appearance of singlettriplet transitions in five out of the six compounds studied, which are not observed as readily in the corresponding carbonyl compounds. The aromatic thione, xanthione (XS), has been studied more extensively (31-36).

Bruhlman and Huber (33) studied the quenching of the XS triplet state in solution and determined the deactivation to be physical in nature and diffusion controlled. Similarly, in a study involving quenching of the XS triplet state by other thioketones and dithioketones (including TMCBDT) Rajee and Ramamurthy (34) concluded that the quenching process must take place by an "out of phase" contact, whereby the thio-carbonyl moieties approach and contact each other in an antiparallel fashion, and that the sulfur non-bonding orbital of the ground state molecule must be responsible for the quenching of the triplet n Tr* state. The interesting point in this work is that no photoproducts could be found even after more than 10 days of irradiation. Fuxthermore all the quenchers chosen had the lowest T state lying above that of XS precluding T-T energy transfer. This suggests that the sulfur atom of the quencher may have acted as an external-heavy atom inducing more efficient intersystem crossing to the ground state, possibly via a S-S exciplex.




7




More recently, Maki et al. (35) have reported a large zero-field splitting (D) in the XS lowest triplet state (in an n-hexane matrix at I.1K) and attributed it to spin-orbit perturbation of TI.
-i -i
Burland (36) determined the splitting to be -11 cm and -20 cm for the two sites of XS doped into xanthone host crystals.

While most of these authors emphasize the role of spin-orbit

effects in the spectra and zero-field splitting (35,36) of the triplet state, only Maki et al. (35) have advanced a reasonable, though limited, account of the spin-orbit activity in xanthione. A recent review of the interesting thiocarbonyl photochemical properties has recently been given by de Mayo (37).

Very little work has been done on the dithiocarbonyl compounds. Of particular interest here is the crystal structure determination of TMCBDT by Shirrell and Williams (38) in 1973; they found that the transannular distance in TMCBDT is equal (within experimental error,
0
less than 0.01 A) to that of TMCBD, which unambiguously refuted the arguments of Ballard and Park, discussed previously.

Soon after this, work began in this laboratory (39) on the single crystal polarized absorption spectrum of TMCBDT at 12'K with the aim of searching for multiple nTr* transitions as found for TMCBD (7). However, due to difficulties with the handling of the crystals and the varying crystal habit progress was slow. Concurrently, in an investigation of the bisimines of TMCBD, Worman et al. (40) reassigned the TMCBDT solution spectrum in the light of Shirrell and Williams' work, as being due to two nTr* transitions split because of the n orbital interaction, which was as yet unconfirmed by direct PES measurements. These were carried out in 1977 by Behan et al. (41) and it was





8





found that the n orbital splitting in TMCBDT is 0.42 ev, the orbital order (n +above n- or vice versa) was not given, however. This PES result was later confirmed by Basu et al. (42) who also reported the n orbital splitting as 0.42 ev; in addition, these workers suggested the appearance of four n T* transitions in TMCBDT based on a room temperature (presumably) unpolarized single crystal spectrum, the PES results and analogy to TMCBD (7,8). This is unfortunately no more informative than Ballard and Park's solution spectrum; the lack of polarization and vibrational resolution renders these experimental findings speculative.

In 1979 a definitive experiment was reported (43) which unambiguously showed that the lowest energy band in the TMCBDT single crystal spectrum was a singlet-triplet transition: the low temperature high field Zeeman absorption spectrum recorded by Trabjerg and Vala (44). Also reported at that time was a detailed account of the spin-orbit activity and the nature of the perturbing states in the free molecule as well as the emission spectrum of TMCBDT single crystals in the temperature range 1.6 K-16 K. The result of the latter experiments is that the emission is found to occur solely from traps and not from the exciton band (43).

Gordon et al. (45) recently reported the polarized single crystal spectrum of TMCBDT at 4 K. Their results are in agreement with Trabj erg et al. (43) on the 3A assignment of the lowest energy transition, however their published spectrum shows that the 0-0 band of the triplet is more than twice as intense as the singlet ( 1A uor 1B l vibronic origin of the same nTr* transition. Their assignment to





9



3 -i
3A of the lowest energy band (16829 cm for TMCBDT-h 2) is u 1

based solely on the basis of the appearance of a single origin in a single polarization which is consistent with the spin-orbit activity in TMCBD (6,20). No attempt is made to explain the dis3 1
crepancy of intensities in the A vs. A transitions. Trabjerg et al. (43) on the other hand reported that the singlet transition is much more intense than the triplet.
1
Gordon et al. (45) also report two n TT* transitions with nearly
-i 1Bg
degenerate vibronic origins near 18000 cm ( A ) and "probably"
u lg
-i
the other set at about 19500 cm Their spectra as reported (45) show remarkably little vibrational structure for a 4*K single crystal
-i
sample examined with polarized light. In the region 18000 cm to 23000cm-I, (both Ic and 11c polarizations) for example, only 22 bands and 17 shoulders can be discerned. Work on this same system has shown that in fact over 100 bands can easily be resolved.

A strict interpretation of the analogies to TMCBD used by Gordon et al. (45) in their TMCBDT assignments should include the circumannular type of through-bond interaction (7,8) to describe the Tr*
1
splitting. The assignments of the n 7* transitions proposed by Gordon et al. (45) however preclude any T* orbital splitting.

Work on the interesting molecule tetramethyl-3-thio-l,3-cyclobutanedione (TMTCBD) has also been reported (42,46), and although
-i
most bands are disappointingly broad (FWHM as large as 1000 cm and as small as 150 cm- ) (46) the assignments (46) demonstrate that the thiocarbonyl and carbonyl chromophores act fairly independently. Assignments to 3A2 and IA2 (nlr* of C=S) states and a 3A 2(n~r* of C=O) 2f 2=02





10




state were made for bands appearing at ca. 17050 cm 18350 cm and 27430 cm- 1.

While Hoffman's explanation of the n orbital splitting (An) using MO theory has been successful in most cases (21-23) Wadt and coworkers (47,48) have demonstrated that, in the case of pyrazine, an equally accurate description of An can be given using a ValenceBond (VB) approach. They showed that the observed (21) order of the n and7T orbitals can be predicted from a configuration interaction approach using a double zeta basis. Furthermore, the n7T* excitation energies are also well reproduced. The outstanding feature of the method is that the n orbitals are split while remaining 90% localized on the nitrogen atoms. Thus an electron excited out of an n orbital can be treated as coming from one nitrogen only, leaving a "localized hole". This is referred to as the localized excitation picture.

In contrast Hoffman's interaction scheme mixes a orbital character into the n orbitals and vice versa resulting in nonbonding orbitals which are delocalized, sometimes extensively, in the a molecular framework (8). An excitation out of the nonbonding orbital now has to be regarded as delocalized; i.e., the hole is now distributed over a large portion of the molecule.

The effect of localization is to lower the ionization and excitation energies. This effect has been investigated by various authors and confirmed (47-53); the amount of energy lowering depends on the symmetry constraints on the wave functions and can vary from one to two or more electron volts. It may happen, however, that the energy lowering can be overcompensated and the calculated result then lies below





11




the experimental one. Thus the results should be used with caution when comparing absolute energies. Inclusion of a modest amount of configuration interaction, however,seems reliable (48). The PES spectrum of pyrazine has been calculated by Von Niessen et al. (54) using a many-body Green's function approach and the orbital ordering and energies compare very well both with experiment (21) and VB calculations (48).

Motivation and Direction

As discussed above, the conclusion of Ballard and Park (12)

regarding the absence of a n 7* splitting in the lowest absorption band in the TMCBDT solution spectrum is subject to question in light of the finding by Shirrell and Williams (38) that the transannular distance in TMCBD and TMCBDT is the same. Furthermore the number of bands in the solution spectrum (12) is greater than that expected for the n Tr* transition region, even if all four transitions in fact occur as in TMCBD (7). Thus in view of the greater spin-orbit activity due to the sulfur atoms it seemed likely that one or more of the weakest bands in the solution spectrum of TMCBDT could be due to direct singlettriplet absorption.

In view of the excellent results obtained in this laboratory (7) and by others(20) using the low temperature single crystal polarized absorption technique, it was decided that its application to TMCBDT was necessary to elucidate the nTr* region in this interesting molecule. In addition, the availability of a high field pulsed Zeeman apparatus

(55) made the investigation of the Zeeman absorption and emission spectra of TMCBDT possible and desirable.





12




The spin-orbit activity of carbonyl compounds as applied to absorption and emission involving singlet-triplet transitions is well understood; howeveras pointed out above very little has been done in this regard for thiocarbonyls. Thus a fairly detailed semiquantitative study has been carried out for TMCBDT using conventional methods (56). Due to the expected proximity of the 3B 2gnjr* states to the lowest 3A state in TMCBDT and the generally lower energies in these states compared to corresponding carbonyl compounds (31), special attention is directed toward the perturbation of the ground electronic state by these triplet states and the ensuing intensity borrowing from electronically allowed triplet-triplet transitions (56).

As a result of the crystal structure of TMCBDT, electronic

transitions polarized along the C=S bonds and out of the molecular plane cannot be distinguished by polarization measurements as in the case of TMCB3D. Polarized Zeeman absorption measurements are therefore indicated to ascertain the extent of these two intensity contributions

(57). The third direction, in-plane but I to the C=S bond axis, can be distinguished from the other two directions by the zero-field polarization measurements.

The excellent work by Maki et al. (35) and Burland (36) demonstrating the existence of a large zero-field splitting (zfs) in the aromatic monoketone xanthione, has stimulated interest in the effects of the zfs on the TMCBDT Zeeman spectrum. Since this effect in xanthione has been attributed to spin-orbit coupling, examination of spin-orbit contributions to the zfs in TMCBDT is carried out. Now two interesting questions arise.





13




(1) What are the effects of the two sulfurs on the zfs of TMCBDT? (2) How does the localization or delocalization of the observed 3nTT* transition and/or the perturbing triplet states affect the magnitude of the zfs? Theoretical work on the localized excitation effects (47-53) has thus far been restricted to the determination of excitation energies, ionization potentials, and orbital splittings. Although application of the Generalized Valence Bond technique (58) to the calculation of force constants has produced good results (59), determinations of other properties has not been done to our knowledge.

with these considerations in mind a qualitative investigation of these effects is carried out for TMCBDT in connection with the Zeeman study. The discussion makes use of some recent ab initic calculations on TMCBD and CBD which have been carried out in this laboratory; the results of this work have been reported elsewhere (60). Because these calculations are performed on the carbbnyl analogues of TMCBDT and due to the lack of configuration interaction at present, only those results necessary for the qualitative discussion of the localization effects as they apply to the TMCBDT zfs discussion are included in this work. For comparison the results of the ENT calculation of the TMCBDT nlT* energies are also included.

