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The electronic spectra of crystalline charge-transfer complexes. Lower, Stephen Kent 1963

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THE ELECTRONIC SPECTRA OF CRYSTALLINE CHARGE-TRANSFER COMPLEXES by STEPHEN KENT LOWER B.A., University of C a l i f o r n i a , Berkeley M.Sc, The University of B r i t i s h Columbia a thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements for the degree of DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept t h i s thesis as conforming to the required standard: THE UNIVERSITY OF BRITISH COLUMBIA July, 1963 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I f u r t h e r agree that per-mission for extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. I t i s understood that copying, or p u b l i -c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. D ate U n r e l a t e d S t u d i e s : T o p i c i n O r g a n i c C h e m i s t r y L . D . H a y w a r d R . S t e w a r t D . E . M c G r e e r T o p i c s i n I n o r g a n i c C h e m i s t r y H . C . C l a r k W . R . C u l l e n P U B L I C A T I O N S T h e P o l a r i z e d c h a r g e - t r a n s f e r s p e c t r u m o f c r y -s t a l l i n e a n t h r a c e n e - T N B c o m p l e x : S . K . L o w e r , R . M . H o c h s t r a s s e r a n d C . R e i d . M o l e c u l a r P h y s i c s 4, 161 (1961). P o l a r i z a t i o n o f t h e s p e c t r a o f c r y s t a l l i n e a z o b e n z e n e a n d m i x e d c r y s t a l s o f a z o b e n z e n e i n s t i l b e n e a t 77° a n d 4.2° K i n t h e r e g i o n o f t h e l o w e s t n — 7T * t r a n s i t i o n : R . M . H o c h s t r a s s e r a n d S . K . L o w e r J . C h e m . P h y s i c s 36, 3505 (1962). T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a F A C U L T Y O F G R A D U A T E S T U D I E S PROGRAMME O F T H E F I N A L O R A L E X A M I N A T I O N F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y o f S T E P H E N K E N T L O W E R B . A . , U n i v e r s i t y o f C a l i f o r n i a , 1955 M . S . , O r e g o n S t a t e U n i v e r s i t y , 1958 M . S c , T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1960 M O N D A Y , A U G U S T 26, 1963, A T 9:30 A . M . I N ROOM 261, C H E M I S T R Y B U I L D I N G C O M M I T T E E I N C H A R G E C h a i r m a n : F . H . S o w a r d N . B a r t l e t t K . B . H a r v e y W . A . B r y c e C . R e i d F . W . D a l b y R . S t e w a r t E . J . W e l l s E x t e r n a l E x a m i n e r : S . M c G l y n n L o u i s i a n a S t a t e U n i v e r s i t y THE ELECTRONIC SPECTRA OF CRYSTALLINE CHARGE-TRANSFER COMPLEXES ABSTRACT Charge=transfer complexes of the aromatic hydro-carbontrinitrobenzene type are s t a b i l i z e d p r i n c i p a l l y by interaction between a dative- and a "no bond" state: The res u l t i n g complexes .usually possess a colour which i s associated with an"electronic t r a n s i t i o n be-tween the ground, state c|>N and a predominantly dative excited state; the t r a n s i t i o n therefore corresponds to the p a r t i a l transfer of an electron from the donor (D- usually the hydrocarbon) to the acceptor (A). Most of the previous spectroscopic work, on CT complexes has been concerned ,with solutions of the complexes; no detailed investigation of a c r y s t a l l i n e complex has been made, The somewhat random nature of CT interaction i n solution tends to l i m i t the amount of information "we "'can gain" from such studies, and this has prompted the present work'oh s o l i d complexes. With a system of d e f i n i t e composition and structure, both the spectroscopic examination and theoretical treatment can be carried out at a more quantitative l e v e l . .. :> ; - -• v The results"of a detailed spectroscopic study of the c r y s t a l l i n e anthracene-trinitrobenzene complex are presented. I t is..shown,, that 1) The CT t r a n s i t i o n moment "is strongly polarized p a r a l l e l to the c-axis _of the cryst a l (approxi-mately perpendicular"to the molecular planes), with a p o l a r i z a t i o n r a t i o greater than that pre-dicted by the simple oriented gas model. 2) A portion of the intensity of the CT state i s derived from mixing with the.more intense ^L a state of anthracene," confirming the prediction of J. M u r r e l l . 3) The c r y s t a l emission spectrum consists almost e n t i r e l y of CT. fluorescence with v i b r a t i o n a l struc-ture s i m i l a r to that of the absorption. The entire spectrum i s blue-shifted with respect to that of the r i g i d - g l a s s solution; as i n solution, there i s a very wide gap between the absorption and fluorescence o r i g i n s . 4) The emission i n t e n s i t y i s strongly tempera-ture dependent; a portion of this dependence is reversible, while the remainder i s apparently connected with the creation of c r y s t a l defects on cooling and cannot be reversed. I t i s suggested that the CT state i s highly de-localized i n the c r y s t a l , and that the t r a n s i t i o n dipole moment connecting the ground- and CT states must be polarized along the £-axis of the c r y s t a l , rather than between the centers of the indiv i d u a l donor-acceptor pairs. A number of TNB complexes of other hydrocarbons were studied, although in much less d e t a i l . Their spectroscopic properties appear to be similar to those of anthracene-TNB. Polarized phosphorescence- and t r i p l e t - t r i p l e t absorption spectra of several aromatic hydrocarbons dissolved i n c r y s t a l l i n e benzophenone are given. This i s the f i r s t reported observation of t r i p l e t -t r i p l e t absorption in cr y s t a l s , and i t i s shown that i t i s polarized mainly i n the planes of the molecules investigated. GRADUATE STUDIES F i e l d of Study? Physical Chemistry Topics i n Physical Chemistry Molecular Spectroscopy Quantum Chemistry Related Studies: S t a t i s t i c a l Mechanics Surface Chemistry Crystallography Chemical Kinetics R.M J.A.R. Coope C.A. McDowell R.F. Snider C. Reid , Hochstrasser J.A.R. Coope R.F. Snider J. Halpern K.B. Harvey J. Trotter G.B. Porter J. Halpern Note: A paperbound copy of this thesis, produced from microfilm by the Xerox pro-cess, i s available from University Micro-films, Ann Arbor, Michigan. i i ABSTRACT Charge-transfer complexes of the aromatic hydrocarbon-trinitrobenzene type are s t a b i l i z e d p r i n c i p a l l y by i n t e r -action between a dative- and a "no-bond" state: <$n= a ^ (DA) + b % (D +A") . The r e s u l t i n g complexes usually possess a colour which i s associated with an e l e c t r o n i c t r a n s i t i o n between the ground state (pN and a predominantly dative excited state; the t r a n s i t i o n therefore corresponds to the p a r t i a l transfer of an electron from the donor (D- usually the hydrocarbon) to the acceptor (A). Most of the previous spectroscopic work on CT complexes has been concerned with solutions of the complexes; no detailed investigation of a c r y s t a l l i n e complex has been made. The somewhat random nature of CT int e r a c t i o n i n solu-t i o n tends to l i m i t the amount of information we can gain from such studies, and t h i s has prompted the present work on s o l i d complexes. With a system of d e f i n i t e composition and structure, both the spectroscopic examination and theor-e t i c a l treatment can be c a r r i e d out at a more quantitative l e v e l . The r e s u l t s of a detailed spectroscopic study of the c r y s t a l l i n e anthracene-trinitrobenzene complex are pre-i i i sented. It i s shown that 1) The CT t r a n s i t i o n moment i s strongly polarized p a r a l l e l to the c-axis of the c r y s t a l (approximately perpendicular to the molecular .planes), with a polar-i z a t i o n r a t i o greater than that predicted by the simple oriented gas model. 2) A portion of the i n t e n s i t y of the CT state i s derived from mixing with the more intense ^L a state of anthracene, confirming the prediction of J . Murrell. 3) The c r y s t a l emission spectrum consists almost e n t i r e l y of CT fluorescence with v i b r a t i o n a l structure si m i l a r to that of the absorption. The e n t i r e spec-trum i s blue-shifted with respect to that of the r i g i d -glass solution; as i n solution, there i s a very wide gap between the absorption and fluorescence o r i g i n s . 4) The emission i n t e n s i t y i s strongly temperature dependent; a portion of this dependence i s revers-i b l e , while the remainder i s apparently connected with the creation of c r y s t a l defects on cooling, and cannot be reversed. It i s suggested that the CT state i s highly delocalized i n the c r y s t a l , and that the t r a n s i t i o n dipole moment connecting the ground- and CT states must be polarized along the c-axis of the c r y s t a l , rather than between the centers of the i n d i -v i d u a l donor-acceptor p a i r s . A number of TNB complexes of other hydrocarbons were studied, although i n much less d e t a i l . Their spectroscopic properties appear to be s i m i l a r to those of anthracene-TNB. Polarized phosphorescence- and t r i p l e t - t r i p l e t absorp-t i o n spectra of several aromatic hydrocarbons dissolved i n i v c r y s t a l l i n e benzophenone are given. This i s the f i r s t r e -ported observation of t r i p l e t - t r i p l e t absorption i n c r y s t a l s , and i t i s shown that i t i s polarized mainly i n the planes of the molecules investigated. abstract approved: X ACKNOWLEDGEMENTS It i s a pleasure to thank Dr. R. M. Hochstrasser for his extensive counsel and assistance during my stay here. His help has been invaluable i n introducing me to the p r a c t i c a l aspects of spectroscopy, i n f a m i l i a r i z i n g me with the f i e l d of molecular spectroscopy i n general, and in d i r e c t i n g the course of much of my work. I am gra t e f u l to Dr. C. Reid f o r suggesting t h i s topic, and for his aid i n in t e r p r e t i n g many of the experimental r e s u l t s . Dr. A. V. Bree has frequently gone out of his way to a s s i s t me on very short notice, and his help i s g r a t e f u l l y acknowledged. I wish to thank Dr. S. C. Wallwork of the University of Nottingham for supplying me with his unpublished data of the c r y s t a l structures of a number of complexes. I also thank Dr. J . Trotter f o r making several X-ray studies for me, and Mr. F. Sawford for constructing several major parts of my experimental apparatus. The assistance i n the form of a Studentship from the National Research Council (Ottawa) i s g r a t e f u l l y acknowledged. V TABLE OF CONTENTS I. INTRODUCTION AND SCOPE 1 Abbreviations 3 II. THEORY OF CHARGE-TRANSFER INTERACTION . . . . 5 III. SPECTROSCOPIC PROPERTIES OF MOLECULAR COMPLEXES 16 Charge-transfer absorption 16 Higher charge-transfer bands 18 Dipole moments . . . . . . . . . . . . . 18 Transition moment and o s c i l l a t o r strength 19 Temper attire and pressure e f f e c t s . . . . 20 Solvent e f f e c t s 21 Fluorescence and phosphorescence . . . . 22 IV. THE SPECTRA OF MOLECULAR CRYSTALS 26 Absorption and absorption measurement. . 26 Molecular c r y s t a l s : The oriented gas approach 29 Energy states of a molecular c r y s t a l . . 34 Second-order i n t e r a c t i o n 41 Fate of absorbed energy 45 Other r a d i a t i v e mechanisms 47 V. MOLECULAR COMPLEXES IN THE SOLID STATE . . 50 Thermodynamic properties 53 Cr y s t a l structures 57 VI. EXPERIMENTAL PROCEDURE AND APPARATUS . . . 59 Instruments 59 Detectors 62 Amplifier 63 Sample preparation 65 Absorption spectra 66 VII. THE ANTHRACENE-TNB COMPLEX 68 Cry s t a l structure 68 v i The absorption spectrum 74 Discussion 77 Selection rules and polarizations . . . 83 Intensities 90 The emission spectrum 95 Emission from r i g i d glass solution . . . 101 Discussion of the emission 102 Pol a r i z a t i o n and i n t e n s i t y 104 VIII. OTHER COMPLEXES 9,10-Dimethylanthracene-TNB 108 Hexamethylbenzene-TNB 112 Fluorene-TNB 114 Stilbene-TNB, azobenzene-TNB 115 Azulene-TNB 117 Chrysene-TNB 120 Triphenylene-TNB 122 Phenanthrene-TNB 122 Pyrene-TNB 125 Perylene-TNB 126 Benzidine-TNB 128 Quinhydrone and phenoquinone 130 APPENDIX A: Atomic coordinates and p r i n c i p a l directions i n the anthracene-TNB c r y s t a l , 133 APPENDIX B: Calculation of inte r a c t i o n integrals 136 APPENDIX C: SUPPLEMENT: Po l a r i z a t i o n of the phosphorescence and t r i p l e t - t r i p l e t absorption i n aromatic hydrocarbons . 138 BIBLIOGRAPHY 152 v i i TABLE I. Thermodynamic properties of hydrocarbon-TNB complexes 55 TABLE I I . Matrix elements f o r in t e r a c t i o n between the CT t r a n s i t i o n and the two lowest excited s i n g l e t states of anthracene 88 TABLE I I I . Approximate ex t i n c t i o n c o e f f i c i e n t s of ele c t r o n i c t r a n s i t i o n s i n c r y s t a l l i n e anthracene-TNB 93 TABLE IV. Atomic coordinates of anthracene-TNB i n the c r y s t a l , 134 TABLE V. Direction cosines of t r a n s i t i o n dipoles i n anthracene-TNB 135 TABLE VI. Angle cosines between lines-of-centers and t r a n s i t i o n dipoles 136 TABLE VII. Integral sums for second-order i n t e r -action i n anthracene-TNB 136 TABLE VIII. Cosines of angular terms of Eq. 28 . . . 137 TABLE IX. Phosphorescence maxima of hydrocarbons i n benzophenone 145 TABLE X. T r i p l e t - t r i p l e t absorption spectra of hydrocarbons i n benzophenone and i n s o l u t i o n 149 FIGURES F i g 1 Energy diagrams for anthracene-TNB 10 F i g 2 Geometrical factors for c r y s t a l interactions 44 Fi g 3 O p t i c a l system for polarized c r y s t a l spectra 64 F i g 4 Block diagram of el e c t r o n i c c i r c u i t r y . . . . 64 v i i i F i g 7 Anthracene-TNB c r y s t a l : view along c-axis . 70 F i g 8 Anthracene-TNB c r y s t a l : projection on (100) 71 F i g 9 Polarized absorption spectrum of anthracene-TNB, d i r e c t method at room temperature . . 75 F i g 10 Polarized absorption spectrum of anthracene-TNB 76 F i g 11 Absorption spectra of TNB and of anthracene 81 F i g 12 The space group C2/c 85 F i g 13 Space l a t t i c e of t r a n s i t i o n moments 85 F i g 14 Anthracene-TNB: c r y s t a l emission spectrum 96 Fi g 15 Combined spectra of anthracene-TNB c r y s t a l 97 F i g 16 Temperature-dependence of emission i n t e n s i t y 99 F i g 17 Combined spectra of anthracene-TNB i n solution 99 F i g 18 Emission spectra of anthracene and anthracene-TNB i n r i g i d glass solution 100 F i g 19 Possible emission processes i n the anthra-cene -TNB c r y s t a l 106 F i g 20 9,10-dimethylanthracene: absorption . . . . 110 F i g 21 9,10-Dimethylanthracene: emission 110 F i g 22 Combined spectra of both forms of DMA-TNB 111 F i g 23 Hexamethylbenzene-TNB emission 113 F i g 24 Fluorene-TNB emission 113 F i g 25 Stilbene- and azobenzene-TNB spectra , . . . 116 F i g 26 Azulene-TNB absorption spectrum 119 i x F i g 27 Phenanthrene-TNB emission 123 Fig 28 Chrysene-TNB absorption and emission , . . . 121 F i g 29 Triphenylene-TNB emission 121 Fi g 30 Pyrene-TNB emission 126 F i g 31 Perylene-TNB and perylene absorption spectra 126 F i g 32 Benzidine-TNB absorption 129 Fi g 33 Quinhydrone absorption 131 F i g 34 Phenoquinone absorption 132 F i g 35 Polarized phosphorescence spectra of phen-anthrene and chrysene i n benzophenone . . . 146 F i g 36 Polarized phosphorescence spectra of naph-thalene and acenaphthene i n benzophenone. . 147 Fi g 37 Polarized t r i p l e t - t r i p l e t absorption of anthracene and naphthalene i n benzophenone 150 I. INTRODUCTION AND SCOPE This thesis consists p r i n c i p a l l y of an experimental spectroscopic study of the anthracene-trinitrobenzene mol-ecular complex i n the s o l i d state. The intensely colored compounds frequently obtained on mixing two suitable c o l o r -less components have been objects of study since the be-ginning of the century, and gave r i s e to much early discussion concerning the nature of the "bond" between the two molecules, and the r e l a t i o n of color to chemical structure. At a time when chemical bonding i n aromatic systems was j u s t beginning to be understood, i t i s not s u r p r i z i n g that l i t t l e headway was made i n explaining these complexes; i t was not u n t i l 1950 that R.S. Mulliken presented his theory of charge-transfer i n t e r a c t i o n that has served as the basis f o r the subsequent t h e o r e t i c a l development of the subject. Interest i n charge-transfer forces has extended be-yond the f i e l d of s t r u c t u r a l and t h e o r e t i c a l chemistry to problems of chemical e q u i l i b r i a (46a) and surface phenomena (59). Szent-Gyorgi (45) has suggested that charge-transfer e f f e c t s may play an important r o l e i n bio-l o g i c a l energy-transfer processes, and t h i s idea has been applied by others to model mechanisms1 <0)f photosynthetic (49) and v i s u a l (72) processes. 