The results of the ab initic calculations are given in Chapter 2. The 3A u- 1 A absorption spectrum of single crystal TMCBDT is given in Chapter 3. Effects of lattice vibrations and the possible excited state distortion are discussed in terms of double minimum potentials in the ground and excited electronic states. The temperature dependence





14




of the absorption and emission (discussed elsewhere, (43))are predicted using this model.

In Chapter 4 the spin-orbit coupling calculations are presented and the relative contributions to the crystal transition moment are discussed.

Because of apparent inconsistencies in the early polarized Zeeman absorption measurements, the effect of field alignment on the observed Zeeman splitting pattern is investigated theoretically using equations derived for a general field orientation with respect to the unit cell axes. This is included in Chapter 5 along with the interpretation of the Zeeman spectroscopy of the (n7T*) 3A u -1A transition in TMCBDT. Discussion of the spin-orbit effects on the zfs parameters is also given in Chapter 5; the results of the calculations presented in Chapter 2 are used to discuss qualitatively the effects of spin-orbit coupling on the zfs parameters.

Finally, in Chapter 6 the work is summarized and suggestions for future research are given.

















CHAPTER 2
RESULTS OF ab initio SCF CALCULATIONS ON CARBONYL ANALOGUES

In a previously reported study on the spectroscopy of the multiple n ff* singlet-singlet transitions (7) Baiardo et al. (8) compared the ability of the EHT and CNDO (/2 and /S) methods to predict the observed in Ir* transitions in TMCBD (4). For this molecule the highest
1
occupied MO's have been assigned as n+ (b lu) lying above n_(b 3g) in the PES work of Cowan et al. (19) and Dougherty et al. (25), in agreement with the semiempirical MO calculations. Since the observed order
1
of the n 7T* excited states was found to be (4) A < B2g < B2g < A the T* (b ) T* (b ) orbitals must be ordered with the + lying above
+ 3u 2g
the -, in agreement with EHT but not with either CNDO parameterization. The resulting excitation energies as calculated in the three methods showed that EHT gave the best correlation with the observed spacings
1
between the n states, while CNDO/S-SECI gave the best correlation with the lowest A state, differing from the experimental result by
u

only 0.02 ev. For this reason and because of its simplicity the EHT method was chosen for the spin-orbit-coupling calculations in this study (Chapter 4).


1. The choice of axis system here does not follow the conventional one
as given by R. S. Mulliken, J. Chem. Phys. 23, 1997 (1955). Instead, z was arbitrarily chosen parallel to the crystal c axis in the later
chapters and x out of plane. This differs also from that used in
ref. 8.





15





16




Making use of Hoffman's ideas (14-16) the observed ordering of excited n T* states was explained by a through-bond mechanism applied to the n and 7* orbitals. Here it was necessary to invoke the so-called "circumannular" interaction of the 7* orbitals (+ and linear combinations) through the relay orbitals localized in the C (ring)-C(methyl) bonds; it was argued that this effect must dominate the through-space, or "transannular", interaction for the observed state order to be consistent with the PES assignment of the n orbital order (19,25). These mechanisms are diagrammed in Fig. 2-1.

As a result of the through-bond interaction the n orbitals are delocalized in the ring. The extent of this delocalization is demonstrated by means of orbital contour and orbital density plots in Fig. 2-2a for the n +(b lu) and Fig. 2-2b for the n_(b 3g) molecular orbitals. These plots were made with molecular orbitals from an ab initio SCF calculation for CBD(61).

Further work was initiated to obtain excited state energies for the 1n i* and 3n W* states of TMCBD and CBD. The spacings between the n T* states could then be compared with experiment (7). The results of these calculations relevant to later discussions (Chapter 5) are presented in this chapter. It would also be interesting to apply the method of Wadt and coworkers (47) to CBD to see if the n orbital splitting and n1T* state splittings could be reproduced.

Additional motivation for this came from the work of Hehenberger

(51) on the (localized) calculation of furan ionization potentials and Jonkman's (53) study of the lowest n7T* excited states of


1. The term "relay orbitals" in through-bond interaction was coined by
Heilbronner and Schmeltzer (Helv. Chim. Acta 58, 936 (1975)) to
describe the common orbital which causes the n orbitals to split.



















4.) 13 En tr
z
4-) (d
0 0
+ .0

0 r rl) 41 0
4 ((1 1 4
U) (1) u
z 0 41
0 4-) 0
> 4 -1-1 C: 4-4 Q) (n
a) U) 4 lq 0 a)
4-) 4 4
4) 0
C r.1 4-)
4 -W 4-) U)
a) 14 En 4 fa
(d 0)
4 0 ra
0) 0 z
4.) 4-) 0 4-) 4 (d
4 fu ul 4 9 C:
$4 -4 a) 4
(1) m > 41
4
tr $4 4.)
a) 4 :3
13 0 En u z u
H () (a 0 r.
U) 0 Z 0
r I 4J ul -H
fa (L) I En r-4 41
41 4 -4 4 (a 0
.r-l 4-) (a Q) 4J (d
U) 4 4J 4-) -4 4
r 4 >1 -,i (a rQ Q)
0 0 r-I 0 4 4) 4 4J
-1 r. -1 4 4 0 z
4-3 0 4J 0 0)
U (a
rd cn
4 r 4.)
(1) It () IQ a) (1) 41
41 4) 0 S., X:
z r. 4-4 0 41 0 4-)
4-4 4J (a
(a (a r. rc:
-l -H 4-)
04 0 Q) 0
0 >4 0 4 r. 0 4-)
4J Q) 0 4 0 r.
Q) m -1 4-) -H a)
R (1) 4-1 4J 4.)
t:n (a 10 () (.) x
4 to (a Q)
0 a) U) 1-1 4 4
-l (4-4 4-) -H 1-4 a) 0 Q) p
4 0 C 4J -4 4J -4 1 4-) Q)
4-) C: 4-) 9 41 9 0 4-)
z 4 U) -ri U -1 ro
0 rd W a)
r-l U) 4 > 4
4-) r. a) 0 0)
u 04 V) 0 0 4-) 4
fa U) -4 -,1 Q g (d
4 1 M 4-) 1 -H
(a (1) rc: 41 U) 4 0 t04 4-) t)) +0 a) 41
ul z ::l -14 0 a)
I U) H 0 4 Q 0 0 >
W 0 8 4 C-) 0
m 0 0 4 + rc:
::I 4J z E-1 r. 0 E-1 E-1 r. E-4 oug
0
4 4-)
0 u
0






4


PLI






18













2





tz


Z71
4- < Cr 0





CK
-OIL
< U) cr) z

D
+ 0 L>


I r













J:r
CED






_OR
I


























Figure 2-2. Density and contour maps for the n and n orbitals
in CBD. These are obtained using the HIDEPLOT program (El) for ab initio SCSCF (see text) wavefunctions.
For all plots the wavefunction is evaluated in the molecular plane containing the C=O groups. In the
"contour" plots each curve represents a value of constant orbital density. The "density" plots give
the value of the square of the wavefunction (42) on
the vertical axis as a function of position in the
molecular plane thus there are peaks in only one
direction. The "orbital" plots give the value of
the wavefunction (f) on the vertical axis as a
function of position in the molecular plane, thus
there are positive (up) and negative (down) regions.

(a) i. Contour plot of the n MO.

(a) ii. Orbital plot of the n+ MO.

(a) iii. Density plot of the n+ MO viewed from above and below the molecular plane.

(b) i. Contour plot of the n MO.

(b) ii. orbital plot of the n- MO.

(b) iii. Density plot of the n MO.





20






























WWI



j Pr 1911 1
al ~ )111 1)1 1 J. I("





21





22

































(b) i
































(b) ii.






23 i AW:

























































fill














-----------





24




benzoquinone, we decided to repeat the calculation on CBD using a reduced symmetry constraint on the wavefunction so that the oxygen atoms were no longer treated as symmetry equivalent centers. A thorough discussion of the symmetry breaking and its effects within

the Restricted Hartree Fock formalism has been given by Jonkman (53) and more recently by Canuto et al. (62). Computational Details 1

The ab initio calculations were performed with the MOLECULEALCHEMY program package which employs the MOLECULE integral program written by Dr. J. Almlif (63) of the University of Uppsala, Sweden.

The ALCHEMY SCF program was written by Bagus et al. (64) and was interfaced to MOLECULE by Dr. U. Wahlgren and P. S. Bagus at the IBM San Jose Research Laboratory.

The double-zeta basis set of Dunning-contracted Gaussian functions

(65) was used in all the calculations. For the carbon and oxygen atoms a 9s5p primitive basis contracted to 4s2p while for the hydrogen atoms a 4s/2s contraction using Dunning's (65) coefficients was employed. The hydrogen exponents were all scaled to fit a Slater orbital exponent of 1.20 by multiplying all the hydrogen primitive Gaussian exponents by (1.2) 2(ref.65). This basis set was used by Dykstra and Schaefer

(66) in their study of the ground and lowest excited states of glyoxal. A calculation of the ground state and lowest excited singlet and triplet states ( 13A ) was first carried out to become familiar with the


1. The many helpful discussions with Drs. Michael Hehenberger, Joseph Worth, Gregory Born, Jack Smith and Henry Kurtz during the (now
and then) course of these ab initic calculations is deeply appreciated. Many thanks are due also to Drs. George Purvis and Richard
Lozes for making their versions of the programs available.





25




various options of the MOLECULE-ALCHEMY package and it was found that the total energies in our calculations were higher than those of ref. 66~ by 0.003 au. The orbital order was the same, however. Communication with C. Dykstra revealed that scaled hydrogen exponents were used in their calculation. All subsequent calculations were performed using the scaled exponents for hydrogen.

The vector coupling coefficients necessary for the calculation of the excited states were obtained from M. Hehenberger (67).

All integral calculations were performed neglecting those

10 -8a
smaller than 10 and approximating (63) those less than 10 In the case of the low (C s) symmetry these tolerances were set to

-8 -6
10 and 10 respectively. The convergence tolerance in the SCF procedure was usually 105 with respect to eigenvectors.

The atomic coordinates used in these calculations are given in Table 2-1, calculated from the X-ray work of Riche and Janot (68) for TMCBD, but taking the ring to be square. For CBD the same coordinates as ref. 8 are used with a C-H bond length of 1.09 A The coordinates for TMCBDT are taken from Shirrell and Williams (38) and are listed in full in Table 4-1.

Results and Discussion

Ionization Potentials

The MO order predicted by the ab initio calculation for the n

orbitals is reversed from that observed by PES for both CBD and TMCBD. Basu et al. (42) obtained the same result for CBD using Gaussian 70 (QCPE N-236); however, the lowest unoccupied orbital (LUMO) ( 7r*) from their calculation lies approximately 15 ev above the highest occupied





26




orbital (HOMO) (n ).In our calculation the ( 7Tr) LUMO is about 12 ev above the n- orbital. Comparison with the results on the azabenzenes obtained by Von Niessen et al. (54) shows that in these molecules the occupied-virtual separation is about 13 ev. It is pointed out that in such cases, where the HOMO-LUMO separation is small, the many-body corrections to the ionization energies can be expected to be large; hence, Koopmans' theorem breaks down and the orbital ordering from an SCF calculation may not correspond to that observed in the PES (54). Thus it appears that CBD and TMCBD fall into this category, and investigation using many-body methods would be of great value.

Using a double-zeta quality basis and a limited configuration space Wadt et al. (48) demonstrated that the correct order of the highest occupied orbitals of pyrazine is obtained when configuration interaction is included in the calculation of the ionization potentials. Thus it seems that the relaxation of the symmetry constraint on the wavefunction somehow introduces correlation corrections (64).

The energies of the highest four occupied orbitals in CBD and TMCBD are given in Table 2-2. It can be seen that attempting to account for electron reorganization in the cationic state (TMCBD) by calculating the total energy for both ground state and ionized state (C n +) and taking the difference (ASCF) does not correct the order on the splitting of the n orbitals. What is lacking is the correlation correction. It should be noted that EHT gives the correct order of n orbital energies and a reasonably good splitting, although the absolute value is not good. The lone pair ionization potential





27




in the reduced symmetry calculation is included in Table 2-2 for comparison with the Koopmans value. If we take the difference between the ASCF and Koopmans values for TMCBDT and use it to estimate a ASCF for CBD, we see that the reduced symmetry value is still lower by about 1 ev.

Excited n T* States

Using the ground state geometry for CBD and TMCBD a separate single-configuration-SCF calculation was carried out on each of the four singlet and triplet n 7* states of both molecules. The results of the ASCF vertical transition energies are given in Table 2-3. Although the n orbital ordering is reversed with respect to the experimental (PES), the calculated transition energies give the correct ordering of states in terms of symmetry species; the n+T* configuration is expected to be lowest, however. The absolute energies are not expected to agree with experiment at this level of approximation (62,66).

Comparison of the energy spacings of the lowest singlet n7T* states with the experimental values and the EHT/CNDO(S) results (8) are given in Table 2-4. These results indicate that EHT gives n T* state splittings which are closer to experiment than any of the other methods at the present level of approximation.

Comparison of the singlet-triplet splitting with experiment is possible for the lowest A state. Spafford et al. (6) assigned the
u
3A origin in TMCBD (single crystal) as 25718 cm-I and the correspondu
1 -i
ing IA has been found to be (7) 27122 cm ; this gives a AEST of
u S
-i
%1400 cm compared with that calculated by the vertical ASCF of
-i -i
%1700 cm and 1790 cm for the two A states. The agreement here
u





28



is rather good. Recalculating the CBD singlet and triplet n 71* excited state vertical transition energies with reduced symmetry (Cs, as described in the previous section) gives the following results:

ASCF (n *) = 3.434 ev

3n 7T*) = 3.095 ev

-i
AE = 0.338 ev (2730 cm

The energy lowering for the singlet excited state amounts to 2.65 ev while 2.78 ev is found for the triplet state. By comparison the energy decrease for pyrazine due to localization is (62) 1.2 ev for the singlet n r* state and 1 ev for the triplet, while for benzoquinone

(53) the values are 2.51 ev and 2.36 ev for the singlet and triplet states, respectively.

The AEST for CBD is seen to increase (cf. Table 2-3) as a result of symmetry breaking whereas for both pyrazine and benzoquinone AEST
1
decreases. This is due to a localization of both the n and 7* (on adjacent atoms) in CBD because the carbonyl groups are not conjugated, whereas the 7* orbital remains essentially delocalized in the other two cases and can avoid the localized n orbital more efficiently.

It is often desirable to determine the amplitude of a particular orbital on a given center, as on the oxygen atoms in CBD or the sulfur atoms in CBDT. The one center spin-orbit-coupling matrix elements, for example, are proportional to the product of two orbital amplitudes on the atom (cf. the term immediately preceding Eq. 4-25). Wadt and S. For pyrazine AE T in D2h is 0.73 ev and in C2v it is 0.56 (62).
For benzoquinone AEST is 0.33 ev in D2h and 0.23 ev in C2v (53).





29




Goddard (47,48) have demonstrated that in the 1,3B 3uad1,3 B2 n 7TT states in pyrazine, the n orbital is localized on one of the nitrogens and the Tr* orbital adjusts itself so as to make the exchange integral

K = < n (1)7r *(2)r1 Tr *(1) n(2) >

a minimum for the singlet state and a maximum for the triplet state. This comes about because the energy of the two states is given by (48)

1E=E + K
0 s

and 3E=E -K


Because K is positive the triplet state energy will be minimized if K is maximum and the singlet energy will be minimized when K is minimum. Thus if the orbital part of the wavefunction is allowed to be different for the singlet and triplet states of a given spatial symmetry the singlet will have less 7f* electron density near the nitrogen atom which has the n orbital localized on it whereas the triplet will have more.

To demonstrate this effect in CBD we again consider the C ssymmetry calculation and look at the net populations in the n and 1T* orbitals of the self consistent excited state. The diagrams in Fig. 2-3 give these quantities in the appropriate points on the molecular framework. The net population is chosen because it most closely resembles the orbital amplitude on the atom. It is readily seen that for both the triplet and singlet states the n orbital population on the excited oxygen is the same, whereas for the Tr* orbital the triplet state clearly

has a greater 7T density on the excited oxygen than does the singlet.



























Figure 2-3. Net orbital populations for CBD in C

(a) Net orbital populations for n and Tr*
orbitals of singlet state.

(b) Net orbital populations for n and ir*
orbitals of triplet state.





31










0.952 0.287



0.016 1.028


0.097 0.097 0.031 0.031



0.005 0.021



0.004 s 0.001




n (a) 7r





0.953 0.356

0.024 1.013

0*024 1,



0.094 0.094 0.025 0.025



0.006 0.019



0.004 T 0.001




n (b) 7r





32




This also demonstrates quite clearly that the excitation is exclusively localized on one of the carbonyl chromophores. This is to be contrasted with the greater mobility of the 7* orbital in pyrazine and benzoquinone which is due to the inherent delocalized nature of the planar benzenoid structures. We conclude that the charge-transfer-like nature of the localized carbonyl excitation is responsible for the greater magnitude of the AEST change in going from the delocalized (D 2h) picture to the localized (C s) picture in CBD.

As was mentioned earlier, the ab initio results which have been included here will be used in a later discussion of the spin-orbit contributions to the zero-field splitting parameters in TMCBDT taken up in Chapter 5.

Having briefly mentioned the success of the EHT method in predicting the nlr* interstate energy separations for TMCBD, it is appropriate to include the analogous calculation for TMCBDT at this time. The bands in the TMCBDT solution spectrum and the calculated values of the transitions are given below:

State EHT Ref.12

2 1A +6050 +5600
u
21B2g + 5000 + 2800


llB2g +1050 +1600
1-i -i
1 A 18710 cm 18400 cm
u



It will be informative to have orbital diagrams for the later

discussions on electronic distributions, thus the orbital energies and MO diagrams (EHT) are given in Fig. 2-4.


























Figure 2-4. Molecular orbitals and their one electron energies
for TMCBDT as calculated by Extended HtIckel method.
The coordinate system is given on the center Figure
in (a). All orbital energies are given in ev.

(a) The lowest 9 vrtual orbitals of TMCBDT.

(b) The highest 9 occupied orbitals of TMCBDT.






34









0g 2u ag





9.631, 6.742
6 .602







y







b2 bu Zb




4.1043.479























0.971 -8.777 -8.906




35




blu b3g b2u

n+-11.227 n. -11.845 cr-12.530






b3u blu

T -3.4 I4 13.459 0'-13.734







b g 1 3 8 5 9 b9 1 3 9 0 9 c r a 1 4 1 1 9


(b)





36





TABLE 2-1
a
ATOMIC COORDINATES FOR TMCBD AND CBD TMCBD

Atom x LZ

Cl 0.0 0.0 2.084575

C2 0.0 2.084575 0.0

CM 2.320533 3.679436 0.0

0 0.0 0.0 4.352295

Hl 3.823699 2.794608 0.0

H2 2.480797 4.748543 -1.368850




CBD

Cl 0.0 0.0 2.084410

C2 0.0 2.084410 0.0

0 0.0 0.0 4.352120

H 1.763150 3.186140 0.0



a. TMCBD coordinates calculated from bond lengths and angles of
ref. 67. For CBD bond lengths and angles are from ref. 8. All
are given in atomic units.





37




TABLE 2-2
ORBITAL ENERGIES (ev) FOR CBD, TMCBD (ab initio, D2h a

Koopmans ASCF PES EHT

CBD TMCBD TMCBD TMCBD TMCBD

n (b ) -11.31 -10.37 -9.44 -9.53 -12.00
-3g
n (blu) -11.65 -10.73 -9.79 -8.80 -11.36

T (b3u) -14.02 -13.46
+ 3

Tr_ (b ) -15.20 -14.57
-2g



An 0.34 0.37 0.35 0.73 0.64

AT 1.17 1.11



2n -9.29b



a. Wavefunction utilizing full D2h point group symmetry. b. Wavefunction utilizing only C symmetry, with ah as the molecular
plane. Value given is ASCF. s h






38











F, 00 0) M
(n 0 r-A Ln
r- 11 I-T
< m C,4 I-q




4,1
U) 'n r,
lz 04 oo m Ln C14
H
4
E-4
Er-,



E-i 0:4 E-4
4J
w Ln Ol 0)
4c 1-4 co w N w
t7) 0 co v
r.
4 1 r:
En (n

H
ril E-i = u E-1 Z

0 r4
rX4 >



im c"I (N 1-4 Ln
co r- Ln IV
CN IT
44 z CV
w u H
4 (n En
<


4

U)
u 4,1
4 4) 0 Lr)
r4 4 -1 r- CN
u 04 o 0 IV 0 4-)
z rq 4-)
0 4 Lr) %D -10
H Eri
Eri 04

z >1
9 M U)
ull 4
E-f

4
u 4-)
H Q) 0
E-4 1-4 0 0 'T Ln 04 r- -4
94 0) Lr) r C*4 r- r-4 ID4
r4 co 1.0 -4
> to co -4 4
U) 4-) Cl) Lr) I
0 co rE-4 41
4)
Q) C r-l
4-) Ln
ra Cl) "T
4-) 1
+ + En U)
41 t-7 I 1;= + t:= I +
4-) ECN3 CN :1 4
PQ al FCC 0 P






39



TABLE 2-4
COMPARISON OF VERTICAL TRANSITION ENERGIES (ASCF) OF n l* STATES
FOR TMCBD WITH OBSERVED AND SEMIEMPIRICAL METHODSa,b

State Expt. EHT CNDO/S ASCF

2 A 0.99 0.89 0.64 1.38
u
2 B2g 0.61 0.64 0.41 0.74

1 B2g 0.37 0.26 0.22 0.68

lA 0 0 0 0
u
(3.363)c (2.328) (4.962) (6.085)


a. All energies are in ev.
b. Experimental values and semiempirical results are from ref. 8. c. All values in parantheses refer to the absolute value of the
lowest state.
