2 Most of the past spectroscopic work on molecular complexes has consisted i n the cataloging of absorption spectra i n solution, and r e l a t i n g the spectra to properties of the components. This work has served to v e r i f y Mull-iken's ideas, and to extend them i n a number of directions, but we are s t i l l without a complete ele c t r o n i c description of this type of complex. In p r i n c i p l e , such a description should be possible i n terms of the electronic structure of the hydrocarbons and substituted hydrocarbons which comprise the complex, and whose detailed t h e o r e t i c a l treatment i s now p r a c t i c a l . Our understanding of the elect r o n i c states of aromatic hydrocarbons has been aided by studies of the i r c r y s t a l spectra, and i t i s hoped that the present work w i l l be of sim i l a r use i n regard to charge-transfer complexes. Most of th i s work was devoted to the study of a single complex, that of anthracene and 1,3,5-trinitrobenzene. A number of phenomena were noted that have not been ob-served i n other molecular c r y s t a l s ; t h i s has necessitated some speculation, based as much as possible on simple quantum-mechanical models, as to the o r i g i n of these e f f e c t s . In order to see whether these p e c u l i a r i t i e s are shargdiby other molecular complexes, a number of other TNB-hydrocarbon adducts were examined, although i n much 3 less d e t a i l . Because the emission spectra of some of the complexes include a component corresponding to hydrocarbon phosphor-escence, experiments on the p o l a r i z a t i o n of tr a n s i t i o n s involving hydrocarbon t r i p l e t states were begun. This work i s now i n progress, and some of the r e s u l t s are reported i n Appendix C. F i n a l l y , a discussion of experimental procedure and apparatus i s included. It i s rather short, and therefore quite out of proportion to the very large amount of time spent i n developing techniques of growing and handling c r y s t a l s , i n designing and building apparatus, and i n ob-tai n i n g reproducible spectra. Abbreviations. The following abbreviations are employed throughout the text: TNB = 1,3,5-trinitrobenzene CT = charge transfer D » donor (usually TNB) A = acceptor (usually a hydrocarbon) S = s i n g l e t T = t r i p l e t 4 Orientations of aromatic molecules i n a c r y s t a l l a t t i c e are expressed i n terms of the i n c l i n a t i o n s of a set of orthogonal vectors L, M, and N with respect to the crystallographic axes a, b, and g_ (or c_' , which i s ortho-gonal to a and b). These vectors correspond to the long-, short-, and perpendicular symmetry axes of the molecule, respectively, and the same l e t t e r s are occasionally used to denote ele c t r o n i c t r a n s i t i o n s which are polarized i n these d i r e c t i o n s . Frequencies (used i n preference to wavelengths) are given i n kiloKaysers (kK), p a r t l y for convenience and pa r t l y to avoid the i l l u s i o n of accuracy created by giving a frequency i n f i v e figures. Reciprocal centimeters, when used, are written j u s t that way, v i z . , 100/cm. 5 II. THEORY OF CHARGE-TRANSFER INTERACTION Molecular complex formation has long been thought to occur as a r e s u l t of the combination of an electron donor (D) with an acceptor (A). Weitz-Halle (89,90) and Weiss (88) suggested an ionic structure D+A~ and predicted that a low io n i z a t i o n p o t e n t i a l of the Lewis base D and a high electron a f f i n i t y of the Lewis acid A would lead to a more stable complex. Brackman (12) came much closer to the present concept by proposing resonance int e r a c t i o n between a "no-bond" and a bonded structure i n which the color of the complex (assuming c o l o r l e s s components) i s due to the complex as a whole, and not l o c a l i z e d within any one com-ponent . The presently accepted views on the nature of the donor-acceptor complex were set f o r t h by Mulliken i n a series of papers beginning i n 1950 (56-63). His o r i g i n a l concern was with complexes of the benzene-iodine type (56), but he l a t e r (59) generalized the theory to include a l l charge-transfer complexes of the weak type. The theory was applied s p e c i f i c a l l y to the TNB-polyacene complexes by McGlynn (53). Formation of a stable donor-acceptor complex i s con-sidered to arise from the inte r a c t i o n of "no-bond" and ionic 6 (charge-transfer) states of the D-A system. The ground state l°N i s $w= aV^(DA) + b ^ A " ) + c</i(D-A+). (la) Corresponding to <£v , the existence of an excited state <£e = c* (f z(D"A +) + b*f(D +A _) - a*^(DA) (lb) is also predicted. Transitions between these two*states give r i s e to the absorption spectra responsible for the ch a r a c t e r i s t i c colors of many CT complexes. More e x p l i c i t l y , V£ can be written as a Slater fun-c t i o n involving a l l n electrons of the complex: (nf) _ i | 6(2) <?,<3)... £n(n)|. (2) The o r b i t a l s % and £ r e f e r to opposite spin states. % i s the normalized M.O. of the highest f i l l e d l e v e l of the donor, and the other are the other M.O.'s which are considered unaffected by the complexing. The dative-bond eigenfunctions and represent the p a r t i a l transfer of an electron from one of the components to the other; f ° r instance, can be written with s D A = ceA % ), - (n!)"* ¥„<D <€A(2) <P,<3)... §,(n), (3) T>u = (n ! T PA(D fe(2) ^ ( 3 ) . . . g,(n), (4) In the l a t t e r two expressions, an electron has been trans-7 ferred from to the lowest u n f i l l e d M.O. ( % ) of the acceptor. The "reverse" dative-bond function £>a i s usually neg-lected; however, i t represents the e n t i r e l y possible i n t e r a c t i o n between a f i l l e d o r b i t a l of the acceptor and an empty donor o r b i t a l . This back-coordination may fur n i s h much of the s t a b i l i t y of the complex i n i t s ground state, and would tend to make the r a t i o a/b of the c o e f f i c i e n t s (as determined from dipole moment data) appear larger than i t r e a l l y i s . For TNB complexes of aromatic hydrocarbons, a and b are o r d i n a r i l y 0.96-0.98 and 0.14-0.20, res p e c t i v e l y (21). Some insight into the energetics of complex formation i s afforded by a simple perturbation c a l c u l a t i o n based on eq (1) when c_ = 0. We f i r s t define So,-/*?.**, Kol=Jy0WtJT (5) The energylof the complex i s given by L _ —_—•—.——• •—-E ~ tO-s^ + zcLb sol TWsi, (6) or E ( a z S 0 0 + 2abS0, + b""-S „ ) = a t(H o t () + 2abH o l + b"H„ (7) Taking f i r s t the derivative with respect to a, and s e t t i n g 8 i t equal to zero, we obtain (8) with £ a minimum when E(2aS 0 0 + 2bS0, ) » 2aH 0 0 + 2bH o l . (9) S i m i l a r l y , minimizing E with respect to b, we have E( aSoi+ bS„ ) = aH o l+ bH„ . (10) Equations (9) and (10) can be rewritten a(H 0 o-SooE) + b(Ho (-S 0 /E) - 0 (9a) a(H / e -S/o E) + b(H„ -S„ E) = 0 (10a) which are s a t i s f i e d when the c o e f f i c i e n t s a and b are such that Hoo~S0o E Hoi ""So/ E = 0. (11) H 0 / -S0/ E H// -S// E In the complex, the hamiltonian operator W3 f o r the separated molecules i s perturbed by t h e i r interaction, giving r i s e to a new operator V - K° + V', (12) and we seek the corresponding energies, defined by V $i - E.- $i (13) The secular equation (11) now becomes Hoo ~(E - Eg) Hoi " ES Hot ~ ES E| -Eo i n which E has been replaced by E 0 i n the second diagonal = 0 (14) 9 element, and H,', has been dropped ( i t i s small compared to EQ - E,°). The determinant i s evaluated by multiplying the second row by the f r a c t i o n (Hoi - E S ) / ( E , - E 0 ) and sub-t r a c t i n g i t from the f i r s t : - O H 0 1 - ^ s (15) (15a) and since the energies are nondegenerate, AE = Hoc - (H}:'£.S) (16) Following the usual convention, we replace E 0 by WQ, the energy of the structure DA, and E, by W, , the energy of D + A~. The ground- and excited-state energies are Ww and W£ , respectively. The r e l a t i o n s between these quant-i t i e s are shown i n the diagram of F i g l a . Equation (16) now becomes o . ( H o . - W o S - ) 1 A F f l = £"- E"o = W « - U/ 0 = Wo W [ _ ^ • (17) S i m i l a r l y , for the excited state deriving from eq l a , we have W E = w , + ^ ^ ( 1 8 ) W , - We, 10 50 30 ) ENERGY, i kK. 10 0 O:A-w, / 4 lo* E, + 0, A ENERGY DIAGRAM FOR ANTHRACENE-TNB 11 The r a t i o of the c o e f f i c i e n t s i s e a s i l y found. From (14), a[H 0' o- (E - Ej)] + b[H 0' - ES] - 0 (19) or, since E = MN i s close to W0, a(W, -W0) + b(H 0. - W0S) = 0 (20) whence a/b =-(Ho. -W 0S)/(W, - Wo). (21) In the above expressions, Wo includes the energies of the separated donor and acceptor molecules as well as a l l the various a t t r a c t i v e and repulsive intermolecular forces. In addition, W, also includes an a t t r a c t i o n energy of co-valeht and ionic bonding. The difference between W, and W 0 i s approximated by the sum of the donor i o n i z a t i o n po-t e n t i a l and the acceptor electron a f f i n i t y ( Fig l a ) . The ground-state resonance energy i s the difference between W C and W„/ , and w i l l be large i f (H o l - SWQ) 1 i s large and (W, - W C) i s small. In the case of r e l a t i v e l y weak com-plexes of the type under discussion (where the perturbation theory i s v a l i d ) , ( W E - W*) should be 0 to 10 kcal (21). Since, to a rough approximation, h v C T = WN - Wg i s a function of the difference of the donor i o n i z a t i o n p o t e n t i a l and the acceptor electron a f f i n i t y , one finds that the points obtained by p l o t t i n g the donor i o n i z a t i o n potentials against the positions of t h e i r CT bands when complexed with a given acceptor tend to c l u s t e r about a straight l i n e (for 12 donors of a si m i l a r type). This r e l a t i o n has been of use i n providing estimates of the i o n i z a t i o n energy of new hydrocarbons from the positions of t h e i r CT bands with common acceptors (38). In order that the resonance energy W,- We be s i g n i f i c -ant, H 0 and S must be non-zero; t h i s requires that ^ 0 and fy be of the same symmetry species i n the point group of the complex. This i s not a severe r e s t r i c t i o n , since com-plexes of the hydrocarbon-TNB type can generally have only a very low symmetry, usually C s at most. Even i n the ben-zene-TNB 1:1 complex (C3 V), the benzene cation has a ground-state symmetry of E l g (D 6 h) and that of the TNB anr-ion i s probably *E" (D3h), but both states transform l i k e E i n C3 V, which i s the site-group of the complex. The theory presented here i s e s s e n t i a l l y that of Mulliken, and has been f a i r l y successful i n i n t e r p r e t i n g a wide v a r i e t y of observations, made mostly on complexes i n solution. Orgel and Mulliken (69) soon recognized, however, that before i t could be used i n a precise way to describe thermodynamic e f f e c t s i n solution, i t would be necessary to consider the s t a t i s t i c a l e f f e c t s of contact charge-transfer ( i n which the complex ex i s t s as such only during a random c o l l i s i o n a l encounter) and multiple CT complexing, which 13 may occur to a considerable extent i n l i q u i d systems. Further refinements of the theory, e s p e c i a l l y by Murrell (65) have provided considerably more insight into the theory of i n t e n s i t i e s of CT bands, and the influence of donor- and acceptor-excited states on the CT i n t e n s i t y . Dewar and Lepley (38) have suggested a molecular or-b i t a l approach to CT in t e r a c t i o n that has c e r t a i n advant-ages over the more common "valence bond" method (with i t s dative and no-bond forms) and w i l l no doubt receive consid-erable use i n the future. Complex formation i s regarded as occuring through the s t a b i l i z a t i o n afforded when a f i l l e d donor o r b i t a l interacts with an u n f i l l e d acceptor o r b i t a l . This view i s p a r t i c u l a r l y valuable when i t becomes necess-ary to consider multiple CT bands or back-coordination from a f i l l e d acceptor o r b i t a l to a higher empty donor o r b i t a l . B r i e f l y summarizing Murrell's ideas, he considers the following zeroth order CT states, which are written as four-electron Slater determinants: H^o (D, A) (ground state) 4> (D*,A) (excited donor) 4\(D,A*) (excited acceptor) 4 J 3(D +A~) (excited CT state) As the four components are brought together, i n t e r a c t i o n 14 amongst the various states can be described i n terms of perturbed states composed of mixtures of the above functions 9 R > the c o e f f i c i e n t s a s^ ind i c a t i n g the extent of mixing with other states s.. The perturbed ground-state function i s ^o(DA) + a20 % (D +A"), while that of the CT state i s %' - Y>(D+A-) + a O J % (DA) + a „ <K (D*A) + aZ3 ^ ( D A * ) . The t r a n s i t i o n moment between the two states i s given by M 0 3 = ( M Q J - S O J M O O ) + a3o (M 3 3- M 0 0) + a 1 3M 0, + a „ MOJl. Since the % and % are orthogonal, they w i l l not con-tribu t e to the CT "bonding", but the moment M O J w i l l be s i g n i f i c a n t , and the f i r s t term w i l l therefore give r i s e to CT absorption whenever D and A are close enough, regardless of the s t a b i l i t y of the complex. The second term depends on a 3 0 , which measures the CT s t a b i l i z a t i o n of the ground state, and i s important i f stable complexes are formed. The l a s t two terms may be quite appreciable i f the t r a n s i t i o n moments M 0 1 and Moa are large. This i s r e a l l y the crux of Murrell's argument- intense CT absorption bands may cause M o l and Moa. to be as large as (M 7 3 - M 3 Q ) . If a stable complex i s not formed ( i . e . , a ? o ~0) , then the (Mo 1 - Moa,) terms can provide the chief source of CT i n -te n s i t y . The c o e f f i c i e n t s a,3 , a, x, a Z 3 etc. depend on the 15 corresponding overlap i n t e g r a l s , which should have larger values than those for the ground state, p a r t l y because of the generally more dif f u s e character of excited o r b i t a l s , and p a r t l y due to the smaller energy difference between the CT state and the l o c a l i z e d excited states of the com-ponent molecules. In complexes of aromatic donors and acceptors, mixing w i l l not occur i f the rings of the two molecules are exactly p a r a l l e l , because the CT state i s polarized perpendicular to the r i n g planes, while the l o c a l i z e d states are mostly in-plane. Since the most stable form of the complex i s probably the parallel-planar one, i t follows that contact CT must be responsible for most of the i n t e n s i t y of CT absorption i n solution. 