CHAPTER 3
THE T So ELECTRONIC TRANSITION IN CRYSTALLINE
TETRAMETHYL-1,3-CYCLOBUTANEDITHIONE Introduction

The spectroscopic technique to be used in this study is that

of low temperature, single-crystal, polarized absorption spectroscopy. Each aspect of this technique possesses distinct characteristics, the combination of which allows one to extract a much greater amount of useful spectroscopic information than the more conventional room temperature solution spectroscopy. Spectroscopic Technique

An isolated molecule possesses many sharp rotational and vibrational energy levels within a given electronic state. In condensed phases, however, rotational energy levels cannot be resolved due to the lack of free rotation. In solution the vibrational structure is severely broadened due to the random interaction of molecules with the solvent; this causes merging of the vibrational features into an unresolvable spectrum. The extent of this effect also depends on the solvent. In the crystalline state, on the other hand, the molecules are fixed in space as part of the crystal lattice and therefore are subject to uniform interactions with their surroundings. The result is that crystalline absorption spectra allow resolution of a much greater amount of vibrational structure.





40





41



In the context of this technique, "low temperature" refers to temperatures below 77 K (the boiling point of liquid nitrogen). In this study, the temperatures used lie in the range from 1.6 K to about 50 K. In this temperature range molecular vibration is usually restricted to its lowest eigenstate, thus eliminating the vibrational hot bands which are the result of transitions originating in higher vibrational eigenstates. For polyatomic molecules containing low frequency vibrations, as is the case of TMCBDT, the quenching of hot bands is not achieved until liquid helium temperature, 4.2 K or lower. With reference to the crystalline state, lowering the temperature causes the molecules to be more rigidly fixed in the crystal lattice thereby reducing the crystal lattice vibrations to their lowest eiqenstates. This reinforces the crystal-induced resolution of the vibrational structure.

In addition to vibrational resolution, crystal spectra can lead to a great deal of information about the direction of the electronic transition moments. By proper orientation of the crystal it is possible to achieve a fixed and known orientation of the molecules with respect to the electric field vector of the incident plane polarized light and thereby obtain information about the polarization direction of a given absorption band. The results of polarized single crystal spectra cannot usually be interpreted in terms of transitions in the free molecule, however, but must be considered in the framework of the crystal symmetry.

Crystal Symmetry

The molecular crystal can be identified with a particular crystal class. within the crystal class further classification is achieved by





42



determining the space group to which the crystal lattice belongs. The overall symmetry is described by both point and translational symmetry; the lattice is invariant under operations of both kinds, the complete set of these constitutes the elements of the space group. It is possible to imagine another group, in which the translational subgroup of the space group behaves like an identity element and the remaining elements of this group consist of the costs R i T, where R i is a point operation and T is the translational subgroup. This new group is called the factor group of the space group and is isomorphic with one of the 32 crystallographic point groups ( 69); this property will provide a means of correlating states in the free molecule with those of the crystal.

This correlation is dependent on the particular site occupied

by the molecule within the translationally invariant unit cell. Each site is characterized by a particular local symmetry which can be described by its own rotation axes and reflection planes, but which necessarily has relationships to those of the full factor group and thus to the symmetry axes and planes of the unit cell. The number of possible sites of a given point group, called site groups, which are admitted by a particular factor group is limited only to those which are a subgroup of the particular factor group. However the distribution of sites differs with the space group for each of the factor groups. The site group can never contain symmetry elements not belonging to the free molecule and is generally of lower symmetry.

with this background, it is appropriate to further amplify that aspect of the technique just described which pertains to the interpretation of crystal spectra.





43



Crystal States

Since the molecules in a unit cell occupy sites, it is clear that the site state corresponding to a given molecular electronic or vibrational state is found by correlation in the two symmetry point groups. These site states are not symmetry-adapted in the factor group, however. This adaptation is carried out in a manner completely analogous to the symmetry adaptation of atomic orbitals to form (symmetry adapted) molecular orbitals in a polyatomic molecule. Whereas one operates on the localized atomic orbitals with the symmetry operations of the molecular point group in that case, the symmetry operations of the crystal factor group are used to operate on the site states (or functionsH 70 ) in the crystal to obtain a reducible representation from which the crystal states can be projected out as linear combinationsof site states. Thus for the case of n molecules per unit cell n factor group states are obtained, each characterized by an irreducible representation of the factor group.

In general, if interaction between the molecules is allowed, the n factor group states are not expected to lie at equal energies. Therefore a single molecular state can split into n factor group states in a crystal with n molecules per unit cell. This type of splitting is called "factor group splitting" or "Davydov splitting". The appearance of this effect in molecular crystal spectra can lead to a greater amount of information concerning intermolecular interactions, at the expense of a more complex spectrum, however.





44




Thus far no specification has been made of the particular

molecular or site state and in this respect the application is to a molecular state having the equilibrium geometry of the around electronic state. In molecular excited electronic states, however, there is often a change in the equilibrium geometry from that in the ground electronic state. For the free molecule this case is discussed in terms of the subgroup common to both the excited state and ground state point groups. When considering a distorted molecular state in a crystal environment, the distortion may be taken as a local perturbation in which the effective site symmetry is then defined by the symmetry elements common to both the distorted molecular point group and the invariant factor group. We will make use of this excited state site symmetry correlation later. Effect of External Fields

When an external field is applied to a crystal the symmetry of

the site is reduced; the extent of this symmetry breaking is dependent on the field orientation with respect to the crystal axes of symmetry ( 71 ). The resulting symmetry is determined by taking the symmetry

elements in common between the site group (where the effect of the field is expected to cause the greatest perturbation) and the group
1
C ooh Obviously, if the field is not along a crystal symmetry axis or in a symmetry plane, the resulting overall symmetry will be C 1* In ref. 71 the symmetry of the point group resulting from application of an external electric or magnetic field applied along a symmetry axis of the point group is tabulated.


1. The magnetic field is Coch and electric field CMv.





45



Features of Crystal Spectra

The proper interpretation of any type of spectrum depends on the amount of information available about the system being studied. With respect to electronic absorption spectra it is important to know the vibrational frequencies of the molecule being considered; although these may be different in the excited electronic state from the ground state, it is often possible to correlate one with the other. Then by comparing the frequency shifts and the intensity distribution of the vibrational bands in the spectrumit is possible to infer the changes in the potential function which governs that vibrational mode.

Since we shall be concerned with spectra of molecular crystals, it will be useful to briefly outline the two most pertinent features found therein; these are crystal vibrations and their effect on optical absorption in the crystal. Crystal vibrations

within a molecular crystal the intermolecular forces are much weaker than the forces acting between the atoms of a single molecule so that, in a first approximation, the molecules retain their individuality. on this basis all possible vibrations of the atoms in a molecular crystal may be divided into two main categories ( 72 )

1. Internal vibrations: these are the intramolecular vibrations
of the atoms in a molecule relative to one another. In
these vibrations, the center of mass (c.o.m) of the molecule
is not displaced and there is no rotation of the molecule
as a whole. These vibrations are encountered in the isolated
molecule. We will also refer to these as molecular vibrations.

2. External vibrations: are the vibrations which describe the
relative motion of the molecules with respect to one another.
They arise because of the rotational and translational degrees





46



of freedom of the molecules even as they are held rigidly
in the crystal lattice. These vibrational frequencies bear no correspondence to those of the molecule in the vapor or solution phase, hence they are called lattice
vibrations. The frequencies of these vibrations depend
on the wave vector q, unlike the internal vibrations
which, in the absence of coupling with external vibrations,
do not. The range covered by these vibrations is from
0-1k,100 cm-1 (72).

In a real lattice of course, there is coupling between the two types of vibrations and the distinction between them vanishes. This is especially true when the molecular vibrations have frequencies comparable to those of the lattice vibrations. Indeed, the molecular vibrations are influenced by the lattice which results in frequency shifts and factor group splitting, as was discussed for electronic states (vide supra The discussion of symmetry as applied to crystal states applies equally well to crystal vibrations. It is possible to deduce the number and symmetry types of crystal vibrations from knowledge of the number and symmetry types of molecular vibrations and the factor group and site symmetry ( 69 ). A breakdown of the various classes 1 of lattice vibrations may be summarized as follows(72).

In a molecular crystal which contains n molecules per unit cell and p atoms per molecule there are a total of 3np crystal vibrations for each wave vector q. Henceforth our discussion will focus on the point q=O. Three of these classes constitute acoustical modes which are characterized by a change of the c.o.m. of the unit cell and, at k=O have zero frequency. The rest of the vibrations (3np-3) constitute the optical class of vibrations, characterized by nonzero frequencies at q=O.


1. The terms class, branch and mode are all applicable and frequently interchanged. The term used here will be "mode".





47




out of all 3np modes of vibrations of the crystal, 6n modes belong to the lattice vibrations (external), three of these are the acoustical modes and the rest, 6n-3, are optical. The optical modes are further divided into 3(n-1) translational-vibrational modes and 3n rotational modes.

All of the remaining n(3p-6) vibrational modes will be determined by the internal (molecular) vibrations of the n molecules in the unit cell and are all optical. Having discussed the vibrational characteristics of the crystal lattice, we now summarize the qualitative aspects of the interaction of the electronic excitation with the crystal lattice. Electronic Absorption

optical absorption in a molecular crystal results in the formation of an exciton. This is an excitation which corresponds to the formation of an electronically excited molecular state on one of the molecules in the crystal. This excitation may then propagate throughout the crystal by hopping from one molecule to another or by fast delocalization in the exciton band. At the instant of its formation the exciton may simultaneously create and/or annihilate a lattice phonon and in

so doing cause an additional band to appear in the optical spectrum.

The extent of interaction of the electronic excitation (exciton) and the lattice vibration (phonon) will determine the spectral outcome and can be characterized by a parameter called the Stokes loss. Di Bartolo and Powell ( 73 ) give simulated spectra for various values of this parameter. one description of this parameter is that it is analogous to the nuclear recoil which occurs with gamma ray emission in Mdssbauer spectroscopy. In the crystal case it corresponds to a shift in the equilibrium position of the molecules within the unit cell.




48




The exciton-phonon interaction manifests itself in phonon sidebands. These often have structure which may or may not bear correspondence to Raman frequencies observed for the crystal. Furthermore, the intramolecular vibrations which fall in the optical phonon branch may have frequencies comparable to those of the lattice optical modes, indeed may even intersect the acoustical modes at q310. Because lattice vibrations are described in terms of all possible motions within the crystal, there is no longer a sharp distinction between intermolecular vibrations and pure intramolecular ones.

Three cases may be distinguished by the Stokes loss (Z) parameter

(74):

1. Z<< 1: the excitation which propagates through the lattice
consists mainly of delocalized excitons (electronic excitation).
The appearance of the Franck-Condon envelope for this case
(cf. Ref. 73, p. 410) is similar to that observed for the
+970 cm-1 and 600 cm-I bands in the TMCBDT crystal spectrum
(Fig. 3-2). Using Eq. 10.11.15 of Ref.( 73 ) it can be
estimated that Z for these modes is about 0.1 and 0.3
respectively.

2. Z t 1: the excitons are strongly coupled with phonons: the
excitation propagates in the form of a polaron which is
described as the electronic excitation together with lattice
phonons. Since the electronic excitation is polarized,
this process has the lattice phonons moving along the preferred direction determined by the exciton. The spectral
manifestation of this is not seen inthe TMCBDT spectra (75).

3. t>>1: the excitation is completely localized at the site of
the exciton formation. In this case the intensity of the phonon sideband is comparable to that of the zero-phonon
line and peaks at a frequency equal to Z quanta of the phonon
mode.

Thus (qualitative) information on the nature of exciton migration may be obtained by noting the appearance of the absorption profile (Franck-Condon envelope). Comparison of the phonon sidebands in the corresponding emission spectrum can supplement the information obtained





49



from the absorption spectrum. In the case of low temperature (21K) the absorption in the Z<< 1 case takes place to the k=O zero-phonon
4. 4.
level ( 74) and to various k+q=O transitions involving phonons of wave vector q which give rise to the phonon sideband. At this low temperature (2K) the excitation will relax into the q=O level (in the case of an exciton band having a concave-up dispersion curve) and transitions will only be possible to the q=O phonon levels of the ground electronic state. Thus, for Z<< 1 only q=O optical phonons will appear in the emission spectrum; this amounts to discrete emissions with little (or no) phonon sidebands and is indicative of delocalized excitons.

In the other coupling cases mentioned, the emission spectrum will contain broad phonon sidebands (k 1) because the q=O selection rule does not hold since the phonon and exciton remain coupled. In the localized exciton case (>>l) the phonon sideband in emission will bear a close resemblance to that observed in the corresponding absorption spectrum.

Crystal Structure

TMCBDT crystallizes in the tetragonal crystal class, in the space group P42/mnm with two molecules per unit cell ( 38 ). Figure 3-1 shows the unit cell and the relative orientations of the two translationally inequivalent molecules which are located at the points (0,0,0) and(1/2,1/2,1/2). The site symmetry at these points is D2h, which requires at least D2h symmetry for the molecules which occupy these sites. The molecular structure is found ( 38 ) to be D2h with the methyl groups eclipsed with respect to one another. The C=S bonds are collinear and both lie in the molecular plane defined by the




50

C











e'7N*
I
I(000


















""~( 1 \)s
C I



IIo io







2 (0,0,0
22

Figure 3-1. Orientation of TMCBDT molecules within the tetragonal
unit cell. The unit cell dimensions are: c=12.549 A, a=6.330 A (ref. 38). The molecular and cell dimensions
are not drawn to scale here, (cf. Figure 3-7). The methyl carbon atoms are shown slightly smaller than those of the ring. The methyl hydrogens have been
cnitted.





51




cyclobutane (planar) ring (cf. Fig. 3-1); the molecular planes of the translationally inequivalent molecules are mutually perpendicular and lie at 450 with respect to the ac planes. The long in-plane axis of the molecule is along the C=S bonds these are mutually perpendicular), we will label this the y molecular axis. The short in-plane axis will be taken as the z molecular axis and is parallel to the c crystal axis; the z molecular axes are parallel. The molecular x axis is out-of-plane and makes an angle of 45' (as the y) with the a crystal axis and is perpendicular to the c crystal axis.

This choice of coordinate system is not unique, but with a right handed axis system on each molecule and the molecular z axes parallel the correlation between molecular (or site) states and factor group states allows construction of factor group symmetry adapted functions by inspection. This is because with this system the symmetric (+) combination of B molecular states correlates with the A 2urepresentation, while the antisymmetric (-) combination correlates with B2u in the factor group.

If the molecular z axes were chosen antiparallel, the correlation

would be B1l (+)/(-)-B 2/A 2. Unless otherwise specified the axis system used throughout this study will be that described above; it seems that having the z molecular axis parallel to the crystal symmetry axis justifies circumventing the more conventional choice of the z axis parallel to the C=S bonds.

The molecular coordinates calculated from the thermally corrected bond lengths and angles (38 ) are given in Table 4-1.








AS mentioned previously the site and factor group symmetry is

usually lower than the molecular symmetry; this leads to a breakdown of the symmetry selection rules operative in the free molecule, thus permitting the appearance of symmetry forbidden transitions in the free molecule. In the case of TMCBDT, on the other hand, the factor group symmetry is higher than the site and molecular symmetry. This arises because the two translationally inequivalent molecules are at right angles to one another thereby requiring a rotation of 'r/2 (followed by a non-primitive translation of [0,0,1/21 to interchange them .

The consequence of this relationship is that the molecular x and y direction (and therefore the B 3uand B molecular electronic or vibrational states) which belong to one-dimensional irreducible representations in the molecular point group correlate with the two-dimensional irreducible representation of the D 4hfactor group (E u). This means that while molecular transitions polarized along the x and y molecular directions in the free molecule could in principle be distinguished, in the TMCBDT crystal these transitions are now both polarized Ic and indistinguishable. Table 3-2 gives the correlations between the free molecule (and undistorted site group) and the crystal factor group for TMCBDT.

The uniaxial nature of the crystal is another consequence of the
2
molecular arrangement within the unit cell. This property is manifested in the optical equivalence of the a and a' directions, that is, any orientation of the electric field vector of plane polarized light

1. The operation consisting of rotation about an axis by 2 7/n followed by a non-primitive translation is called an n-fold
screw axis ( 70 ).
2. This discussion applies only in the absence of external fields, see Chapter 5.





53



in the aa' plane is equivalent to any other orientation in this plane. On the other hand if the plane polarized light is incident on an ac face, the liIc and j-c directions will be mutually exclusive. Thus a single crystal placed with the ac face parallel to a set of crossed polarizers will cause total extinction when the crystal is rotated so that the c crystal axis is parallel to one of the polarizers. If total extinction does not occur, it means that the c axis is not exactly parallel to the polarizer, which in turn could mean that the c axis is not parallel to the developed plane of the crystal.

The most important consequence of the molecular orientations in the unit cell is that for any electric dipole allowed transition in the free molecule there can be no factor group splitting in the crystal states. This is a consequence of the symmetry correlation discussed above. The x and y polarized states in the molecule each become degenerate (E u), while the z polarized molecular states become A 2u(+ combination of site states) and B 2u(- combination of site states). The E u are electric dipole allowed ic. The A 2u is allowed 1 Ic but the B 2uwill not be seen unless the transition is assisted (vibronic) by a b crystal vibration -this gives both factor group components 1c polarization, or by an e crystal vibration which gives theC) combination Ic polarization.

This effect is interesting but not observed in the TMCBDT triplet spectrum and will therefore not be considered further. Crystal Growth

Earlier work ( 39) has shown that the preferred method for TIMCBDT

crystal growth is that of sublimation. TMCBDT readily sublimes at room temperature and will form minute crystals on the container walls even





54



while stored at %10*C. A few of these crystals were placed in a pyrex glass tube which was evacuated to -10_2 torr at 77 K for 15 to 30 minutesand then sealed. The tubes were then mounted (at %450 angle from the vertical, and in a dark room) about one meter above a hot plate whose temperature was %50*C-60*C. The distance from the hot plate was varied to get sublimation rates which were slow enough to produce as few growing nuclei as possible; these usually formed at the end of the tube farthest from the hot plate. When well-developed single crystals failed to form, the tubes were simply inverted with the newly formed crystals now toward the hot plate.

Several other methods were tried but none gave qood results. For example, attempting to cool a minute spot on the opposite end of the tube immediately resulted in many pin-point centers which disappeared when cooling ceased. The most successful method, described above, produced good crystals in about two weeks. Crystal Orientation

The crystals used in this work were all similar in habit; their general appearance is shown in Fig. 5-3 in connection with the Zeeman apparatus; they may be described as being nearly hexagonal plates with

the c axis lying in the f ace of the developed plane. Identification of the c axis direction was done by x-ray crystallography (76) and the alignment of the crystal for mounting was achieved through conoscopic examination with a polarizing microscope. By far the best results were obtained with those crystals which could be used directly without polishing (crystal D).





55



Experimental Details

The polarized absorption spectrum was recorded on Tri-X

film ( 77 ). The sample was mounted in an immersion type liquid helium dewar and cooled to approximately 1.6K by evacuating the helium vapor. Some spectra were photographed above 4.2 K after the liquid helium level had dropped just below the sample. These

were given minimum exposure times (1 minute) and no attempt was made to control the temperature. The optical arrangement consisted of a quartz-iodine lamp focussed onto the sample and the transmitted light refocussed onto the slit of a Jena 2 meter spectrograph by a reflecting microscope objective placed after the sample. The slit width of SOVI and the grating dispersion of 7.28 A/mmn provided a resolution of about 0.3 A, about 0.9 cm at 5900 A. A Wollaston prism adjacent to the slit produced both parallel and perpendicular polarizations simultaneously. To compensate for the polarizing effect of the grating a circularly-polarizing X/4 plate was placed between the Wollaston prism and the slit, effectively scrambling the radiation incident on the slit.

Spectra taken at temperatures above 10K were recorded on a Gary 14 spectrophotometer using slit widths from about 601j to about 100pi, giving a resolution of about 2.1 A and 3.5 A (corresponding to '-5 and 9 cm1 ) respectively. The crystals were mounted between an

indium mask and a copper plate attached to the cold finger of a closed cycle helium cryostat (Air Products, Displex CSW-202). A gold-chromel thermocouple was mounted as close to the crystal as possible with

cryogenic grease, and connected to a digital voltmeter. The reference junction was immersed in an ice bath at 00C. It is estimated that temperatures measured in this manner are accurate to + 1.





56



Densitometer tracings of the films from the low temperature

spectra were recorded with a Leeds and NOrthrup Model 6700-A2 microdensitometer equipped with an RCA 1P28 photomultiplier tube. The signal from the photomultiplier was amplified by a Keithley Model 416 picoammeter and recorded on a Heath Model 700C strip-chart recorder.