16 I I I . SPECTROSCOPIC PROPERTIES OF MOLECULAR COMPLEXES Charge-transfer absorption. The intense colors that characterize many molecular com-plexes, e s p e c i a l l y i n the s o l i d form, led to much of the earl y i n t e r e s t i n them, and also to much conjecture regard-ing the o r i g i n of the co l o r . Briegleb (14) and Murakami (64) suggested that the v i s i b l e absorption arose from a Stark-effect s h i f t of one of the component absorption bands, or from removal of the forbiddeness of s i n g l e t - t r i p l e t ab-sorption. Bayliss (5) i d e n t i f i e d the CT bands of benzene-halogen complexes with the (highly shifted) halogen absorp-t i o n bands. Mulliken's charge-transfer theory predicts the e x i s t -ence of an o p t i c a l t r a n s i t i o n s i m i l a r to the bands that have long been observed i n molecular complexes. According to the theory, a CT band should exh i b i t a number of unique c h a r a c t e r i s t i c s , and their experimental observation has re-sulted i n general acceptance of Mulliken's ideas. With acceptors such as TNB, TNT, p i c r i c acid, etc., aromatic hydrocarbons form complexes that generally absorb i n the short-wavelength end of the v i s i b l e region. Benzene-TNB i s c o l o r l e s s ( i t ' s CT band i s i n the u l t r a v i o l e t ) , but hexamethylbenzene-, naphthalene-, and phenanthrene-TNB are 17 yellow, anthracene- and pyrene-TNB are orange, and perylene-TNB i s deep red. Complexes containing amino groups have intense, deep colors, the CT band frequently extending into the near i . r . CT absorption bands are usually located to the red of the lowest S—>S absorption band of the donor, but th i s i s not always the case; i n azulene-TNB, the CT band f a l l s be-tween the two lowest S->S bands, while i n azobenzene- and tetracene-TNB the CT band i s hidden by the lowest S S band. There now exists a large amount of experimental data on the absorption spectra of CT complexes i n solution; t h i s has been reviewed by Andrews (1) and Briegleb (21). L i t t l e spectroscopic work has been done on the s o l i d com-plexes, and most of th i s has consisted of the measurement of di f f u s e r e f l e c t i o n spectra or the absorption spectra of non-oriented p o l y c r y s t a l l i n e samplex i n KBr p e l l e t s or o i l mulls- generally y i e l d i n g l i t t l e information beyond what i s already known from solution spectra. The only examination of single c r y s t a l s was made be Nakamoto (66), who found that the CT absorption i n hexa-methylbenzene-TNB i s greater for l i g h t polarized perpen-dicul a r to the r i n g planes. 18 Higher CT bands. Orgel noted (70) that the CT bands of chloranil-sub-stituted-benzene complexes show evidence of being composed of two separate broad t r a n s i t i o n s , and suggested that t h i s i s an expected r e s u l t of the s p l i t t i n g of the E^g degenerate ground state of the donor, under the perturbing influence of the substituent group. Briegleb (21) has reviewed the evidence for multiple CT bands a r i s i n g from i n t e r a c t i o n of the acceptor with d i f f e r e n t donor lev e l s , and has shown that differences i n energy of the multiple CT bands remain constant as the ac-ceptor i s changed. A strong acceptor l i k e tetracyanoeth-ylene commonly shows two or three d i s t i n c t CT bands with c e r t a i n donors, and i t i s reasonable to suppose that other acceptors would do likewise i f the higher CT bands were not hidden by the l o c a l i z e d t r a n s i t i o n s of the donor or acceptor. Dipole moments. The contribution of the dative-bonded structure to the ground state of a CT complex containing non-polar compon-ents gives r i s e to a permanent dipole moment JJL^ , given (59) by where r< i s the vector distance of the i t h electron from 19 an o r i g i n and e i s the ele c t r o n i c charge. This can be re-lated to the c o e f f i c i e n t s a and b by MM= Mi (b* + ab S) where ju, i s the dipole moment corresponding to complete one-electron transfer from donor to acceptor. From the r e l a t i o n a*(b + aS) » b*(bS + a) which must hold i f % and % axe orthogonal, i t i s seen that a knowledge of // M and M, and an estimate of S permits the c a l c u l a t i o n of these c o e f f i c i e n t s and hence of the per-cent io n i c character of the complexes. Tran s i t i o n moment and o s c i l l a t o r strength. The N<^E t r a n s i t i o n i s accompanied by a t r a n s i t i o n d i -pole moment i which can be calculated from the c o e f f i c i e n t s a, b, a*, and b*. The t h e o r e t i c a l o s c i l l a t o r strength i s given by A. where V i s the wavenumber of maximum absorption. The values of f calculated i n thi s way (16, 21) agree w e l l with those of the observed o s c i l l a t o r strength f, which i s r e -20 lated to -IA , the half-width of the absorption band: f' = 1.35 x 10~*€(v-vx). Since f ~ f t h e n / ^ a n d e (the maximum ex t i n c t i o n c o e f f -i c i e n t ) are related by ~ j.srs-x/o-7 e The o s c i l l a t o r strengths of TNB-hydrocarbon complexes are mostly around 0.1, with of the order of 8-13 D*. Temperature influences, both on e and -0 , are var-iable i n both magnitude and sign (21, pg»69) and l i t t l e systematic study has been made. Temperature changes would be expected to a l t e r the r e l a t i v e importance of non-equil-ibrium configurations and contact charge-transfer, which strongly influence the observed spectra of complexes i n s o l -ution. However, the many variables involved here permit no general conclusions to be drawn. Pressure e f f e c t s have been studied both i n solution (40, 68) and i n the s o l i d compounds. An increase i n absorp-t i o n i n t e n s i t y and a s l i g h t r e d - s h i f t appear i n both cases, although these e f f e c t s i n solut i o n can-at least i n some cases be accounted for through pressure e f f e c t s on the equilibrium constant and p a r t i c u l a r l y on the r e f r a c t i v e index of the 21 solvent (6, 68). In c r y s t a l s , the chloranil-hexamethylbenzene complex has been found (81) to e x h i b i t a pronounced li n e a r increase i n absorption i n t e n s i t y up to 50,000 atm. This i s probably a d i r e c t r e s u l t of the reduction i n intermolecular separat-ion which must occur under such conditions. Solvent e f f e c t s on the p o s i t i o n and i n t e n s i t y of the absorption spectra have been studied by a number of workers (9, 16, 35, 77), but the d i f f e r e n t systems examined and the various methods of approach have i n some cases yielded seemingly anomalous r e s u l t s . The nature of the CT trans-i t i o n would suggest that more polar solvents should tend to s h i f t the absorption maximum toward longer wavelengths, and this i s indeed the case, with only a few observed ex-ceptions, although the degree of s h i f t i s highly v a r i a b l e . The e x t i n c t i o n c o e f f i c i e n t , on the other hand, may increase, decrease, or remain unaffected i n going to a more polar s o l -vent, depending on the p a r t i c u l a r complex. In naphthalene-TNB, £ seems to be quite independent of solvent, while i n aniline-TNB i t decreased greatly as solvent p o l a r i t y i s increased. 22 Fluorescence and phosphorescence. Emission from hydrocarbon-TNB complexes, both i n r i g i d glasses and i n s o l i d form, was f i r s t studied by Reid (55, 76). He noted the s i m i l a r i t y i n sp e c t r a l location and structure of t h i s emission to that of the pure hydrocarbon phosphor-escence, and suggested that the observed emission from the complex was a c t u a l l y donor phosphorescence, reduced greatly i n l i f e t i m e and enhanced i n i n t e n s i t y and broadness. It was assumed that the complex was excited to a d i s s o c i a t i v e upper state (the ground-state binding energies, mostly less than 3500/cm, were c i t e d as evidence for the nature of this excited s t a t e ) . After d i s s o c i a t i o n of the complex, the hydrocarbon would be i n i t s t r i p l e t state; enhancement of the phosphorescence was attributed to breakdown of the S<-*T spin s e l e c t i o n r u l e as a r e s u l t of rapid change of the f i e l d i n the v i c i n i t y of the donor, which i s expected to accompany a CT t r a n s i t i o n . Doubt regarding t h i s mechanism was aroused by the seemingly anomalous behaviour of the anthracene-TNB complex, whose broad emission spectrum extends from 5200 A into the inf r a r e d . The phosphorescence of anthracene had been pre-v i o u s l y reported to begin at 6800 A (48); t h i s assignment was subsequently v e r i f i e d by further studies (23, 53). 23 The problem was c l a r i f i e d by Bier and Ketelaar (10) who demonstrated the approximate mirror-image r e l a t i o n s h i p of the absorption and emission bands of the anthracene- and phenanthrene-TNB complexes. This was followed by a study of a wide v a r i e t y of donor and acceptor combinations by Czekalla and his group (29, 30, 31). The mirror-image r e l -ationship was found to be quite c h a r a c t e r i s t i c of CT com-plexes, as a consequence of the fluorescence and absorption maxima s h i f t i n g i n the same manner as donors of d i f f e r e n t i o n i z a t i o n potentials were used. Thus the p r i n c i p a l emission of these CT complexes i s a CT fluorescence, the re-verse of the N—^E absorption. These fluorescences are generally structureless and of normal l i f e t i m e (ca 10"''sec). In c e r t a i n complexes an a d d i t i o n a l emission, apparent-ly corresponding to donor phosphorescence, was observed (29, 31a). It i s rather weak, lacks much of the o r i g i n a l f i n e structure, and the l i f e t i m e s are much shorter than i n the free donors, ranging between 1 to 10~3 sec i n r i g i d glasses, and s l i g h t l y less i n the s o l i d s , the exact values depending on the acceptor as well as the donor. Some explanation of these phenomena was furnished by McGlynn and Boggus (53) who combined t h e o r e t i c a l consider-ations and experimental observations to obtain an approx-imate c o r r e l a t i o n diagram which i s i n accordance with the 24 observed properties of most complexes. The excited state r e s u l t i n g from absorption i n the CT band i s usually represented with a deep minimum i n i t s po-t e n t i a l curve. The bulk of the emission should a r i s e from the reverse of the absorption process, the band being some-what displaced i n wavelength due to the rather strong de-pendence of equilibrium intermolecular distance on the degree of dative bonding (see F i g l b ) . If the t r i p l e t state of the donor l i e s below the CT l e v e l , then intersystem crossing to a d i s s o c i a t i v e l e v e l w i l l compete with CT fluorescence, leaving the donor i n i t s t r i p l e t state and subject to phosphorescence emission or r a d i a t i o n l e s s decay. The phosphorescence, photographed through a phosphor-oscope, and subtracted from the t o t a l emission, reveals a CT fluorescence (54) which, l i k e the CT absorption, i s quite devoid of structure. The structure of the t o t a l emission i s thus due to the superposed hydrocarbon phosphorescence. Whether i t should be c a l l e d donor- or complex-phosphor-escence i s occasionally a matter of discussion; although the t r i p l e t state i s d i s s o c i a t i v e , the actual increase i n physical separation of the two components i s limited by the v i s c o s i t y of the r i g i d glass or the structure of the c r y s t a l l a t t i c e . Czekalla (31a) has shown that as one passes from 25 the free hydrocarbon donor to the complex i n solution ( r i g i d glass) and f i n a l l y to the c r y s t a l , the phosphoresc-ence becomes more di f f u s e , s h i f t s s l i g h t l y to the red, and decreases i n i n t e n s i t y by an order of magnitude i n each step. Detailed analysis of the v i b r a t i o n a l structure of the complex phosphorescence by McGlynn, Boggus and Elder (54) shows that the emitting hydrocarbon i s almost c e r t a i n l y bound i n a CT complex; changes i n the v i b r a t i o n a l frequen-c i e s which were noted i n th i s study were shown to be qual-i t a t i v e l y predictable, considering the changes i n electronic charge d i s t r i b u t i o n which CT binding i s expected to bring about. These changes also corresponded to changes i n the infrared and Raman spectra of anthracene when i t i s complexed with TNB. McGlynn's conclusion i s that excess energy of the d i s s -o c i a t i v e t r i p l e t state i s r a p i d l y dissipated, the complex reforms and the hydrocarbon portion emits i t s character-i s t i c phosphorescence. It would thus appear that complex phosphorescence i s r e a l l y perturbed donor phosphorescence; either of these terms i s correct , but 11 CT phosphorescence" i s obviously unacceptable, as th i s would imply a formal r e l a t i o n s h i p to the CT fluorescence which i s not supported by present evidence. 26 IV. THE SPECTRA OF MOLECULAR CRYSTALS Absorption and absorption measurement. In measuring the i n t e n s i t y of l i g h t absorption by a medium at a given wavelength, we are concerned with the t r a n s i t i o n of the system between two states i and k, at a rate given by Bjk f - t ^ - I ^ V / 1 " ? ( i ) i n which B j k i s Einstein's c o e f f i c i e n t of induced absorption, £ i s the energy density (related to the e l e c t r i c f i e l d strength) of the electromagnetic f i e l d , and /*jKi.s the trans-i t i o n dipole moment, given by JJ.JK = <j | r|k>, where r i s the radius vector specifying the d i r e c t i o n of the moment. If the l i g h t passes through a length d 2 of material containing N' molecules per cubic cm, the reduction i n i t s in t e n s i t y w i l l be - d l = B;r e hxfeN' *l • (2) Light i n t e n s i t y i s the amount of energy passing through unit cross-section area i n one second; thus I = c p , (3) - d l = (87r73h 3)|yi^(I-)hv^ it (4) where N i s Avogadro's number, C i s molar concentration, and c i s the v e l o c i t y of l i g h t . 27 The actual quantity measured is the optical density D, the log ratio of the intensities of incident to transmitted light: D - log ( I 0 / I ) . (5) The form of this expression derives from the Beer-Lambert law - d l » OL I C 61 (6) in which the absorption coefficient oc ( y ) describes the de-crease in light intensity after the beam has penetrated a distance dl through an absorber of concentration C. We note that, from Eq (4), oc= (8/rJ73hz)•\fcKr\ih N/c). (7) Integration of (6) yields a - a/Cl) In ( I 0 / I ) . (8) The extinction coefficient € is similar to this quantity, but the common logarithm is used: € = 2.3 oc = D/CZ (9) Since the absorption band w i l l be distributed over a range of frequencies, the theoretically more important quantity is the integrated absorption coefficient A: A - f (XM dv (10) In the same manner as we obtained (7) from (4), we can 28 obtain a sim i l a r expression f o r the integrated absorption c o e f f i c i e n t : A = (8nV3hc ) i 4 K / , M a10" J d D which r e l a t e s the observed spectrum to the t h e o r e t i c a l l y calculable t r a n s i t i o n moment. If the motion of a single electron i s described by a harmonic o s c i l l a t o r wave function, then the corresponding integrated absorption c o e f f i c i e n t i s A e = (Ne 2)/1000 c.me) = 2.31 x 10-8 Cm2mol-'liter. The r a t i o of the A obtained for a given band to A e i s known as the o s c i l l a t o r strength f; i t i s a useful comparative measure of the i n t e n s i t y of a t r a n s i t i o n , since i t takes into account the entir e absorption band: f = 4.33 x 10" 9 foi(v) <tv The l i g h t absorbed or emitted by a t r a n s i t i o n dipole o s c i l l a t o r i s polarized with i t s e l e c t r i c vector p a r a l l e l to the dipole. I f th i s l i g h t i s observed through a device that transmits only one p o l a r i z a t i o n , then i t s apparent i n t e n s i t y w i l l be proportional to the square of the projection of the dipole onto the p o l a r i z i n g d i r e c t i o n i n the plane perpen-dicul a r to the d i r e c t i o n of observation. The p o l a r i z a t i o n  r a t i o i s simply the r a t i o of the i n t e n s i t i e s measured par-a l l e l to two dir e c t i o n s , usually symmetry axes of the system. 29 In absorption, o p t i c a l density r a t i o s are usually measured; these are meaningful p o l a r i z a t i o n r a t i o s at a given wave-length i f the band shapes and peak locations are i d e n t i c a l i n each d i r e c t i o n . Otherwise, the r a t i o of the integrated absorption i n t e n s i t i e s ( i . e . , the r a t i o of the squares of the dipole lengths) i s the fundamental quantity. Molecular c r y s t a l s : oriented gas approach. It i s known experimentally that the energy levels of organic molecules are perturbed only s l i g h t l y when they are brought into a molecular c r y s t a l l a t t i c e i n which the p r i n -c i p a l s t a b i l i z i n g forces are of the van der Waals type. In gross aspect, the absorption spectra of c r y s t a l s are gener-a l l y quite s i m i l a r to the solution or vapour spectra, a l -though a s h i f t of the vapour- or solution band positions to lower energies (red s h i f t ) usually occurs i n the pure c r y s t a l . These facts led to the f i r s t view of the spectra of mol-ecular c r y s t a l s , i n which the c r y s t a l was regarded as an oriented gas, with each molecule held i n a fix e d p o sition and having the same properties and elec t r o n i c states as i n the vapor phase. The spectroscopic properties of the c r y s t a l are thus those of the isola t e d molecules; polarized dipole r a d i a t i o n (observed i n a d i r e c t i o n normal to a 30 c r y s t a l face) should have an in t e n s i t y proportional to the square of the t r a n s i t i o n dipole moment projection onto t h i s face. The f i r s t detailed studies of the spectra of aromatic hydrocarbon c r y s t a l s showed that t h i s view cannot adequately explain the many new phenomena that appear; changes i n the d e t a i l s of structure occur, with the i n t e n s i t y d i s t r i b u t i o n over the various bands often quite d i f f e r e n t i n opposite p o l a r i z a t i o n s . Individual bands may s p l i t into components separated by thousands of wavenumbers, and polarized along d i f f e r e n t c r y s t a l axes. The po l a r i z a t i o n r a t i o s themselves are usually s u b s t a n t i a l l y less than the oriented-gas model would predict. The e a r l y work i n thi s f i e l d , c a r r i e d out mostly by Prikhotfko (75), Obreimov (67) and the i r coworkers, led Davydov (36) to apply the ideas developed e a r l i e r for i n -organic c r y s t a l s by Frenkel (39) to the problem of aromatic molecular c r y s t a l s . The r e s u l t i n g theory, further elabor-ated by Davydov (37) and Winston (92), was applied i n some d e t a i l by Craig (24, 25) to the interpretation of the crys-t a l spectrum of anthracene. 31 Resonance int e r a c t i o n i n a molecular c r y s t a l . If a molecule that i s completely described by a hamil-tonian H i s placed i n a c r y s t a l l a t t i c e containing, say, one other i d e n t i c a l molecule, the perturbed hamiltonian can be written where AV i s the perturbing p o t e n t i a l . We s h a l l assume that the system i s i n a stationary state, and use the stationary state eigenfunctions i n our expansion. The Schrodinger equation f o r the s_-th eigenfunction i s <K" + A V ) ^ = E s 4 i (3) and the eigenfunction i t s e l f i s given by the expansion M = H cns u n • (*) n Inserting (4) into (3) and using the r e l a t i o n j¥°un = E ; un (5) together with the orthogonality of the U n, we obtain Cms< Es " O = * £ V m n C n s > <*> n where . <= ( U l V I U ). (7) mn m1 1 n The f i r s t - o r d e r perturbation r e s u l t i s C = V / ( E ° - E° ) ms ms s nr with E S °= V s g > and thus E S - E ° + *V S S . 32 This treatment i s v a l i d only for m 4 S'% i n the system of two i d e n t i c a l molecules, double degeneracy can always occur, and i n such cases we must write, according to Eq. (6), c i <Ef - V • M » i i c i + v12c2) C 2 ( E f - E Q) = A ( V 2 i C + V 2 2 C 2 ) in which Ef and E Q are eigenvalues common to both molecules. If we set V j ^ = ^22* a T 1 <* n o t e t n f l t V 2^ = V- 2^, then the solution i s E f " E o " V l l * ± MV12| with V 1 2 -|V 1 2| exp (-i<?). Thus c 2 / c ^ = + exp i£ ; i f the phase factor i s taken as zero, the zeroth-order approximation gives us d « (U L + U 2) (9) and the energies are E ± - E Q + A V U + >(V 1 2|. (10) From (9) we see that the two zero-order unperturbed eigenstates contribute equally to the new state; extending th i s argument to larger numbers of degenerate l e v e l s , i t i s c l e a r that the p r o b a b i l i t y of fin d i n g the system i n any one of the o r i g i n a l states i n inversely proportional to the number of states contributing to the system. *See Bohm, Quantum Theory . pg 463. Prentice-Hall, 1951. 33 One can write time-dependent functions ^ U , t ) - (U, + U Z) exp - i C E o + XV.^) t / f i ; (11) I f ^ = U at time t = 0, then at a l a t e r time: (12) % (x,t) =v?exp(-iE (,/fi)[^exp(-iAV, it/ii) + 0exp(-i*V l t t/fi) . This i s formally equivalent to an o s c i l l a t i o n of the system between the two states and U2 at a frequency proportional to A v i 2 * T * l e ^ca1Poi:tSL1}ce °f thi s arises when we consider a system of N i d e n t i c a l molecules, only one of which i s i n an excited state. The state of the entir e system must now be described i n terms of a linear combination of N degener-ate functions, each representing a configuration i n which a d i f f e r e n t molecule i s excited. The e x c i t a t i o n energy can be regarded as a quasi-particle (exciton) which hops around from molecule to molecule i n the c r y s t a l . Two very import-ant physical consequences of this process w i l l be discussed i n d e t a i l i n succeeding sections of this chapter: 1) an exchange in t e r a c t i o n energy arises, which i s expressed i n terms of in t e r a c t i o n integrals I j ^ . In the dipole approx-imation these summed integrals take the form M j ^ / r ^ , where j and k represent any two molecules separated by a distance r . The e f f e c t of these terms on the observed spectrum i s to s p l i t i t into a maximum of as many bands as there are molec-ules i n a un i t c e l l , and to displace the spectrum (usually 34 toward longer wavelengths) r e l a t i v e to that of the free molecule. 2) The fate of the absorbed r a d i a t i o n depends strongly on the rate at which the exciton travels between molecules, compared to the l i f e t i m e of the electronic excited state and the periods of v i b r a t i o n a l processes which are i n -volved i n the degredation of the e x c i t a t i o n energy into heat. Energy states of a molecular c r y s t a l . The following notation i s employed (37): "Hnti - hamiltonian for molecule at a t h s i t e i n nth unit c e l l . Vn«,mfi~ i n t e r a c t i o n p o t e n t i a l operator between mol-ecules n OL and mf . cp, E - eigenfunctions and energies of stationary states of the e n t i r e c r y s t a l . ^,°„,E*n- eigenfunctions and energies of ground states of isolated molecules. - antisymmetrized eigenfunction for a c r y s t a l state i n which the noc-th molecule i s excited to the f - t h l e v e l . - non-antisymmetrized form of <s~ - number of molecules per unit c e l l . The ground state of the c r y s t a l can be written as the product of i n d i v i d u a l molecule eigenfunctions, neglecting intermolecular interactions; not 35 If one molecule i s excited to the f - t h state, t h i s becomes Taking electron exchange degeneracy into account, we write V I where P v i s the operator representing one of the (SerN) ! possible permutations of the S o p t i c a l electrons. In order to completely describe the system, we must show that the e x c i t a t i o n can appear with equal l i k e l i h o o d on any molecule i n the c r y s t a l . This i s done by expressing the zero-th order eigenfunction of the excited state of the c r y s t a l by The p r o b a b i l i t y of e x c i t a t i o n appearing on the n<X th mol-ecule i s (anfl(|/tf-N. Fpllowing Davydov (37), we write the equation for the eigenfunctions <f> and stationary states E of the c r y s t a l : V - F ) $ = ° (5) Here K i s the hamiltonian for the molecule occupying the po s i t i o n noL and V i s the p o t e n t i a l energy operator for inte r a c t i o n between t h i s molecule and another located at mp . The <£ used here i s the ground-state form of Eq (*/). The 36 corresponding energy i s £ ° - £ foi * * IT [<*;< (D\V^91 < £ , 0 r ) > -(6) where (I) and (II) r e f e r to a pair of electrons which are permuted i n a l l /*• possible ways between the two centers. The energies En* are ac t u a l l y s l i g h t l y d i f f e r e n t from the isolated-molecule energies as a r e s u l t of the weak c r y s t a l f i e l d interactions, but t h i s w i l l be neglected here. Using now Eq (4) for the excited state of the c r y s t a l , substitution into (5) y i e l d s the set of equations H = ° (7) where <l V C, 001 Vnai mf ] C en) C <r)> \ - > , ( 8 ) ~ L to % a n / / K: m <?icn> i s the e x c i t a t i o n exchange i n t e r a c t i o n i n t e g r a l ; these are commonly denoted by Craig's notation I j ^ and their c a l c u l -ation i s considered presently. The energy of the excited state i s EF- £F- ^ , - Z fo\ + (r))K / C (Ej> (9) — ^ ^ (electron 4xcb*Hyg. berms] 37 Subtracting the ground-state energy from this quantity, we obtain the e x c i t a t i o n energy of the c r y s t a l : ^ E f - + Dm ? + £ f (10) f where A. E i s the e x c i t a t i o n energy of one molecule, and D • ° L - £ C<fi;<»lX^ICtt>>*-<fetcir)|*K^/Piao;/<ii) i s the difference between the t r a n s i t i o n energies of molec-ule m p and a l l the other molecules i n the c r y s t a l ; i t i s analogous to a m.o.-theory " coulomb" term. Before solving Eq (7) for £ , i t i s s i m p l i f i e d by making use of the t r a n s l a t i o n a l symmetry of the c r y s t a l : = ff« G (12) The wave vectors k are related to the r e c i p r o c a l l a t t i c e vectors a by (13) where -Ni/2 :<ni , i - 1,2,3. (14) The B^ are defined by <r Yl L' ^ 8 , - eF% =- o ( 1 5 ) i n which 4 ? (k) - YL ^,mp e x P fik(m-n)] . (16) 38 Equation (14) can be solved for £ i n terms of k, as many values being obtained as there are molecules i n the unit c e l l : c~/-<f/rr ; , > « s / , * . . . < r - . (17) The difference i n energy for the various u n i t c e l l members depends on the matrix elements (k), which are periodic f functions of the M ^ ^ . In order to determine these l a t t e r matrix elements (Eq 8), i t i s f i r s t necessary to consider the form of the inte r a c t i o n energy operator V. To a good approximation, we are interested only i n the in t e r a c t i o n between the trans-i t i o n dipole moment of molecule n <*• with those of a l l other molecules m ^  i n the c r y s t a l . This i n t e r a c t i o n depends on the i n t e n s i t i e s of the dipole t r a n s i t i o n s , on the distances between the dipoles, and on a geometrical factor. By taking only the f i r s t terms of a power series derived from c l a s s -i c a l electrodynamics, s u b s t i t u t i n g i t into eq (8) and r e -taining only the f i r s t term, we obtain (2 cos 9* cos 0 Z -cos 0* cos 0*, - cos 0* cos 0£) (18) The cosine terms r e f e r to the angles between each i n t e r -acting t r a n s i t i o n moment and the coordinate system. The e x c i t a t i o n energy E ^ of each member of the unit c e l l gives r i s e to /J, bands of excited states: 39 E%W - 4 ^ + D£,+ . (19) The p . values of £ from Eq (17) are substituted into (15), giving a system of c o e f f i c i e n t s B£ which determine the contribution which each of the stationary states makes to the f - t h excited state: $ / ( o ) = ( o - N P ^ B * (20) Here, only the zero wave vector states (k = 0) are considered; th i s s e l e c t i o n r u l e i s v a l i d when the wavelength of the l i g h t i s small compared with the l a t t i c e constant. It corresponds to the assumption that the momentum transferred to the l a t t i c e by the incident quanta i s negligable. The correct values of the B« are simply those which give a set of ju. orthogonal eigenfunctions, and are e a s i l y found by inspection. For a c r y s t a l containing two molecules per uni t c e l l , they take the form: #r = <»•»"* H e * ' . * *»o (21) #: = cm)- 4 ! : According to Eq (3), the T^noc a r e f o r m e d from the mol-ecular eigenfunctions and must therefore transform i n the same manner under the operations of the molecular sym-metry group. In order to f i n d the sel e c t i o n rules and 40 polarizations of tr a n s i t i o n s i n the c r y s t a l , we must f i n d the c r y s t a l point groups to which the functions <Q n of each molecular point group symmetry correspond. The operations common to both the molecular point group and the c r y s t a l l o -graphic space group constitute the s i t e group, and the eigen-functions (21) are c l a s s i f i e d according to the i r r e d u c i b l e representations of the s i t e group. I t i s apparent that A ( k ) i n Eq (19) depends on the unit c e l l element only through the l a s t term. Consequently, the energy differences (Davydov s p l i t t i n g ) between the oppositely polarized components of the t r a n s i t i o n are given by A E = (constant) + £ L,p ± £ I j n i > ; n (22) where the I j ^ are the in t e r a c t i o n integrals (17) between molecules j and k; p runs over a l l molecules t r a n s l a t i o n a l l y equivalent to j , and the m, n, etc. run over a l l molecules related to j by the other symmetry operations of the unit c e l l group. The constant term consists of the D m^ of eq (11) and the other general ewak interactions which are being neglected i n thi s treatment. This term, together with the the sums of I j p over t r a n s l a t i o n a l l y equivalent molecules, brings about the displacement of the spectrum of the c r y s t a l with respect to the free-molecule spectrum. 41 The geometrical factor i n Eq (18) i s best written i n a form that s i m p l i f i e s the computation of the I j k : I j k = -(e 2/r| k)|M 2|[3 cos 9j cos 0 k - cos 9 j k](23) where 0j and 9 k are the angles made by the t r a n s i t i o n mo-ments i n molecules j and k with the l i n e j o i n i n g t h e i r centers, and 9 j k i s the angle between the two t r a n s i t i o n moments. The summed in t e r a c t i o n integrals are taken i n the allowed l i n e a r combinations corresponding to Eq (21). Some idea of the e f f e c t of the geometrical factor can be gained by a study of F i g 2a (pg 44), i n which values of the factor are given for various orientations of the trans-i t i o n moments. Second-order interactions. The e f f e c t s predicted by the theory presented above are of appreciable magnitude only when the tr a n s i t i o n s are f a i r l y intense ( f ~ l ) . The 2500 A C 1 ^ ) system of anthra-cene, for example, has an o s c i l l a t o r strength of f = 2.3. It i s long-axis (L) polarized, and as Craig and Hobbins (24) have shown, the two c r y s t a l components are s p l i t by 16 kK, i n good agreement with t h e i r c a l c u l a t i o n s . Weaker t r a n s i t -ions having i n t e n s i t i e s around f * 0.1 (such as the anthra-cene 3800 A t r a n s i t i o n , and CT tran s i t i o n s ) give only s l i g h t 42 s p l i t t i n g s , of the order of a few hundred wavenumbers at most; Craig (25) has shown that mixing of such trans-i t i o n s with strong systems can r e s u l t i n i n t e n s i t y - s t e a l i n g and - r e d i s t r i b u t i o n e f f e c t s which, although they act amongst tra n s i t i o n s of a l l strengths, become e s p e c i a l l y important when they a f f e c t a weak system i n which an increase i n in t e n s i t y i s experimentally more noticeable, and where the e f f e c t s are not masked by large Davadov s p l i t t i n g s . The energy matrix f o r t h i s type of in t e r a c t i o n consists of the diagonal elements H r r, which are the f i r s t - o r d e r terms previously considered: p m The new matrix elements H r s are written H " - + + E ' - S • <«> p m p m Here the superscripts r and s_ r e f e r to d i f f e r e n t free-mol-ecule excited states, s_ being the higher. The elements K J P - e j l v j P I ?p) <"> vanish i n the dipole approximation, but are a source of third-order i n t e r a c t i o n which may i n some cases make an 43 observable contribution (25). The p r i n c i p a l quantities to be calculated i n the second-order case are J]l ' % [<?J<?jl vj Pl «?PPP> + <P| * S l ' j p l <?P>] ( 2 7 ) which are given by Jj p = ^ - (e2/r|p)/Mr||Ms|;2 cos ©^cos 0^+ 2 cos ©fjcos 0 ^ r s s r r s - cos 0j2cos 0p2~cos 0j2cos 0p2 - cos Oj^cos 0p3 - cos 0*2 cos 0 p3j * (28) When r = s, the Jj£ reduce to the 1.^. The 0 ^ r e f e r to angles between the t r a n s i t i o n moment to the f - t h excited state of the j t h molecule, and the l i n e j o i n i n g the centers of the j t h and i t h molecules. The matrix elements H R S are calculated from the JJ^J and the second-order perturbation energy becomes E = H 1 1 + YL ( H L R ) 2 / H U - H R R (29) which holds to good approximation when H1*1 - H3*^. The geometrical dependence of thi s i n t e r a c t i o n i s i l l u s t r a t e d i n F i g 2b (following page). Intensity r e d i s t r i b u t i o n s occur according to the follow-ing formula, derived by Craig (25) for monoclinic c r y s t a l s 44 a. Geometrical factors for f i r s t - o r d e r i n t e r a c t i o n and Davydov s p l i t t i n g . b. Geometrical factors f o r second-order in t e r a c t i o n . The two t r a n s i t i o n dipoles r and §_ are shown i n d i f f e r e n t colors and are assumed to be orthogonal to one another i n the molecule. Fi g . 