The band positions were determined by comparison with a potassium discharge tube spectrum recorded on one of the films. The Wollaston spectra consisted of sets of two adjacent exposures containing the TMCBDT spectra. The potassium spectrum was superimposed on the perpendicular to c polarization of one of the sets. A recording of this exposure gave the distance of the TMCBDT absorption 0-0
0
band with respect to the longest wavelength potassium line (5895.923 A).
0 0
The 25 potassium lines between 5895 A and 4641 A were used to obtain a least squares fit to the quadratic equation

= b 0+ b d + b2d2


where d is the distance from the 5895.9 A potassium line. The root
0
mean square deviation of the fit was +0.134 A. The constants, b., have to be determined for each chart recorder speed and densitometer scan speed combination. For the tracings presented here the values
-5
b0= 5896.1396, bl= -1.8068877 and b2= -2.2417152xi0 were used; this gives a wavelength of 5943.104 A for the 0-0 band of TMCBDT. The other band positions are calculated using the above formula with d equal to their distance from the TMCBDT 0-0 band plus the distance of the
0
0-0 band from the 5895.9 A potassium line. This method insures that the band positions are correct relative to the 0-0 band.

The potassium emission lines were very sharp and determining 'd' for these involves little error (+ 0.2 division). It is estimated






















04
-4
a):
0-4 rz '0 N C :
C,4
a)-4 C
04
E-q 0 4
n 0 10

Cd a)
-4 En4

4





4- 0 Q
-4 0 E
-44



1 C

a) 4
-4 E 0 i

02~ 41 41


a) ) Cd 4 4-0 a))

a)4 04 r E4 4 -4 U (a
4J' 44'
I a)

04'4


0 00C
4.0)



4' 4
.14 I 00X4 -






58






















Ile
0 0





0

OL







0 E
r- c




In CD
z
w
-i
w

0
tO
0

tc) 00 to



0

+0 0 to
1'L




59



that for the TMCBDT bands which are not as sharp, the band position is in error by about + 3 cm

Re suits

Low Temperature

Polarized absorption spectra (single beam mode) of several

crystals were taken at temperatures below 10K in the spectral range of 600 nm to 400 nm. Bands to the blue of 550 un were much more intense and required greater exposure times. The latter region has been reported as the vibronic 1 A u*- 'Atransition ( 43, 45 ) and will not be discussed here. Densitometer traces of several exposures were made and the best ones chosen; these will be referred to as crystals D (taken at 1.6K) and F( taken somewhat above 4.2K but below 10K). These are shown in Fig. 3-2. The frequency (in cm1 ) and vibrational assignments are given in Table 3-1. Temperatures Above 10K

Crystal E was run on the Cary 14 (double beam mode) at 11K, 20K and 47K. There was no difference between the first two of these in either band position, band contour or intensity; the 20K and 47K spectra are shown in Fig. 3-3. As for the low temperature spectra, bands to the blue of 550 m were very intense. Although some changes with temperature appeared to take place in this region, the resolution was inadequate for proper observation of these effects. The blue shift and broadening of the bands in the triplet region (600 m to 555 m) will be discussed later.

In addition, because the developed planes of this crystal were not parallel, the subsequent polishing resulted in a mounting with uncertain c axis direction. Since the cryostat could only be rotated






60







as




4-I 04
-0)







(0

C)
NN








0 4 0






I -4 D 0




0 ~~

4)

04

0
U)





00

r4
0 Ul0






d 3:)NVSNdSV




61




about its vertical axis, it was not possible to remove the contaminating 11c polarization. Although the intensity variation serves to reinforce the conclusion that Eq. 5-20 fits the observed polarization behavior, the polarization contamination in the region below 555 nm (where the 1 A U transition occurs) renders the temperature dependence in that region useless.

In the next section an account of the temperature dependence and band intensity distribution is presented.

Vibrational Analysis of the T S o Transition


Table 3-1 lists the observed frequencies, displacements from the origin, assignments and calculated positions (vide infra). The major bands are located at 0 cm %300 cm 600 am and %950 cm from the electronic origin (0-0). These bands are discussed in turn below. The 0-0 Band

The pure electronic origin located at 16822 cm (5943.1 A) is assigned as the 3 E U 1 A lg crystal transition (43); this is an electric dipole allowed transition which arises via spin-orbit coupling of the
3 A lu crystal state to 1 E u crystal states. This corresponds to the lowest 3 nTr*( 3 A u ) state in the free molecule, in which the spin-orbit
1 1 1
coupling is mainly to Tr7T* ( B 2u or B 3u ) states. The dominant pathways for spin-orbit interaction in TMCBDT are treated in detail in Chapter 4. Table 3-2 gives a correlation diagram between the molecular point group (D 2h site group) and the crystal factor group (D 4h ).

The 0-0 band is %3 cm- 1 wide (FWHM), has a very sharp red edge and somewhat broadened blue edge. This is a good example of the band shape that arises in the case of weak exciton-phonon interaction, Z << 1, as discussed earlier. (See also Ref. 78.)





62




A series of very weak, irregularly spaced bands is found on a broad absorption whose maximum occurs at rL-50 cm~l Two of them (+47 and +87) are built on the other strong vibronic bands: this sequence could be due to lattice modes or a low frequency molecular vibration Wvide infra). Regardless of their origin, their energy distribution can be described by a double minimum potential (DMP). A brief description of the fitting procedure and resulting potential function parameters will be given later.

Table 3-1 gives the calculated values of these energy levels. A similar series of bands is observed in the emission spectrum of crystalline TMCBDT 1at 1.6 K, except that in the latter spectrum the bands are very intense, some are very sharp, and overlapping with trap emission bands occurs. A DMP was fit to this sequence of bands giving the potential function for the ground electronic state. The 300 cm1 Band

This band, located at +309 cm 1, has a somewhat different appearance than the 0-0 band and the other sharp bands at +600 cm1 and

-1 -1
+970 cm .There is also a shoulder at +329 cm which undoubtedly

causes the broadening. The red edge is not sharp and appears to be lacking the zero-phonon line. A look at Fig. 3-2 and Fig. 3-3 shows that upon increasing the temperature above 4K (but below 20K) the

-1l -1
band at +329 cm increases relative to the one at +309 cm This might indicate that the 329 cm- band represents a transition from a level located about 20 cm1 above the zeroth level in the ground state, which becomes more populated on warming. However, since this band is seen at 1.6 K we assign it as a separate molecular mode.


1. The emission experiments (43) will not be included in this work, but
will be referenced as needed to complement the discussion of the absorption experiments.





63




TABLE 3-1
VIBRATIONAL ANALYSIS OF T S ABSORPTION OF
CRYSTALLINE TMCBDT POLARIZED PERPENDICULAR TO c

Observed
Frequ ncy Av1 Assignment Calculated a1
(cm) ( ) (cm1 (cm- (cm-)

01 16822 0 0+- 0

16869 47 1+ 47 0

16880 58 1- 54 +4

16897 75 lattice 75 0

(16907) (85) 2+ 87 -2

16925 103 2- 106 -3

16956 134 3+ 133 +1

17007 185 4+ 186 -1



02 17131 309 309




03 17151 329 329

17197 375 329 + 47 376 -1

17223 401 309 + 87 396 +5

17248 426 329 + 87 416 +10

17311 489 309 + 2 x 87 483 +6




04 17422 600 600

17471 649 600 + 47 647 +2

2 x 329 658 -9

309 + 329 638 +11

17513 691 600 + 87 687 +4


continued





64



TABLE 3-1 continued

2 x 329 + 47 705 -14

309 + 329 + 47 685 +6

17600 778 600 + 2 x 87 774 +4

309 + 329

+ 87 + 47 772 +6




05 17735 913 913

600 + 309 909 +4

600 + 329 929 -14



06 17791 969 969

913 + 47 960 +9

600 + 329 + 47 976 -7

17843 1021 969 + 47 1016 +5

17867 1045 969 + 87 1056 -11

17898 1076 3 x 329 + 87 1074 +2

17963 1141 969 + 2 x 87 1143 -2


a. Multiple assignments are given where it was not possible to make a
unique assignment or where more than one band is likely to be present
even if not resolved. 02 through 06 define the vibronic bands.
b. Calculated band position based on assignment. The difference between
the observed band positions relative to the 16822 cm-1 origin (0-0)
and this calculated value appears in the last column.





65




The 600 cm-1 Band

The shape of this band resembles the 0-0 and the 970 cm -1bands. It is clearly a separate vibration and has the weaker series of bands to the blue. Several possibilities are given (cf. Table 3-1) for these since any one cannot be ruled out in an obvious manner. The temperature behavior of this band is similar to the one discussed above.

The 970 cm- Bands

The broad, weak band at +913 cm- is assigned to a separate

vibration for the same reasons as the 300 cm1 band. A sharp band

resembling the 0-0 and 600 cm1 which appears at +970 cm- is assigned as a separate vibration as well. The weaker bands to the blue can be assigned as various combinations. Polarization 1c

For crystal E at 1.6K a very sharp symmetrical (Gaussian like) but very weak band was noted at the same position as the 0-0 band polarized 1c. All attempts to remove this by rotating the polarizer failed. The intensity ratio is about 1:620 for I1c:Ic. While this could be a real manifestation of a spin-orbit route inducing 1 intensity, a definite conclusion could not be reached. Summary

The T S- 0 transition in crystalline TMCBDT is Polarized exclusively Ic and therefore corresponds to spin-orbit coupling of the 3A molecular state with 1B 2uand / or 1B molecular states. of the possible choices for a 3 nff* state (C A uor 3B 2g), inspection of Table 3-2 immediately shows that the 3B state ( 3n 7T*) could not be seen in first order.
2g + +
This shows that the lowest triplet state in TMCBDT is 3A which implies





66




TABLE 3-2 (STATIC) CORRELATION BETWEEN MOLECULAR (SITE) GROUP AND FACTOR GROUP

D2h D4h


Alg


A g
A2q (Rc Blg (R )

B
ig

B 2 g ( R )

B2g

B3g (R)

Eg (Ra Ra )




Alu

A

u2
A2u (c)

Blu (Z)

Blu B2u (Y)

B2u

B (x)

E (a,a')
u

z c









x a





67




that 1A uis lowest in the singlet manifold. The active vibrations

-1 -1 -1
in the transition are found to be 309 cm 330 cm 600 cm 913 cm and 970 cm By analogy with TMCBD we assign the 309 cm and 600 cm1 to skeletal vibrations and the 970 cm1 mode to the C=S stretch (symmetric), and the 913 cm1 mode to C-C stretch or CH 3 bend.