2. Geometrical factors f o r dipole-dipole i n t e r a c t i o n . T r a n s i t i o n moments are assumed to be phased as i n d i -cated and are a l l i n the same plane. A l l angles 6 are multiple of 45°. The factors given are the cosine terms i n the R.H.S. brackets of Eqs 23 and 28 (pgs 41 and 43). 45 having two molecules per unit c e l l : wR,p= £ ( * : ± y < ) + X I ' ^ i ^ K ^ ) oo) The upper sign r e f e r s to B u and the lower to c r y s t a l states. The M r are t r a n s i t i o n moments for the two molecules i n the unit c e l l . Fate of absorbed energy. After absorption of l i g h t by a c r y s t a l , the e x c i t a t i o n energy of the molecules must be dissipated, since thermo-dynamic equilibrium i s maintained. This energy can be r e -leased either by re r a d i a t i o n of l i g h t or by transformation into heat. The l a t t e r process, which corresponds to ex c i t a t i o n of l a t t i c e v ibrations, i s probably always involved to some extent, even i n strongly luminescent s o l i d s . Aromatic mol-ecules o r d i n a r i l y emit from the lowest vibronic l e v e l of their lowest excited s i n g l e t (or t r i p l e t ) states, even i f i n i t i a l e x c i t a t i o n has been to a much higher vibronic l e v e l . This would indicate that the excess vibronic energy can be -8 transferred to l a t t i c e modes within the l i f e t i m e (~10 sec) of the electronic excited state- i . e . , with very high e f f i c -iency. As was mentioned above, there are two alte r n a t i v e ways 46 of describing an excited state of a molecular c r y s t a l : l o c a l i z e d : ^ p F= 9,° K ' " ? P C , (2) delocalized: $ P = (ff -N)" 4 ^J An«Xn« (4) noc Winston (92) has pointed out that whether we use the l i n e a r combination (4) or the antisymmetrized version of (2) de-pends on the time sc^ale of the process. I f two adjacent molecules inter a c t with an energy A E , then the e x c i t a t i o n i n i t i a l l y on one of them at time t = 0 should appear on the other a f t e r h/AE seconds. A reasonable value of A E for a -12 molecular c r y s t a l i s 100/cm, corresponding to h/AE = 10 second. Electronic states have l i f e t i m e s usually greater -9 than 10 sec, so i t i s necessary to describe such states i n terms of the delocalized functions. Intramolecular v i b r a --13 tions, however, may have periods of 10 sec, and may be regarded as l o c a l i z e d at a given center when the i r possible i n t e r a c t i o n with el e c t r o n i c states i s being considered. When the e x c i t a t i o n becomes l o c a l i z e d on a molecule, the net i n t e r a c t i o n that t h i s molecule experiences with the re-mainder of the l a t t i c e w i l l be altered, and the molecule w i l l tend to move to a s l i g h t l y d i f f e r e n t equilibrium pos-i t i o n i n the l a t t i c e . If the e x c i t a t i o n (exciton) i s jumping 47 from molecule to molecule very rapidly, the molecular motion w i l l not have time to get started, and the exciton "sees" only a uniform l a t t i c e . Such a "free exciton" w i l l probably luminesce before much of i t s energy i s transferred to the l a t t i c e . If, on the other hand, the electronic e x c i t a t i o n travels slowly, the exciton and the molecular displacement may move through the l a t t i c e together. In such a case the coupling of e l e c t r o n i c e x c i t a t i o n to l a t t i c e modes may be more e f f i c i e n t , and t h i s w i l l probably provide the c h i e f means of deactivation, e s p e c i a l l y at higher temperatures. Other r a d i a t i v e mechanisms. There are several other important possible routes of decay which may p a r t l y or completely replace the transfer of e x c i t a t i o n energy to l a t t i c e modes, or i t s d i r e c t rad-i a t i o n from the lowest s i n g l e t excited state of the c r y s t a l . Intersystem crossing to the t r i p l e t state i s one com-mon process (74), and becomes e s p e c i a l l y important i n some c r y s t a l s , such as benzophenone (discussed i n Appendix C). C r y s t a l defects, such as cracks, dislo c a t i o n s , vacan-c i e s , impurities, or any other disruption of the trans-l a t i o n a l symmetry of the l a t t i c e may provide s i t e s at which elec t r o n i c e x c i t a t i o n w i l l be more s t a b i l i z e d than i n the 48 uniform part of the c r y s t a l . Such s i t e s may give r i s e to trapping lev e l s below the energy of the excited c r y s t a l state. The excitons so trapped can radiate a c h a r a c t e r i s t i c defect emission, transform into l a t t i c e v i b r a t i o n s , or ( i n some cases) simply remain trapped u n t i l thermally excited back into the exciton band. An e s p e c i a l l y important instance of the above process occurs when impurities are introduced into a l a t t i c e of host molecules whose lowest s i n g l e t excited states are above those of the guest impurity molecules. The non-ra d i a t i v e transfer of e x c i t a t i o n energy to guest molecules i n such a c r y s t a l was studied t h i r t y years ago (93) and i s s t i l l the object of much attention (39a). A c l a s s i c a l ex-ample of thi s type of system i s the anthracene-tetracene -4 mixed c r y s t a l (11); concentrations as low as 10 molar tetracene i n anthracene w i l l quench the anthracene lumin-escence and r e s u l t i n the exclusive emission of tetracene fluorescence. '"ZZ-.l I f the absorption band of one species i n a c r y s t a l overlaps the emission band of another, then energy transfer can take place by simple reabsorption of emitted ra d i a t i o n , or by resonance transfer between molecules (38a). These l a t t e r processes, of course, are not unique to c r y s t a l s . 50 V. MOLECULAR COMPLEXES IN THE SOLID STATE Except for some early work on melting-point curves, nearly a l l of the thermodynamic studies and spectroscopic work to date has been limited to solutions of the compon-ents, usually i n ethanol, ether, chloroform (which are a l l known to inter a c t with TNB themselves) or hydrocarbons. Because the degree of s t a b i l i z a t i o n afforded by CT i n t e r -action i s of the same order of magnitude as hydrogen bonding and other strong solvent e f f e c t s , i t i s important to keep i n mind the f a c t that r e l a t i v e l y l i t t l e i s known about the r e a l nature of the single donor-acceptor pair, isolated from i t s interactions with surrounding molecules. More fundamental than t h i s , however, i s the d i f f i c u l t y of dealing with a single system of d e f i n i t e structure i n solution. CT i n t e r -action i s not r e s t r i c t e d to those geometrical configurations of donor and acceptor which represent the most stable form of the complex, nor i s i t limited to distances of separation as small as the van der Waals r a d i i of the components. Thus i n addition to the p r i n c i p a l form of the complex, s t a b i l i z e d by only 4-10 kcal (compared with RT = 0.6 at room temperat-ure), we must consider the existence of other less stable configurations, which may nevertheless together make a 51 major contribution to the observed spectroscopic properties; such a contribution may even be made by configurations having no thermal s t a b i l i t y at a l l , a r i s i n g from the random c o l l i s i o n s of solute molecules i n thermal motion. This l a t t e r process has been termed "contact charge-transfer" by Orgel and Mulliken (69), who discussed i n some d e t a i l i t s e f f e c t s on some of the measured properties of complexes i n solut i o n . They showed how serious errors could be introduced into the equilibrium constant data obtained by the Benesi-Hildebrand spectrophotometrie method (8), and p a r t i c u l a r l y into the values of the CT ex t i n c t i o n c o e f f i c -ients obtained by thi s method. The contribution made by contact charge-transfer to the absorption c o e f f i c i e n t can r e s u l t i n considerable overestimation of e , e s p e c i a l l y i n weak complexes. Important for the present work i s the t h e o r e t i c a l study by Murrell (65) on the i n t e n s i t y of the CT ele c t r o n i c t r a n s i t i o n , from which i t i s concluded that the major con-t r i b u t i o n to the CT i n t e n s i t y derives from i n t e r a c t i o n of the CT-state with excited states of the donor. According to his r e s u l t s , the "contact" states are primarily respons-i b l e f or the bulk of the CT absorption i n t e n s i t y ; i f the most stable form of 1:1 hydrocarbon-TNB complexes i s that 52 in which the two rings are situated i n p a r a l l e l planes, one above the other, the d i f f e r e n t polarizations of the two states would minimize this interaction, and hence the most stable form may make the smallest contribution to the CT band i n t e n s i t y . This may explain the r e s u l t s of a number of studies, t y p i c a l of which i s that of Andrews and Keefer (2), who found that the CT absorption i n t e n s i t i e s decrease as the series of iodine-methylated benzene complexes becomes more stable (on changing the number and positions of substituent methyl groups). Contact CT probably also contributes to the broadness and lack of structure that i s c h a r a c t e r i s t i c of the absorp-t i o n spectra of CT complexes i n solution, even at low temp-eratures. Briegleb and Czekalla (19) have noted that the widths of the CT absorption bands of a series of TNB com-plexes decrease at the CT bonding energies increase, a probable r e s u l t of the lessening contribution of random and non-equilibrium interactions as a preferred configuration assumes greater r e l a t i v e importance. The study of c r y s t a l l i n e complexes affords the oppor-tunity of examining molecules which are held i n almost fixed positions. If the c r y s t a l structure i s known, such a well-defined system permits the detailed study of i n t e r -53 molecular processes and also of non-isotropic e f f e c t s such as conductivity, magnetic s u s c e p t i b i l i t y , and spectra. By measuring the absorption and emission spectra p a r a l l e l to known crystallographic axes i n polarized l i g h t , i t i s possible to f i n d the d i r e c t i o n of the t r a n s i t i o n moment and to deduce from t h i s the symmetry species of the e l e c t r o n i c states involved. The forces that hold the molecules i n the c r y s t a l give r i s e to e f f e c t s which may r a d i c a l l y change the appearance of the spectra from the solution or vapor state; these e f f e c t s were discussed i n d e t a i l i n the preceeding section. Although the intermolecular forces responsible for these phenomena are common to a l l organic c r y s t a l s , they may be e s p e c i a l l y important i n CT complexes, i n which the r e s -onance in t e r a c t i o n s t a b i l i z i n g the complex i s of an i n t e r -molecular nature. One would therefore predict a much greater change i n the thermodynamic and spectroscopic properties of CT complexes on going from the dissolved- to the c r y s t a l l i n e form, than i s the case with pure hydrocarbons and other organic substances. Thermodynamic properties of s o l i d complexes. C r y s t a l l i n e molecular complexes of TNB, chloroquinones, etc., with aromatic hydrocarbons are generally intensely 54 colored needles having melting points which l i e i n a narrower range than those of the pure components; the melting points of the complexes and of the components do not bear any app-arent r e l a t i o n to each other. The molar volumes of the s o l i d complexes usually exceed the sums of the component molar volumes (80). The small amount of thermodynamic work on s o l i d com-plexes i s s t i l l s u f f i c i e n t to i l l u s t r a t e the dangers attend-ant i n applying measurements made i n solution to predictions of the properties of the s o l i d s . Hammick and Hutchison (41) determined the free energy of formation of the s o l i d complex from i t s c r y s t a l l i n e com-ponents by observing the concentration of TNB obtained from the complex and from pure c r y s t a l l i n e TNB i n equilibrium with water. The r e s u l t s are summarized i n Table I (following page), which also shows heats of formation of s o l i d complexes both from the pure c r y s t a l l i n e components and from the vapor phase (the l a t t e r determined from heat of sublimation ex-periments), obtained by Suzuki and Seki (82). For the s o l i d - t o - s o l i d process, All, AF, and AS are a l l much less than i n solution, while formation of c r y s t a l s from the vapor phase releases more than ten times the energy than does formation from solu t i o n . hydrocarbon hcbn. complex s o 1 u t i o n (CC1 4) s o ] . i d (a) mp mp Kc AF A H T A S ^ F ( S ) ^ H ( s ) anthracene 205 162 15(b) - -4.4 -- -0.8 -0.3 -46.9 hexamethylbenz-ene 168 173 7.1 -2.5 -4.7 -2.2 -1.3 naphthalene 80 152 4.0 -2.1 -4.3 -2.1 -2.1 -1.1 -40.7 phenanthrene 100 164 11.7 -2.8 -4.3 -1.5 -2.4 --benzene 5 dec. 0.2 -0.5 -1.7 -1.2 -- -0.7 -34.9 TABLE I. Thermodynamic properties of hydrocarbon-TNB complexes. (Briegleb, r e f 21) Values of A F , AH, and T AS are i n kcal/mole-C°. (a): subscripts s_ and g r e f e r to formation of complex from s o l i d or gaseous components, respectively, (b) 37 C; a l l other equilibrium constants at 20°C. Data from Briegleb (21), Ross & Labes (77), and Suzuki and Seki (82). 57 This work shows that the s o l i d complex i s only s l i g h t l y s t a b i l i z e d i n i t s ground state, compared with the s o l i d com-ponents, and suggests that van der Waals forces are the p r i n c i p a l s t a b i l i z i n g influence here, as i n most molecular c r y s t a l s . This view i s substantiated by Wallwork's obser-vation (85) that molecular positions of the components i n c r y s t a l l i n e complexes of TNB with anthracene, benzidine, and naphthalene, etc., do not appear to be highly influenced by io n i c forces; the perpendicular separations along the (ABABAB...) stack (see below) are only s l i g h t l y less than the expected van der Waals separations. Cr y s t a l structures. Determinations of c r y s t a l structures of TNB-hydrocarbon complexes were f i r s t undertaken by Hertel and co-workers about t h i r t y years ago, but i t i s only recently that data on the atomic positions has been available (84,85,87). Most of the complexes have a stacked arrangement, i n which the planes of the donor and acceptor components are approximately p a r a l l e l and c o a x i a l l y aligned i n i n f i n i t e columns. The smaller aromatic hydrocarbons often form monoclinic c r y s t a l s , but the larger ones, which may e a s i l y interact with more than one acceptor molecule, and those known to form complexes of other than 1:1 stoichiometry, 58 usually y i e l d c r y s t a l s of more complicated structure. In view of the simple stacked arrangement of donors and acceptors i n many c r y s t a l l i n e complexes, one may ask to what extent should we consider a discrete 1:1 complex to e x i s t i n the c r y s t a l . This question can be answered immediately i n s t r u c t u r a l and thermodynamic terms, but from the standpoint of the CT ele c t r o n i c t r a n s i t i o n , we must also consider whether l o c a l i z e d t r a n s i t i o n s between discrete D-A pairs have any r e a l meaning i n the c r y s t a l ; t h i s w i l l be discussed further i n conjunction with the experimental r e s u l t s i n Section VII. 59 TO.. EXPERIMENTAL PROCEDURE AND APPARATUS Determination of the absorption and emission spectra of c r y s t a l s i s fundamentally very simple, but i n practice there are c e r t a i n d i f f i c u l t i e s which require considerable practice and experimentation to overcome. The wide var-i e t y of o p t i c a l arrangements required makes currentl y com-mercially-available spectrophotometers of l i t t l e use for the study of polarized c r y s t a l spectra, and the usual prac-t i c e i s to employ a monochromator or spectrograph and mount the sample, sources, optics, etc. on o p t i c a l benches. This provides for greater f l e x i b i l i t y which i s required when, for instance, absorption, emission, and e x c i t a t i o n spectra must be measured on the same sample. Instruments. Two dispersing instruments were used. In the e a r l y part of the work, only a Hilger E2 Medium Quartz Spectrograph was ava i l a b l e . It was equipped with a photoelectric scanning attachment containing a 1P28 photomultiplier. Both the d i s -persion of the quartz prism and the response of the photo-tube are poor i n the red region of the spectrum, and the instrument was abandoned as soon as a more suitable appar-atus became avai l a b l e . 60 Since i t appeared that the study of some f a i r l y weak emissions would be necessary, i t was decided to construct a fluorescence spectrophotometer e s p e c i a l l y suited to t h i s project. The r e s u l t i n g instrument was b u i l t around a Hilger D285 high-aperture monochromator employing a glass prism i n a Wadsworth mounting. Using t h i s prism, the dispersion was around 230 A/mm at 5000 A. S l i t widths commonly used ranged between 0.1 - 0.2 mm i n absorption, and 0.1 - 0.6 mm i n emission work. The high aperture of f/4.4 p a r t l y com-pensated for the low r e s o l u t i o n c a p a b i l i t y of the instrument. It was f e l t that the measurement of r e l a t i v e i n t e n s i t i e s was more important than accurate wavelength values, e s p e c i a l l y i n the measurement of CT spectra which are inherently broad. The o p t i c a l arrangement i s outlined i n F i g 3; i t i s quite straightforward and permits both absorption and emiss-ion work. Light from the c r y s t a l i s picked up by a lens, made p a r a l l e l , and passed through a Glan-Thompson p o l a r i z i n g prism. An image of the sample i s focussed on the s l i t by a second lens. Both lenses exactly match the aperture of the monochromator. To obtain absorption spectra, an 18-ampere r i b b o n - f i l -ament lamp provided a good source of 3000°K color temperature r a d i a t i o n extending from 3200 A to 26,000 A. In emission 62 studies, e x i c t a t i o n was furnished by a 1000 watt AH-6 high pressure mercury arc lamp. The e x c i t i n g wavelength was selected by a Bausch & Lomb 250 mm grating monochromator and an appropriate Corning f i l t e r . This monochromator was equipped with a motor drive for e x c i t a t i o n spectrometry. Detectors. Several kinds of photomultiplier tube were used during the course of the work. Most of the absorption spectra were run with a 1P28 or a 5819, both of which are rather d e f i c -ient i n r e d - s e n s i t i v i t y . The fluorescence spectrometer was designed to take one of the most sensi t i v e photomultipliers available, the RCA 7265. This i s a 13-stage end-on type with a rated median s e n s i t i v i t y of 200 amperes per lumen at 2100 v o l t s . The response peak i s at 4800 A, and extends out to 8000 A. For studies extending farther into the infrared, a type 7102 was used; t h i s has a very broad s e n s i t i v i t y curve extending out to 11 000 A. Its s e n s i t i v i t y drops be-low that of the 7265 below 7500 A. In order to u t i l i z e the f u l l s e n s i t i v i t y of these tubes, and p a r t i c u l a r l y of the infrared photomultiplier, provision was made to operate them with their photocathodes at l i q u i d nitrogen temperature. Considerable d i f f i c u l t y was experienced i n arranging a proper Dewar ves s e l to insulate 63 the low-temperature parts while maintaining the rear of the phototube at atmospheric pressure (necessary to prevent corona discharge from the high-voltage terminals). The housing which was f i n a l l y evolved provided e f f i c i e n t rad-i a t i v e cooling of the cathode while a heated vacuum seal held the phototube i n p o s i t i o n . In addition:to the s i g n a l due to incident l i g h t on the monochromator s l i t , the output of a photomultiplier includes a dc component that i s present even i n the absence of any i l l u m i n a t i o n . This dark current i s due to thermionic emiss-ion from the photocathode and i s e s p e c i a l l y prominent i n infr a r e d - s e n s i t i v e tubes. Although the e l e c t r o n i c c i r c u i t r y i s i n s e n s i t i v e to steady dc currents, there i s a f l u c t u a t i o n noise component associated with the dark current that ser-iously l i m i t s the signal-to-noise r a t i o of the system. Since the Richardson equation f o r thermionic emission predicts an inverse exponential dependence of emission on temperature, i t follows that cooling the photocathode w i l l have a marked e f f e c t on the dark current and thus on the signal-to-noise r a t i o . Amplifier. f Even a f t e r c o o l i n g the photocathode, there are several other sources of noise, some of which depend on the s i g n a l , 64 1000 watt l i q u i d nl t rogan-coolad • U u l o u l t Lp l l a r housing u i B i L grat ing monochromator with notor dr lv« Hi lgar D28J • o n o c b r o u t o r f A.4, g lass p r l s u , Motor dr lva 4^  ad Jus tab la quartz opt ica for focussing 4 glass achroaMts y \ . — T f tungstan ribbi J ( fllaaamt laarp nata l aaapla- 1 6 r o l t a . 18 m Dawar- adjustable ClaB-Thoapson polar I t lag pr laa r i on -V for abaorptlan or nits Ion work FIG. 3. Op t i c a l system for polarized c r y s t a l spectra. FIG 4. Block diagram of elec t r o n i c c i r c u i t r y for measurement of weak emission spectra. PHOT OMULTIPLI ER CONTROL, CKT BKR 1 M I HIGH VOLTAGE SUPPLY K E I T H L E Y VTVM WITH SH*UNT 2-STAGE h PREAMP 2- S T A G E A M P . TUNED 27-5 CPS V T V M "> RECORDER L (20 MV) 65 and some only on the applied voltage. In order to Improve further the signal-to-noise r a t i o , advantage was taken of i t s inverse dependence on the square root of the system-bandwidth by designing and constructing an amplifier sharply tuned to 27.5 cps. The l i g h t from the c r y s t a l i s chopped at t h i s frequency before passing through the s l i t , and the phototube s i g n a l (taken from i t s anode load r e s i s t o r through a capacitor) i s fed through an attenuator into a low-noise untuned preamplifier having a gain of 35. This i s followed by a two-stage amplifier having a gain of/^bout 1600 at the — /a center frequency. Tuning i s effected ^ c^iwo twin-T net-works, and the time constant of the enti r e system! i s \about one second. Attenuators are provided between a l l stages to ensure l i n e a r operation. The output passes into a standard VTVM c i r c u i t with f u l l - s c a l e d e f l e c t i o n of 0.5 - 1 v o l t ; a tap provides f o r balanced output to a 20 m i l l i v o l t recorder. Samples. The c r y s t a l l i n e samples consisted mostly of thin (5-50 micron) films obtained by melting a small quantity of i" the s o l i d between glass or quartz disks.. Some c o n t r o l over the thickness could be achieved by applying pressure to the disks during cooling. To obtain a large area of uniform s i n -gle c r y s t a l i t was usually necessary to anneal the sample by 66 remelting a portion, and then allowing a c o r r e c t l y oriented unmelted c r y s t a l to seed the melt. The sample was mounted on a copper disk so that the area to be studied covered a pinhole on the disk. With the c r y s t a l oriented so as to extinguish along marked l i n e s on the copper disk, the e n t i r e assembly was placed i n the sample Dewar i n correct r e l a t i o n to the o p t i c a l system. In absorption studies the sample was illuminated through the pinhole. In emission work, a larger hole served merely to transmit v i s i b l e l i g h t used to focus an image of the c r y s t a l onto the s l i t . E x c i t a t i o n of the sample was usually by front-face illumination, the c r y s t a l face making an angle of about 50° to the o p t i c a l system. Absorption spectra. Most of the absorption spectra were obtained by compar-ing the amount of l i g h t transmitted by the c r y s t a l at var-ious wavelengths with the s p e c t r a l output of the tungsten source which was determined i n a separate run. D i f f r a c t i o n e f f e c t s involving the pinhole, interference from sample and disk surfaces, and r e f l e c t i o n of incident light,were not corrected f o r , and very frequently contributed to peculiar and non-reproducible r e s u l t s . Reflection usually accounted for 0.02 to 0.15 u n i t of apparent o p t i c a l density outside the 67 absorption region, and i f t h i s was c h i e f l y from the glass or quartz disk, should not vary with wavelength. Some of the room-temperature spectra were determined by a d i r e c t method i n which the sample was moved back and f o r t h over the pinhole so that readings of incident- and transmitted l i g h t (and hence of o p t i c a l density) could be made d i r e c t l y at each wavelength increment. It was possible to orient the c r y s t a l s more accurately i n thi s system, and the i n t e n s i t i e s obtained by thi s method, p a r t i c u l a r l y i n r e -gions where the s e n s i t i v i t y of the detector i s changing rap i d l y , are probably a b i t more r e l i a b l e . A Beckman DU monochromator was used. A l l emission spectra were corrected f o r photomultiplier s e n s i t i v i t y , using manufacturer's data on the spe c t r a l response of the photocathodes. 68 VII. THE ANTHRACENE-TNB COMPLEX This complex was selected for detailed examination be-cause i t i s t y p i c a l of a large number of stable molecular complexes between aromatic acceptors and hydrocarbon donors, and has been the object of considerable study and discussion by others. The c r y s t a l structure i s now known (87), the polarized infrared spectrum has been studied (47), and a de-t a i l e d study of the solution emission spectrum has been made by McGlynn and coworkers (54), who have also discussed some of the t h e o r e t i c a l aspects of the complex (55). The CT absorption and emission bands are located i n a convenient s p e c t r a l range i n which to work, and are s u f f i c -i e n t l y removed from the strong (localized) aromatic absorp-ti o n bands to prevent the l a t t e r from obscuring the CT bands. Because the CT band i s above the anthracene phosphorescence o r i g i n at 14.9 kK, we should expect to see t h i s emission i n addition to the CT fluorescence. A l l TNB complexes share a disadvantage i n t h i s respect however, since the phosphor-escence from t h e i r s o l i d forms i s usually not measurable (31a). * C r y s t a l structure. The orange a c i c u l a r prisms of the complex, obtained by c r y s t a l l i z a t i o n from ethanol-isopropyl ether, tend to develop a p r i n c i p a l face which shows p a r a l l e l e x t i n c t i o n and a strong 69 dichroism, the orange c o l o r being most intense when the l i g h t i s polarized p a r a l l e l to the needle axis. The r e -f r a c t i v e index corresponding to th i s d i r e c t i o n was found to be 1.502 + 0.002 (at 6250 A); at r i g h t angles to t h i s (along the other e x t i n c t i o n direction) the index was greater than 1.8, the index of the most r e f r a c t i v e immersion f l u i d a v a i l a b l e . The c r y s t a l structure has been determined by Wallwork (87); the space group i s C2/c ( C ^ ) * with four molecules (complex pairs) per unit c e l l . The unit c e l l dimensions at room temperature are a - 11.70, b - 16.20, c - 13.22 A; £ - 132.8°. The donor and acceptor molecules are stacked a l t e r n a t e l y (in a staggeredjmanner) i n columns p a r a l l e l to the c-axis, but are not quite perpendicular to this axis. The molecules are located at the s p e c i a l positions as follows: anthracene: 0,0,0; 0,0,%; %,%,0; TNB: 0,y,%; 0,y,3/4; %,%+y,%; %,*H-y,3/4. Figure 7 shows a single complex pair, viewed along the c-axis. Atomic positions were calculated from the data of Wallwork (86), and from these the projection of the c r y s t a l structure onto the (100) face was constructed (Fig 8). The atomic coordinates are given i n Appendix A. From the prop-e r t i e s of the space group C2/c (Fig 12), i t i s seen that each 70 i i a A N T H R A C E N E - T N B C R Y S T A L -VIEW A L O N G c - A X I S F f G . 7 71 72 anthracene molecule i s located at an inversion centre, and that successive complex pairs are b u i l t up by a screw trans-l a t i o n along the c-axis. Samples for spectroscopic study were prepared by melt-ing a few c r y s t a l s between quartz or glass disks. The r e -s u l t i n g thin sections showed the same o p t i c a l properties (including r e f r a c t i v e index) as the p r i n c i p a l face of crys-t a l s grown from solution. In order to interpret the spectra, i t i s necessary to know/ Sow the crystallographic axes are oriented with respect to the face developed i n the prepared samples. Unfortunately, d e f i n i t e information on these points i s s t i l l lacking, and we must use the available o p t i c a l evidence to predict the most l i k e l y p o s s i b i l i t y . In a monoclinic c r y s t a l , one axis of the i n d i c a t r i x corresponds to the b-axis, and the other two must l i e some-where i n the ac_ plane. The fa c t that the section shows par-a l l e l e x t i n c t i o n indicates that the face i s probably an ac zone. The c r y s t a l structure (Fig 8 ) and our knowledge of the nature of CT spectra suggest that the t r a n s i t i o n should be polarized most strongly along the c-axis. Since the strong-est component of CT absorption i s observed along t h i s axis, we can conclude that the c-axis l i e s i n the zonal plane 73 containing the needle axis; i t may or may not correspond to the needle axis, but the observed i n t e n s i t y of the CT absorp-t i o n i n this d i r e c t i o n suggests that the angle between the two axes i s not large. We can therefore say that the c r y s t a l section probably contains the b- and c_-axes, the former corresponding to either the slow or intermediate i n d i c a t r i x axis. The face developed i s (lOz) and may be (100); the l a t t e r seems l i k e l y ; X-ray evidence has been unable to confirm t h i s , but i t does not preclude such an assignment (83). The c a l c u l a t -ions of expected p o l a r i z a t i o n r a t i o s were ca r r i e d out under the assumption that the face i s (100) (be); i n discussing the experimental r e s u l t s , allowance w i l l be made for the present uncertainty i n t h i s assignment. 74 The absorption spectrum. On the following page i s shown an absorption spectrum of anthracene-TNB c r y s t a l , made by the d i r e c t method (see Section VI) at room temperature. Three separate absorption systems are c l e a r l y seen i n t h i s spectrum: a) A broad CT band, showing a trace of structure, and polarized along the c-axis; i t extends from 19.5 to 26.0 kK, and i s centered at 22.0 kK (4550 A). The o p t i c a l density r a t i o of the f i r s t peak (near 20.6 kK) i s 5.6:1 (c:b). b) An oppositely polarized band of somewhat less i n -ten s i t y but more structure. I t i s centered near 28.1 kK (3560 A), and has peaks at 27.2, 28.0, and 28.9 kK. The o p t i c a l density r a t i o i s 1.8-2.4:1 (b:c). c) A t h i r d band, centered at 31.0 kK, showing no s t r u c t -ure. Its p o l a r i z a t i o n corresponds to that of the CT band. The polarized absorption spectrum of a c r y s t a l at 78°K i s shown i n F i g 10; the spectrum of the same c r y s t a l at room temperature i s also shown for comparison. The most apparent difference between the two i s the more pronounced v i b r a t i o n a l structure and s l i g h t (~ 200/cm) b l u e - s h i f t of the low-temperature spectrum. The v i b r a t i o n a l peaks i n the CT region are quite broad, even at 78° K. This broadness makes i t d i f f i c u l t to locate the exact maxima of the peaks, most of which appear to con-s i s t of more than one v i b r a t i o n a l component. The f i r s t main peak i s located at 20.15 kK, and the others are spaced at 2.5 2.0 1.5 i.o r-0-5 L 560 millimicrons j i L j L 520 480 440 400 360 320 FIG. 9 . Absorption spectrum of anthracene-TNB single c r y s t a l at room temperature by direct method . 