Crystal Vibrations in TMCBDT

In the previous section the 0-0 band has been assigned to an electric dipole allowed transition induced by spin-orbit coupling. This means that any vibrations observed must have g symmetry, since the electronic state is E u, any of the g vibrations in D 4hwill allow the transition to be observed 1c; this was experimentally observed. It is clear from the earlier general discussion of crystal vibrations, that the vibrations observed at 300 cm ,600 cm and 970 cm

must be due to internal modes. This leaves the low frequency vibrations built on the 0-0 band which must be explained. Because only the far infrared spectrum is available (gas phase, room temperature, see Ref. 83) for TMCBDT, it will be necessary to draw on analogies with TMCBD infrared and Raman spectra ( 4) .

From the Raman spectra of TMCBD we find only one vibration below 200 cm1 in solution, polycrystal and single crystal; this is about 160 cm 1. We expect two bands corresponding to this molecular band to appear in the crystal spectrum of TMCBDT, at approximately the same value of energy and not split (see arguments on factor group splitting).

If the 216 cm1 band of TMCBD is included, and if it can be assumed to shift to lower frequency, we can only account for two





68



-i
of the eight observed bands in the range 0 to %200 cm relative
-l -i
to the 0-0 band. We can assign the 134 cm band and 213 cm band (cf. Table 3-3) observed in TMCBDT to correspond to the 160 cm-i
-i -l
and 216 cm Raman bands (see Table 3-1) of TMCBD. The 75 (or 85) cm
-l-i -l
and the 185 cm-I bands correlate with the 42 cm and the 186 cm bands, respectively, observed in the far IR spectrum of TMCBDT in the gas phase. This correspondence is based on analogy with the TMCBD
-I -i -i
bands at 58 cm and 180 cm in the gas phase which shift to 82 cm and 186 cm-I in the polycrystal. This assignment accounts for 4 of the 8 observed bands (cf. Table 3-3). If all four bands are due to internal modes, the remaining four bands must be due to lattice modes. These are examined briefly below.

To determine the lattice modes in the factor group, a correlation method will be used (69). The lattice or intermolecular vibrations are derived from the translational (transform as the molecular axis vectors) and the rotational (transform as the rotations about the molecular axes) degrees of freedom of the molecules within the lattice. Thus, we may correlate the symmetry species of these motions in the free molecule to obtain the factor group symmetry adapted coordinates for the lattice modes--these correspond to symmetry coordinates in the free molecule vibrations. Taking the appropriate linear combinations we obtain

(/)(RZl R z) a2g (+); b (-)


(1//2) (R yl+ R y) e (2, degenerate)


(i//i) (Rxl+ R x) e (2, degenerate)
x2 g
Here only the g type modes have been constructed as demanded by the E electronic transition. These modes correspond to in-phase and
u





69




out-of-phase rotational oscillations about the molecular axes, keeping the c.o.m. of the unit cell fixed, and are thus optical modes. Furthermore, they are all Raman active except the a 2gmode.

The b 2gand a 2gvibrations are acceptable because they give E when the direct product with the E electronic representation is taken. The e modes, however, give

E x e = A + B + B + A
u g lu lu 2u 21i

none of which are allowed. So from the 6 gerade lattice modes only two are candidates for the observed bands, the a 2qand b 2qvibrations.

Thus, there can only be two lattice mode fundamentals. If these two are assigned to the 47 cm- and 58 cm1 bands the 103 cm1 band can be assigned to the combination of these two. These assignments leave one band unexplained: the 85 (or 75) cm1 band.

An alternate assignment for the low frequency vibrations rests on the assumption of a large zero-field splitting in TMCBDT.

A large zero-field splitting (D= -11 cm1 has been found for xanthione (see Chap. 5 and references therein). If the same were true for TMGBDT, the isolated molecule 3A state would have two nearly degenerate spin sublevels located about 11 cm- below the third spin sublevel. The two frequencies 47 cm1 and 75 cm- could now be assigned as two g lattice vibrations and transitions from the ground electronic state to one of the lower spin sublevels of the 3A state

-1 -1
would appear at 0-0 + 47 cm and 0-0 + 75 cm,. Transitions to the

3 1
upper spin sublevel of A would occur at 58 cm and 86 cm For

this to occur, however, the transition moments to the two triplet sublevels involved must be nearly equal. The spin-orbit-coupling results (Table 4-4) and analogy with carbonyl transition moments, preclude this.





70



Furthermore, such a large zero-field splitting would have been easily observed in the Zeeman experiments (see Chapter 5) but was not. On the basis of these inconsistencies therefore, this model is ruled out.

In the next section another model, involving a double minimum potential, is proposed that explains all the observed bands as well as the temperature behavior in absorption and the emission band positions (43).

The Double Minimum Potentials

Fitting Procedure and Results

The method of Coon, Naugle and McKenzie ( 79 ) was chosen to fit the weak irregularly spaced bands in the region +0 to +220 cm- 1. This method described the DMP function as a harmonic oscillator of frequency V which is perturbed by a Gaussian barrier centered at
0
the equilibrium position (Qor the mass weighted coordinate) of a simple harmonic oscillator (SHO). To implement this method, a system of computer programs was written (Fortran IV). A more detailed documentation of these and the graphical method of Coon et al. (79 ) may be found in a separate report ( 80 ). A brief outline of the method and a description of the parameters is given here to facilitate discussion of the results.

The DMP function of Coon et al. can be characterized by the three parameters P, B and V The parameter p describes the relative slopes
0
of the barrier walls and the outer walls of the potential (79); B is related to the height of the barrier (b) through the relation b = BV 0 The wavefunction of the perturbed oscillator is taken as a





71



linear combination of SHO functions and the eigenvalues and eigenvectors of the various levels are determined by direct diagonalization of the perturbed SHO Hamiltonian. Due to the symmetry properties of the SHO functions ( 79 ) the resulting eigenstates will be divided into even (+) and odd (-) states. These eigenstates are described by linear combinations of even and odd SHO eigenfunctions ( 81) respectively. In the case of TMCBDT the symmetry of the potential is still D2h and the (+) levels will be a while the (-) levels will
2h g

have the symmetry of the mode in question.

The fitting procedure is based on the fact that the eigenvalues relative to the potential minima [V(Qm)] may be written as G/V and
0

the quantity



= G(i) G(0+ + (3-1)
G/V i) -G/V 0(0

is then plotted as a function of the parameter B for a given value of p. The G(i) are the observed frequencies. The intersection of the V versus B curves for several levels (i), will occur only when the
0

two parameters pand B give eigenvalue differences which fit those observed.

The number of basis functions to include in the SHO expansion will depend on the values of p and B (79,80 ) and is chosen to give correct eigenvalues for the lowest 14 levels.

The results of the fit to the observed absorption and emission frequencies at 1.6 K is given in Table 3-3. The DMP potentials are shown in Figs. 3-4 and 3-5. The important conclusions from the fit are





72




TABLE 3-3
DMP DESCRIPTION OF THE LOW FREQUENCY VIBRATIONS OBSERVED AT 1.6K IN CRYSTALLINE TMCBDT SPECTRA

1 3
Alg A lu



Emission Bandsd Absorption bands

Observed Calculated Assignment e Observed Calculated Assignment
+ 0+
0 0 0 0 0 0

-22 14.9 0 0.84 0

-47b 47.0 1+ 47b 46.9 1+

-68 72.6 1 58 54.0 1

-103b 102.0 2+ 85b 86.6 2+


-129 130.2 2 103 105.7 2

-159b 159.2 3+ 134b 133.2 3


-183 188.1 3 158.4 3

-216b 217.1 4+ 185b 185.5 4+

-237 246.1 4- 213c 212.3 4-280 275.3 5+ 239.8 5+

304.4 5 267.2 5

DMP
Parameters

1.80 p 2.10

0.80 B 3.30

29.3 V (cm-) 28.7
0

23.4 b (cm- ) 94.7

1.30 x 10-20 IQ1 (gl/2cm) 2.31 x 10-20


a. See Ref. 43.
b. Observed frequency used in fit. c. Taken from run with more pronounced sideband. d. All quantities are in cm e. Labels refer to DMP levels, see Figures 3-4 and 3-5.




73





ENERGY (cm') 'AIg calc. obs.
130.2 2- 129.




102.0 2+ 103.




72.6 6 8.



47.0 47.




14.9 22.

0.0 00

234
TMCBDT -- -16.1
I I I I I1I
-6 -4 -2 6 +2 +4 +6
Q /( IO- g"2 cm)

Figure 3-4. Double minimum potential for ground state. The energy
levels are obtained from a fit using the emission bands (43) in Table 3-3. The parameters are p=1l.80, B=0.80,
vo=29.3 cm-1, barrier height, b, is 23.4 cm-1 and
minima occur at Q"=l.30xl0-20 gl/2cm.




74


ENERGY (cm') 3A u calc. obs.
133.2 3+ 134.



105.7 2- 103.


86.6 2+ 85.




54.0 -58.
46.9 1+ 47.




9 4.7

0.84.
0.0 O+ 0.



TMCBDT -- -269

-6 -4 -2 0 +2 +4 +6
Q 0 -20 g1/2 M
Q/(I0O g"2 cm)

Figure 3-5. Double minimum potential for triplet excited state. The
energy levels are obtained from a fit using the absorption bands in Table 3-3. The parameters are C=2.10, B=3.30,
Vo=28.7 cm-1, barrier height, b, is 94.7 cm-1 and minima
occur at Q'=2.31x10-20 gl72cm.





75




1. The barrier height in both states is low enough to
preclude observation of a bent molecular structure in the room temperature X-ray determination and infrared
or Raman spectra. In fact it may be shown that for the
ground electronic state based on the level populations at ambient temperature and the value of the transition amplitudes (82) only a single band will be seen at the frequency V 0. (A broad band at 42 cm-1 is observed in
the gas phase IR at room temperature (83)).

2. There is a difference in the potential minima, Qbetween
the ground and excited electronic states: although it is not possible to translate this into an angle since we do not know the reduced mass of the motion, it is seen that
the Q'm'Q"m is about 1.8 (cf. Table 3-3). This amounts
to a 77% change.

3. At 1.6 K the system is constrained to the lowest level so
that the effective symmetry of the potential changes from
D (in the molecular group) to C 2vdue to loss of the mirror
plane of symmnetry.

The Calculated Spectra at 1.6 K

Using the above DMP models absorption and emission spectra may be calculated as a function of temperature (80). The Franck-Condon factors may be found using

F = A' R B (3-2)

where A (B) is the eigenvector matrix for the ground (excited) electronic state and the prime denotes the transpose. R is the overlap matrix over the SHO eigenfunctions of the ground electronic state, V)", and
0
those of the excited electronic state, V'. In this case since the
0

SHO frequencies are nearly the same R is very close to 1. Here it is assumed that the electronic transition moment M e, is independent of v (+), and that the electronic transition is allowed. In the case of a vibronic transition R becomes and the electronic transition moment now involves matrix elements of O~M e AQ) Qobetween the ground and excited electronic states (70). These will not be considered here.