76 >- O I 1 1 1 I I I I I I 1 1 L CO ttK. FIG. 9. POLARIZED ABSORPTION SPECTRUM OF ANTHRACENE-TNB SINGLE CRYSTAL 77 int e r v a l s of 1300-1500/cm. A s l i g h t s p l i t t i n g of the energies of oppositely polarized maxima was apparent i n some of the spectra; the c-polarized peaks appear to be centered about 100/cm lower i n energy than those of opposite p o l a r i z a t i o n . The broadness and i r r e g u l a r i t y i n the peaks makes t h i s small s h i f t d i f f i c u l t to see, e s p e c i a l l y i n spectra of high o p t i c a l density, where the peaks are much less pronounced. Discussion. Complete discussion of the c r y s t a l spectrum must of co course be deferred u n t i l the emission experiments are pre-sented, but some of the points relevant to the absorption spectrum w i l l be mentioned here. The most obvious difference between the absorption spectra of the pure c r y s t a l and of the solution i n r i g i d glass i s the appearance of v i b r a t i o n a l structure. This i s a new feature of CT spectra and has not been observed i n solut i o n . The reason for th i s i s undoubtedly connected with the weakness of CT i n t e r a c t i o n forces, which r e s u l t i n an extremely shallow ground-state p o t e n t i a l energy curve for the dimeric species i n solu t i o n . If CT e l e c t r o n i c t r a n s i t i o n s can take place between randomly oriented molec-ules on contact or near-contact, the r e s u l t i n g spectrum 78 should be influenced l i t t l e i f at a l l by the vibronic states of the i n t e r a c t i n g species. In addition, the t r a n s i t i o n energies of the many D-A pairs of d i f f e r e n t or-ientations should extend over a range comparable to v i b r a t i o n -a l i n t e r v a l s of the components, thus o b l i t e r a t i n g any structure that might otherwise tend to appear i n the spectrum. The c r y s t a l structure places a constraint on the mol-ecules that does not e x i s t i n solution; the p o t e n t i a l energy curve based on r D A must now r i s e steeply from both sides of a much sharper minimum, and CT in t e r a c t i o n w i l l be r e s t r i c t e d to a narrower range of configurations. There i s no longer any p o s s i b i l i t y of the complex d i s s o c i a t i n g , and intramol-ecular vibrations which are excited i n the CT process w i l l couple with the CT t r a n s i t i o n and influence the shape of the absorption band. Even at l i q u i d nitrogen temperature the bands are rather broad, suggesting that the molecules may s t i l l posess considerable freedom of movement i n the l a t t i c e . Intermolecular v i b r a t i o n a l modes must be strongly excited during a CT t r a n s i t i o n , and the resultant rocking and bobbing motions may contribute to the broadness at these temperatures. Meaningful analysis of the v i b r a t i o n a l structure of the CT band must await studies at 4°K, where the bands should be much more well-defined. The present spectra r e -79 veal the presence of a 1070/cm i n t e r v a l , and possibly one of 1320-1350/cm. These may be related to the 1068/cm and 1341/cm frequencies noted by Kross (47) i n the polarized infrared spectrum of the c r y s t a l . Both are thought to correspond to vibrations involving the TNB molecule. None of the bands assigned by Kross to anthracene vibrations i s apparent i n the ele c t r o n i c absorption spectrum of the complex. Comparison of the mean frequencies of CT absorption i n the c r y s t a l with those i n various solvents shows that a d e f i n i t e b l u e - s h i f t occurs on going to the s o l i d form. This i s opposite to the behaviour of most simple aromatic hydrocarbons, and may be connected with the intermolecular nature of the process. Each donor, for instance, sees two acceptors, and the energy required to bring about CT between a given pair must be s l i g h t l y increased by the. presence of another acceptor which tends to draw charge i n the opposite d i r e c t i o n . CT max i n chloroform 21.8 kK (21) E.P. glass 21.6 kK (31b) c r y s t a l 22.0 kK Beyond the CT region the p o l a r i z a t i o n reverses, and the strongest absorption component i s polarized perpendicular 80 to the needle axis, presumably along the b-axis. This corresponds to a t r a n s i t i o n moment l y i n g i n the planes of the component molecules, and i t i s reasonable to a t t r i b u t e t h i s absorption to the 7r-electron tr a n s i t i o n s that normally occur i n the free anthracene and TNB molecules. According to the theory given above, these l o c a l i z e d t r a n s i t i o n s should s t i l l occur i n the complex, with l i t t l e change i n energy or i n t e n s i t y . Absorption spectra of pure anthracene and TNB i n solution are given i n F i g 11. TNB i s seen to show a broad weak shoulder at 30 kK, blending gradually into the stronger absorption at 45.51 kK. No assignment of these t r a n s i t i o n s has yet been made, but the former band could be a n - T t * t r a n s i t i o n involving the n i t r o groups, while the other could correspond to the or L a band of benzene. Anthracene has a weak system at 3800 A, giving r i s e to prominent peaks ( i n solution) at 27.8, 28.1, and 29.5 kK, with a maximum ex t i n c t i o n c o e f f i c i e n t of 8000. It has been assigned to a short-axis (M) polarized t r a n s i t i o n of B 2 u (*"La) symmetry (25). Recent studies of the polarized absorption spectrum of anthracene i n fluorene (13) have shown that the longest wavelength components, including the (0-0) vibronic band, are polarized most strongly along the long 81 FIG l i b . Absorption spectra of anthracene i n iso-octane solution and i n the pure c r y s t a l . (From A. Bree, Ph.D. Thesis, Sydney, 1958). C R Y S T A L (B-AXIS) 26 28 30 32 34 36 38 40 42 4 4 46 82 (L) axis. Unfortunately, the broadness of the peaks pre-vents r e s o l u t i o n of the vibronic components and th e i r i d e n t i f i c a t i o n i n terms of the known vibrations of anthra-cene. A broad structureless band centered at 31.0 kK appears i n the room-temperature spectrum of F i g 9. On the basis of i t s p o l a r i z a t i o n perpendicular to the r i n g planes, the band can be attributed to ann-7v* t r a n s i t i o n l o c a l i z e d i n the TNB, or to a second CT band. If the band near 30 kK i n TNB i s ann-n* t r a n s i t i o n , then i t should be polarized normal to the TNB r i n g , and should therefore appear only along the c-axis when viewed normal to the be face of the c r y s t a l . The e x t i n c t i o n c o e f f -i c i e n t i n solution i s 300; i f no d r a s t i c changes i n intens-i t y occur on incorporation into the c r y s t a l l i n e complex, the observed i n t e n s i t y along c i n the (100) projection should be about 675. The measured i n t e n s i t y of the 31.0 kK band of the complex i s about three times this value ( i n t e n s i t y measurements w i l l be discussed i n d e t a i l below), and i t would seem p r o f i t a b l e to consider other possible assignments of t h i s band. The solution spectrum of anthracene-tetracyanoethylene (TCNE) shows two CT bands, separated by 8.0 kK (21,22). We 83 might therefore expect a second CT band (corresponding to the t r a n s i t i o n (DA-^D*4*, A~) to appear i n the anthracene-TNB complex, centered about 8 kK above the f i r s t CT band, or near 30 kK. Its i n t e n s i t y should be roughly the same as that of the f i r s t CT band. On the basis of the present evidence, i t would seem most reasonable to t e n t a t i v e l y i d e n t i f y the observed 31 kK band with a second CT t r a n s i t i o n - however, the other i n t e r p r e t a t i o n (that i t i s a n - n * band of TNB) cannot be excluded. Selection rules and p o l a r i z a t i o n s . In considering the nature of the CT t r a n s i t i o n i n the c r y s t a l (and neglecting, f o r the moment, second-order i n t e r -actions with donor- and acceptor states), we must f i r s t determine which c r y s t a l states correspond to the molecular CT states. As was discussed i n Section IV, the c r y s t a l states are determined by the space group of the c r y s t a l , but the unique nature of the t r a n s i t i o n ( i . e . , i t s intermolecular nature) demands an e s p e c i a l l y c a r e f u l consideration of the symmetry relationships involved. The space group C2/c describes the c r y s t a l structure i n terms of the operations required to b u i l d up the l a t t i c e from a complex D-A pair located at an o r i g i n (Fig 12). In most c r y s t a l s that have been treated t h e o r e t i c a l l y , the 84 t r a n s i t i o n moments are considered to be centered at the molecular o r i g i n s , and can be regarded as forming a l a t t i c e having the same space-group symmetry as the c r y s t a l ; the c r y s t a l states are then constructed i n conformity with the symmetry properties of thi s transition-moment l a t t i c e . CT t r a n s i t i o n s are intermolecular, and the t r a n s i t i o n moments are not centered at the molecular o r i g i n s , which for c rystallographic purposes have been placed at the centers of the anthracene molecules (which are a l l located at s p e c i a l p o s i t i o n s ) . If a new l a t t i c e based on the t r a n s i t i o n moments i s envisioned, i t i s apparent that the inversion symmetry at the s p e c i a l positions has been l o s t , and the space group i s now C/c. This space group builds up the c r y s t a l by means of glide planes p a r a l l e l to (010). The isogonal point group i s C g (m), which contains only the oper-ations E and mz (<s~z), where the z-direction i s taken par-a l l e l to the c-axis. There are four moments per unit c e l l , but two of these are t r a n s l a t i o n a l l y equivalent and make no contribution to the c r y s t a l s p l i t t i n g , so we can consider, for the present purpose, smaller u n i t c e l l s c o n s i s t i n g of two moments. (With the same r e s u l t s , we could have con-sidered the space group to be P2^, and used the isogonal point group C2). 85 , - 0 c ° < - - O O i -±*©7o I : i i i i ! -.'1i o i ' o 1 ! . 1 i • i -A. n 1 O O i - j. i | * > o i C j N C j N 1 c ! O ! '1. 0 i t i i *•* 1 3 4 ' 4 ... \' . THE SPACE GROUP C 2 c ~ C|n FIG. 12 ANTHRACENE MOLS. AT SPECIAL POSITIONS FIG. 13 SPACE LATTICE OF TRANSITION DIPOLES: ANTHRACENE-TNB CRYSTAL 86 We s h a l l assume that the predominant species i n solu-t i o n belongs to the point group C g. The observed p o l a r i z -ation i n the c r y s t a l and the f a c t that our concept of the CT process predicts a z_-polarized ( i . e . , perpendicular to the r i n g planes) t r a n s i t i o n moment, has led to the assign-ment *A^ for the upper state. The eigenfunctions 0, and Qfa of the two non-trans l a t i o n -a l l y equivalent CT states are combined to belong to the oc-and $ representations of the s i t e group, giving r i s e to the two c r y s t a l functions The operation m_ changes the sign of t//^, so that the char-acters of the two site-group representations are +1 and -1, respectively, corresponding to the A' and A" representations of C s. I f the t r a n s i t i o n i s t o t a l l y symmetric i n the mol-ecular point group, then i t must belong to the t o t a l l y -symmetric site-group representation; since the two groups coincide i n t h i s c r y s t a l , the problem becomes t r i v i a l and the t r a n s i t i o n w i l l of course be z-polarized i n the c r y s t a l as w e l l as i n the molecule. According to the theory, the energy of the t r a n s i t i o n i s given by E = W + £ I. + £ 1- > where the pos i t -87 ive sign r e f e r s to the A' state and the negative sign to the A" state. The index p runs over a l l t r a n s l a t i o n a l l y equiv-alent molecules, and q runs over a l l others. The other terms have the same meaning as i n Eq 22, Section IV. The s p l i t t i n g depends on the magnitude of the second i n t e g r a l sum, while the f i r s t adds to W to cause a s h i f t of the entir e spectrum. If the summed in t e r a c t i o n i n t e g r a l over q i s posi t i v e , the z-axis polarized component of the CT band should be lower i n energy than the oppositely polarized component. Calculation of the matrix elements for the mixing of anthracene t r a n s i t i o n s with the CT t r a n s i t i o n i n the c r y s t -a l l i n e complex was c a r r i e d out, i n accordance with Eqs. 22-30, Section IV. The crystallographic data of Wallwork (see appendix A) was used to cal c u l a t e the d i r e c t i o n cosines of lin e s connecting a c e n t r a l molecule with i t s eighteen nearest neighbors i n the c r y s t a l l a t t i c e . The molecules are here considered to be situated half-way between a l t e r -nate pairs of anthracene and TNB molecules; thus the centers of the CT t r a n s i t i o n dipole vectors are taken as the centers of the complex molecules . The r e s u l t i n g l a t t i c e arrange-ment i s shown i n F i g 13 (pg 85). Some of the more important d i r e c t i o n cosines and angular rel a t i o n s h i p s entering into the c a l c u l a t i o n s are given i n Appendix B, and the calculated 88 matrix element trans, eq. nontrans. eq. sum - 380/cm + 480/cm + 100/cm - 720 + 3140 + 2400 H L L - S900 + 6560 + 5600 „EM + 240 - 2510 - 2270 + 580 - 800 - 220 TABLE I I . Matrix elements f o r in t e r a c t i o n between the CT (E) t r a n s i t i o n , and the anthracene 3800 A (M) and 2700 A (L) systems. The second and t h i r d columns sum the elements f o r a l l molecules related to the reference molecule by t r a n s l a t i o n and screw axis, respectively. values of the various matrix elements are presented i n Table I I . From Eq (22), Sect IV, i t i s apparent that the Davydov s p l i t t i n g of the CT band should be twice the value of the E E matrix element H f o r the non-translationally equivalent molecules. This corresponds to about 1000/cm; i f divided up amongst four vibronic bands ( i n accordance with the weak coupling approach), the predicted s p l i t t i n g becomes 250/cm, with the strong (c-polarized) component of absorption at a lower energy. From the atomic p o s i t i o n data of Appendix A, we can cal c u l a t e the projections of the vectors directed along E and M (corresponding to the assumed directions of the 89 CT- and anthracene ^L^ moments, respectively) onto the (100) face of the c r y s t a l . The r e s u l t i n g oriented-gas p o l a r i z a t i o n r a t i o s are as follows: E: 5.6:1 (c:b) ( f u l l i n t e n s i t y ) M: 5.7:1 (b:c) (0.385 intensity) Because the M vector has a large projection normal to the be plane, i t s observed i n t e n s i t y must be corrected by the factor 1/0.385 = 2.6. C r y s t a l forces should mix the CT t r a n s i t i o n with l o c -a l i z e d states of the anthracene (and possibly the TNB) molecule. Using the matrix elements of Table II and Craig's data (25) on anthracene, i t can be shown that the CT t r a n s i t i o n should mix predominantly with the 3800 A short-axis (M) polarized system of anthracene (the L-pol-arized system, being e n e r g e t i c a l l y farther removed from the CT t r a n s i t i o n , mixes with i t to a much smaller extent). As a r e s u l t , the weak (in-plane) component of the CT band should be strengthened, and the p o l a r i z a t i o n r a t i o should be reduced to about 1.8:1, s t i l l (c:b). The observed r a t i o i s 5-6:1 (c:b), very close to the oriented-gas prediction. F a i l u r e of the theory to predict the observed e f f e c t s i n this system i s probably not due to inadequacies i n the theory i t s e l f , since there i s no reason to believe that 90 these inadequacies (such as the dipole approximation) should manifest themselves any more i n this system than i n anthracene, where the intermolecular distances and molec-ular dimensions are comparable. I t would seem more l i k e l y that the present d i f f i c u l t i e s stem from the use of an i n -adequate or incorrect model of the system, and possibly from the neglect of the e f f e c t s of int e r a c t i o n of the CT moment with higher states of TNB. The assumption that seems p a r t i c u l a r l y suspect concerns the d i r e c t i o n of the CT t r a n s i t i o n moment, which has been assumed to l i e along the line-of-centers between the anthra-cene and TNB molecules (represented by arrows i n F i g 8). It may be, for instance, that the CT moment i s a c t u a l l y directed along the c-axis i n the c r y s t a l , i n which case the oriented-gas p o l a r i z a t i o n r a t i o would be 1:0 (c:b), and mixing with anthracene states would reduce t h i s to the observed value of 5-6:1 (c:b). This i n t e r p r e t a t i o n w i l l be considered further i n conjunction with the fluorescence experiments. I n t e n s i