76




To calculate the spectrum the band positions are first determined relative to the 0 +_ 0 +band (0 cm- 1 The intensity for a particular
++
band, (v" = 0+ to v' = 1 at +47 cm ,for example) is then proportional to the square of F (IF 0+12 for this example). All the intensities

are then multiplied by the appropriate fractional (Boltzmann) population factor (N 0+in this case) and the resulting values normalized to the largest intensity.

Normally the displacement (or normal) coordinates Q" and Q' have the same origin in the case of two DMP functions (84); then due to the even/odd symmetry of the SHO eigenfunctions Eq. 3-2 will factor into even and odd components. The resulting spectrum is then strictuly govenred by the (+)-(+) and (--()selection rule and at 1.6 K the transitions to (-) bands should be absent in absorption. In the present model (cf. Table 3-3) transitions to (-) levels in the ground state are predicted in the emission spectrum at 1.6 K because the 0 +and 0 levels of the excited state have a 53% and 47% population distribution.

However, at this low temperature, we can consider the ground state system with the entire population in the 0 + level which is just below the barrier maximum. Then the symmetry is reduced (if the model is applied to a low frequency intramolecular torsion in a planar molecule, for example, the symmetry would be reduced from D 2hto C 2v) and the point group which now determines the selection rules is the subgroup common to both. If we apply this to the TMCBDT (crystal), we find that, if the DMP describes a torsional mode, its symmetry in D 2his (cf. Table 3-2) B 3ufor the (-) and A 9for the M+ levels. In the crystal

factor group these become E u(-) and A (+)M. Since the pure electronic





77




transition is observed Ic, it is E which correlates with either a B 2uor B molecular state. Thus the vibronic species will be



E ,[A lg E Uallowed ic
u E u A g+ B g+ B 2gnot allowed


For the C distorted molecule, the site group is determined by the symmetry elements in common with the unchanged crystal factor group; this is C S. Table 3-4 gives the appropriate correlation among the groups. Here we label the axes differently so that the torsional mode now becomes B .u This becomes totally symmetric in the site; hence, all vibrational levels are symmetric. The electronic state now will be Bl or B 2uwhich become totally symmetric in the site; thus all the vibronic levels become allowed (and ic polarized) in the crystal factor group. (The correlation tables may be found in Ref. 8], Appendix X.)

The above argument justifies calculating R using two displaced SHlO potentials, in which case it is no longer factored ( 80, 84 ) into even/ even and odd/odd blocks. The displacement is taken as the difference in IQmI between the two electronic states. Now the Franck-Condon overlaps will be nonzero for mixed even/odd integrals, even when the even/ odd wavefunctions retain the higher symmetry. For example, for the transition 1 + +_ 0-, which occurs at +47-15=32 cm -1, we would have < 0(-)11(+)>=< [0.99< 11+0.11< 31] 1 [0.6610 >-0.2912 >-0.6914 >

-0.11 6 >]

=(0.99[(0.66) <110 >-(0.29)< 112 >1+...

=0.46 +..

The values for the R elements (< 110 > etc.) are calculated ( 80, 84)





78













4
0 0- 7Z;l
4J ::$
0 tr
W C14 1-4 CN
FJ-4 0









E-4
E



Er-I

x ro

4J
0 -14 0 4J U) 4



0



E-4


4 U)

E--f

E-4
Ix 0
rO W A A
W(a
4-)
W N x
m 0 u 0
< 4-) a) p
E-1 1-4 u (N
0
z 0
P



0




A A
0
W p I
p u :1
0-1 0) CN cli r-I
4J : 4) 0:4
Ul U 4.)
.rq (1) -4 1 4J
10 r-q En N x x N c
0 % Q 0
M: La u






79


















4J 4J -H
>-, 4J


a) Q) (D :: 4 r-i
-H 4j a) 4-4
w >1
4J

0
4 0 tr 4 U) 0)
4 4J
0 41 ro
-4 4J M 0 4-4 04 U)
1 4
0 m En 4J -i -P U
U) 0 -H >4 U 4J 44 4 W Z 0
0
r:: -H 4 4J
41
tW 4J 4J
0 4 o ro in 04 4j ::$ V) 0 -H
4 0
4

x
> En 4-) -4
N Q4 41
u 41 4 H
ra 4j W U) r. 0 (13 4J
0 0 0 41
-r-I 4-) (1) 4 r A 0 9 0 41 rz U) 0 -4
4 N a
>1

4j cn a im
-H 4J E-4
>
-,q
0)
4-) r-I p 0) 0 4J 0 4
r. 4-) (n
0 U) w
-4 4j a) 0 4J U) U i A C: It 4
N E-H fn 44 W



E-4





80



on the basis of (v"/x)')1/2= 1 and a displacement equal to 19.1- Io"I 0 0 m _m

from Table 3-3.

Temperature Dependence of Spectra

Using the model just described we can calculate (approximate)

spectra for various temperatures; Fig. 3-6 shows the effect of raising the temperature from 2-K to 60 K. With this model, the effect of trap emission ( 43 ) can also be simulated by superimposing the 0 +- 0+ band from the calculated spectrum on the wavenumber at which the trap emission onset with decreasing temperature is observed ( 43 ); only one band (-159 cm- ) used in the fit corresponds to an observed trap band.

The essential features in the observed spectra which have been discussed earlier are clearly reproduced by the present model. Considering absorption only in Fiq. 3-6, it can be seen that as temperature increases the 0- v'+ bands increase at the expense of the 0 +- v' bands. As temperature increases still further, more bands to the red of the 0- 0 grow in. There is a limit to the increase of the

O_1+band at +32 cm- for example, because the population (fraction) in the 0 level of the ground electronic state increases (from zero at 1.6K) to a maximum of about 0.31 at 40 K and then decreases as temperature increases. This trend accounts for the observed behavior in the 329 cm- band, for example, since it does not continue to increase above 47 K. In the observed spectrum, the bands continue to broaden and no large shifts in maxima occur above '150 K. Physical Nature of DMP

Thus far the nature of the low frequency vibration that accounts for the observed series of bands built on the 0-0 band has been
















r.
0
.rl
41

0 E-4 44
((5 .
0
(n


rz
0 oll
z
P4
X



4J



U) 4-) :3 ro
,a 41
41 ro CN cli
4-) 4-)
0
r-4 U) 4.) $4 4
4-) 41 41
rn ri
04 Q4 04
4J 4-) 4J ri) U) W

ol U)+ 0 0 0
ul a) 0 H -1
(j) 4-) 4-)
(1 1 04 04 04
0 0+ 4 4 4
.rl 0 0 0 0
U) a) U) U) U)
U) (1) .0 4 4
-4 $4
a) 4-) 4-) ra ro
,a --1 0
-1 4.)
0 0 0
4 > r4 -4 rq
0 0 -r-f U) En En
-1 rX4 4j U) M ul
4-) M rq rq -4
04 rz s E
$4
0 $4
U) $4 10 a
4-) 4 41 4J 4-)
ca (d (13 (0 (0
4 q 14
a) U) 0 :3
4J (1) Ei r r:
ru -4 .14 H H
r-I m (n ul co
0 4J 4
14
En 0 a)









44




82









z
0
z 0
a- 0 cr ; 0
0 +
U)

LLJ




Ole









\000,
C\j

F-




83












z
0

0. Z ct 0
0 co




84











z
0
z 0
a- 0 -0
cr
0 cf) +
U) U)







LLJ





0
0





85




considered to be the TMCBDT torsional mode. This choice is rationalized on the basis of the 42 cm- vibration observed in the f ar-infrared spectrum of TMCBDT vapor ( 83 ). This is assigned to the b 3utorsion due to its low frequency and infrared activity, assuming the molecule is D 2h'

In this section another motion is considered which, qualitatively, is consistent with the DMP calculations. This is the lattice vibration (B 2g) which involves out of phase rotation about the z molecular axis. Using the molecular distances and lattice parameters from the

x-ray structure ( 38 ) the spatial relationships of the molecules in the crystal is shown (to scale) in Fig. 3-7. The view is along the line a=a'. In this view the sulfur non-bonding p orbitals are vertical (11Ic). It can be seen that the motion described by the B 2glattice vibration involves the translationally equivalent molecules all moving in phase with respect to each other and out of phase with respect to their translationally inequivalent counterparts; all the molecules labeled 1 move in phase with each other, as do the ones labeled 2, but all the 1, 2 pairs move out of phase with respect to each other.

The direction of motion is shown in Fig. 3-7 with an arrow for motion in the plane of the paper and with + and for motion out of this plane. It can be seen that positions A and B represent points of closest approach where electrostatic repulsion might give a maximum in the potential function. If the coordinate of the motion is described by the angle of rotation about the z axis, a value of zero for this corresponds to this maximum. motion along the coordinate simultaneously increases the sulfur-sulfur distance at A and the sulfur methyl group




86













































Figure 3-7. Molecular displacements involved in the Bg lattice
vibration. The view shown is along an aa diagonal
(cf. Fig. 3-1) in the unit cell. Two adjacent unit
cells are shown. The methyl groups on one side of
the molecular plane are omitted for clarity. The
direction of motion is indicated by arrows for motion
in the plane of the paper and by + or for motion out
of the figure plane. The circles represent van der
Waals rAdii; those labeled 1 and 2 are the sulfur atoms,
all others are methyl hydrogens. The figure is drawn to scale, taking the van der Waals radii as 1.85 R for
sulfur and 1.20 A for hydrogen, the unit cell dimensions from Fig. 3-1 and the atomic coordinates from Table 4-1.




87




distance at B. This type of behavior could describe a DMP in the ground electronic state.

when the electronic transition to the 3A (rn*) state occurs,

the C=S bond distance is expected to increase. Inspection of Fig. 3-7 shows that in this case the angle of rotation (coordinate of the B 2g motion) would have to increaseto accommodate the elongated C=S bond, while at the zero position (where all translationally equivalent molecules are collinear) the barrier would increase. This is consistent with the DMP descriptions for the ground and excited electronic states described previously.

While both the intramolecular torsion and intermolecular lattice modes can account for the observed low frequency series of bands near the 0-0 band, there is no direct experimental evidence presently available that can confirm one model or the other. Semiempirical calculations (INDO for example) of the energy as a function of the rotation (and torsion) coordinate could be performed on a cluster of several TMCBDT molecules to determine the potential energy of the ground and lowest triplet state as a possible means to reinforce one model or the other.

In connection with Fig. 3-7 it is seen that if the van der Waals radii for the atoms are taken into account, the TMCBDT molecules are rather close together. In this respect it is not surprising that only one vibrational quantum of the C=S stretch is observed in the absorption spectrum. This fact means that the change in equilibrium position for that coordinate is slight. Whereas in the free molecule the change in this same coordinate could be expected to be greater, in the crystal the lattice restricts this expansion somewhat. A lattice distortion