t i e s . In order to determine the ext i n c t i o n c o e f f i c i e n t of a c r y s t a l section at a given wavelength, i t i s necessary to know the thickness of the section and the molar volume of the c r y s t a l . Probably the most convenient method of measur-91 ing the thickness of a thin section of a c r y s t a l i s that of Bree and Lyons (13a), which depends on the destructive interference of rays r e f l e c t e d from the front and rear surfaces of the c r y s t a l when a beam of l i g h t passes through normal to the face. The use of t h i s method requires a knowledge of the r e f r a c t i v e index of the c r y s t a l . In anthracene-TNB, the r e f r a c t i v e index for l i g h t polarized p a r a l l e l to the needle axis i s 1.502, so close to that of the glass on which the section i s mounted that the interference amplitude was too small to measure. Light polarized at r i g h t angles to the * needle axis gave reasonably strong interference peaks, but the r e f r a c t i v e index i n t h i s d i r e c t i o n was too high to measure with the immersion f l u i d s a v a i l a b l e . Attempts were made to measure the birefringence (and hence the unknown r e f r a c t -ive index) from the retardation of the section, using a Berek compensator. However, i t was not possible to obtain (or perhaps to recognize) bands of compensation, due to the intense color of the c r y s t a l and possibly to the large b i -refringence of the rather thick sections. It was therefore necessary to resort to a more crude method of thickness determination. A wedge-section showing third-order interference colors between crossed polars was 92 isolated on a quartz disk, and the o p t i c a l density of the weakly-absorbing component of the CT band was measured. The surface area of the section was found, and the c r y s t a l was dissolved i n a known volume of ethanol, and the o p t i c a l density of the anthracene 3800 A bands were measured. From these quantities and the molar volume of the c r y s t a l (80), the thickness was found. These ranged between 3-8 microns, and are t y p i c a l of the samples studied i n absorption experi-ments . From these r e s u l t s , the thickness of another sample was found, using Lambert's law; t h i s section gave strong interference peaks with l i g h t polarized perpendicular to the needle axis, and the positions of the maxima were used to c a l c u l a t e the r e f r a c t i v e index i n the slow d i r e c t i o n : 1.89. For a c r y s t a l of thickness 7.2 microns, the o p t i c a l den-s i t y of the CT band maximum (4600 A) i n the weakly-absorbing d i r e c t i o n was 2.2, corresponding to an e value of 880. Two other s i m i l a r samples yielded e x t i n c t i o n c o e f f i c i e n t s of 600 and 1400, and so there i s some uncertainty as to the correct value; for the present, an approximate value of 900 w i l l be assumed. Using t h i s figure, the i n t e n s i t i e s of the various bands i n the spectrum (Fig 9) of the c r y s t a l l i n e complex were calculated, and are given i n Table I I I . 93 t r a n s i t i o n c polar, b polar, t o t a l solution x 3 CT I 5200 900 6100 4000 (9) anth 3900 10 000 13 900 24 000 (39b) CT (?) 2900 1200 3100 TABLE I I I . Approximate ex t i n c t i o n c o e f f i c i e n t s of trans-i t i o n s i n c r y s t a l l i n e anthracene-TNB. Last column gives values reported for solutions of anthracene-TNB, and pure anthracene, respectively, corrected for random or i e n t a t i o n of molecules. In c a l c u l a t i n g these i n t e n s i t i e s , i t was assumed that the o p t i c a l density measurements were made on the (100) face of the c r y s t a l . If the face were (lOz), then a l l intens-i t i e s given i n the f i r s t column (c-axis polarized) w i l l be too low, and the difference between the CT i n t e n s i t y i n the c r y s t a l and i n solution w i l l be greater than i n -dicated above. The only room for serious error here i s i n the value of € = 900 f o r the b-polarized component of the CT trans-i t i o n . Although the r a t i o s of the various e's are correct, t h e i r absolute values (and t h e i r r a t i o s to the solution values) depend on the correctness of th i s f i g u r e . If iy i t i s within 25% of the actual value, then the r e l a t i v e values of the i n t e n s i t i e s given i n the l a s t two columns can be taken as evidence of mixing and transfer of i n t e n s i t y 94 from the anthracene H , a system to the CT band. The figures i n the l a s t column of Table III are intended to r e f e r to ex t i n c t i o n c o e f f i c i e n t s i n the absence of such in t e r a c t i o n . If mixing occurs i n the c r y s t a l , i t may also account for a portion of the i n t e n s i t y i n solution, i n which case we should compare the figure 6100 for the t o t a l CT i n t e n s i t y i n the c r y s t a l to. a quantity less than 4000. 95 The emission spectrum. The polarized emission spectrum of s o l i d anthracene-TNB complex i s shown at both 78° and 300° K. i n F i g 14. Because the room-temperature emission i s so weak, i t i s shown separately i n F i g 14a, i n which the scale has been ex-panded by a factor of about s i x . E x c i t a t i o n of these spec-t r a was by 4358 A l i g h t ; i d e n t i c a l r e s u l t s were obtained with 3650 A r a d i a t i o n . In F i g 15, the absorption and emission (the l a t t e r con-verted to logarithmic scale) are plotted together so as to f a c i l i t a t e comparison of the band shapes and o r i g i n s . The difference between the spectra at the two tem-peratures i s very s t r i k i n g . At room temperature, a w e l l -oriented single c r y s t a l emits only weakly, and almost exclus-i v e l y p a r a l l e l to the c-axis; the p o l a r i z a t i o n r a t i o i s about 15:1 (c:b). The broad structureless peak i s centered at 16.85 kK, and shows a rather i n d i s t i n c t i n f l e c t i o n near 17.8 kK. As the c r y s t a l i s cooled down to 78° K, the i n t e n s i t y increases considerably, the amount varying from sample to sample; increases of as much as 14-fold have been observed. Much of thi s increase consists of b-polarized emission, with the r e s u l t that the p o l a r i z a t i o n r a t i o usually drops to <7X Old RELATIVE INTENSITY 96 ABSORPTION EMISSION FIG 15. ANTHRACENE-TNB CRYSTAL: Absorption and emission spectra plotted together to show mirror-image r e l a t i o n s h i p . Only strong component of emission i s shown, plptted as log r e l a t i v e i n t e n s i t y . Absorption ordinate i s o p t i c a l density. Both spectra at 78°K. 98 around 3:1 (c:b). Most of thi s increase i s i r r e v e r s i b l e ; i f the i n t e n s i t y i s measured continuously as the c r y s t a l i s cooled, an immediate increase i s noted as the temperature begins to drop, but at a c e r t a i n point i t suddenly jumps up by a factor of three or four, and then continues to increase uniformly at about the same rate as before. If ex-amined l a t e r at room temperature, the p o l a r i z a t i o n r a t i o w i l l be no greater, and usually less, than the low-temper-ature r a t i o , but w i l l vary greatly with the c r y s t a l . Other complexes that have been studied at two temperatures were found to behave i n much the same manner. A c r y s t a l that has been annealed by undergoing th i s temperature change several times s t i l l exhibits a strong temperature dependence of emission int e n s i t y , but i t i s uniform, reasonably r e v e r s i b l e , and the i n t e n s i t y increase over the range studied i s much le s s - only about f o u r - f o l d . In F i g 16, the i n t e n s i t y i s plotted for such a c r y s t a l as the temperature i s changed: the slope corresponds to an Arrhenius energy of about 2200/cm. The low-temperature emission spectrum i s characterized by prominent but broad v i b r a t i o n a l i n t e r v a l s , s i m i l a r to those seen i n absorption. The most prominent peaks are at 18.30, 17.00, and ca. 16.0 kK. 99 0 3 0 4 •05 0 6 07 0 8 l / T , * K . E M I S S I O N I N T E N S I T Y V S . T E M P E R A T U R E • A N T H R A C E N E - T N B C R Y S T A L FIG. 16 A » t o A P T ( O W tMtsStOA/ FIG. 17. Absorption and CT fluorescence spectra of anthracene-TNB i n r i g i d glass, plotted to show mirror-image r e l a t i o n s h i p . (From McGlynn, r e f . 54, pg 360). 100 3 w C O M P L E X : 3650 A. EXCITATION * / PHOSPHORESCENCE: ' . / PURE ANTHRACENE / * k K. 18 16 15 14 13 12 Comparison of emission of pure anthracene °* with that of the TNB complex, both i n r i g i d glasses. (above) 20 19 T 8 17 16 15 14 kK. Emission spectra of complex i r r a d i a t e d b. at two d i f f e r e n t wavelengths. ANTHRACENE-TNB- EMISSION FROM RIGID GLASS, 78* FIG. 18 101 Emission from r i g i d glass. The emission spectrum of anthracene-TNB i n E.P. r i g i d glass has been thoroughly investigated by McGlynn and co-workers (54), and there i s l i t t l e that t h i s study can add to t h e i r work. Some experiments were done, however, and are summarized i n F i g 18, which shows emission spectra of two d i f f e r e n t samples i n EP glass. Because i t gave better i n t e n s i t i e s , 3650 A r a d i a t i o n was used i n preference to 4358 A l i g h t . The spectra were very s i m i l a r ; although absorption of 3650 A by the uncomplexed anthracene, followed by d i r e c t phosphorescence not involving the complex at a l l i s a d i s t i n c t p o s s i b i l i t y , there i s evidently not enough free anthracene present (at these temperatures) for t h i s to be an important process. Experiments on these and other complexes i n r i g i d glasses tended to give somewhat variable r e s u l t s , e s p e c i a l l y i n the v i b r a t i o n a l features. For instance, the spectrum i n F i g 18a i s from a sample that did not crack, while that of 18b did. Both show a CT-fluorescence peak at 16.0 kK and a phosphorescence o r i g i n at 15.1 kK, s l i g h t l y blue-shifted from the 14.9 kK location i n pure anthracene. The only new feature seen here i s the v i b r a t i o n a l structure i n the fluorescence. The inter v a l s are small, 102 only 300-600/cm, and are observed at energies well outside the phosphorescence band, which has formerly been thought to be the source of structure i n the emission of the com-plex (54). Discussion of the emission. The v i b r a t i o n a l i n t e r v a l s appearing i n the c r y s t a l emission are sim i l a r to those noted i n absorption, and may correspond to the 1341/cm and 1068/cm vibrati o n s found by Kross and coworkers (47) i n the infrared spectrum of the c r y s t a l . Both of these vibrations are assigned to TNB, the former being a symmetric -NO2 stretch, and the l a t t e r a r i n g stretching mode. Neither of them are apparent i n the s o l -ution studies of McGlynn (54). Since no phosphoroscope was used, i t i s not possible to make any d e f i n i t e statements about the extent to which phosphorescence may be superposed on the fluorescence. Czekalla (31a) found that tetrachlorophthalic anhydride (TCPA) complexes of hydrocarbons generally give a phosphorescence i n the s o l i d form that i s about a tenth of the i n t e n s i t y of the solution spectrum, and i s shi f t e d by varying degrees (100 to 1500/cm) to lower energies. In the i r experiments, the phosphorescence from s o l i d TNB complexes was too weak to measure accurately, and was not reported i n d e t a i l . 103 In the present work, no c l e a r l y I d e n t i f i a b l e phosphor-escence i s apparent, but the weak i n f l e c t i o n near 15.05 kK may be due to phosphorescence; this i s about where i t occurs i n r i g i d ' glass solution. \ Examination of F i g 15 (pg 97) shows that a very wide (2150/cm) gap exists between the fluorescence and absorption o r i g i n s . A s i m i l a r gap was noted i n the solution spectrum by McGlynn, Boggus and Elder (54), whose composite spectrum i s reproduced i n F i g 17 (pg 99). The 0-0 frequencies about which the absorption and emission are centered are 18.4 kK i n s o l u t i o n and 18.9 kK i n the c r y s t a l - a b l u e - s h i f t of 500/cm on going to the c r y s t a l . This may have i t s o r i g i n i n e f f e c t s brought about by each donor i n t e r a c t i n g with two acceptor molecules i n the c r y s t a l , as was discussed previously. Gaps between the absorption and emission o r i g i n s common-l y occur i n polyatomic molecules, and are explained on the basis of the well-known Frank-Condon p r i n c i p l e , according to which the 0-0 band w i l l not appear strongly i f the upper-state p o t e n t i a l curve i s s h i f t e d so as to cause a v e r t i c a l t r a n s i t i o n from the center of the lower-state curve to i n t e r -cept i t at a higher v i b r a t i o n a l l e v e l . Since the observed gap i s quite wide, we can assume that the d i s p a r i t y between the two curves (thinking primarily 104 of the curves whose distance coordinate i s r D A ) i s large; t h i s i s not unexpected, i f our view of the nature of the CT excited state i s cor r e c t : on undergoing a CT t r a n s i t i o n , the l a t t i c e changes from a van der Waals type to an essent-i a l l y ionic one. These would n a t u r a l l y have widely d i f f e r -ent l a t t i c e constants, p a r t i c u l a r l y along the c_-axis, and th i s rather drastic change i n the nature of the c r y s t a l forces would be expected to r e s u l t i n a s i m i l a r l y marked change i n the p o t e n t i a l energy surfaces. The same e f f e c t should occur i n a r i g i d glass, p a r t i c u l a r l y i f the p r i n -c i p a l CT i n t e r a c t i o n i s not between D and A molecules i n t h e i r most stable (presumably plane-to-plane) configuration. P o l a r i z a t i o n and i n t e n s i t y of the emission. The i n t e n s i t y and p o l a r i z a t i o n properties of the crys-t a l emission are rather unusual, p a r t i c u l a r l y i n regard to the following two points: 1) The p o l a r i z a t i o n r a t i o from a newly prepared single c r y s t a l i s higher than the oriented-gas model would predict. (In most aromatic hydrocarbon c r y s t a l s , the observed p o l a r i z a t i o n r a t i o of luminescence i s close to or less than the oriented-gas r a t i o ) . 2) The emission i n t e n s i t y depends strongly on the temperature, and i s greatest at low temperatures. In discussing these phenomena, and the properties of the absorption spectrum mentioned on ppg 89 and 93, i t would seem 105 worthwhile to reconsider the oriented-gas model that we have been using. In ordinary intramolecular t r a n s i t i o n s , the t r a n s i t i o n moments l i e along symmetry axes of the molec-ule, but i t may not be proper to assume that the t r a n s i t i o n moment of an intermolecular CT t r a n s i t i o n i s s i m i l a r l y directed along the p r i n c i p a l axis of the complex molecule , that i s , from the center of D to the center of A. In the c r y s t a l the i n d i v i d u a l DA pairs are somewhat i n d i s t i n c t ; as was suggested previously (pg 58), i t may be better to not think of DA pairs at a l l , but rather a stacked p i l e of i n t e r -acting donors and acceptors, the complex molecule being an extended portion of the c r y s t a l l a t t i c e ; the CT dipole moment would be directed along the c_-axis of the c r y s t a l . If t h i s were correct, then the oriented-gas p o l a r i z a t i o n r a t i o would be 1:0 (c:b). The observed luminescence polar-i z a t i o n r a t i o would then require no s p e c i a l explanation, and the r a t i o f o r absorption would be reduced as a r e s u l t of mixing of the CT state with oppositely polarized donor states (the r e s u l t s i n Table III, pg 93 constitute independ-ent evidence of such mixing). As a f i r s t step toward the explanation of the temper-ature e f f e c t s , the diagram of F i g 19 has been constructed. Absorption i s from the ground state N to the excited CT state 106 E D T 1 2 i n N FIG. 19. Possible routes of decay of excited CT state i n anthracene-TNB complex. E (process I ) . In a newly-prepared single c r y s t a l , e x c i t --9 ation w i l l be followed by fluorescence (II) a f t e r about 10 sec (30), intersystem crossing (III) to the t r i p l e t state T, or by thermal e x c i t a t i o n to the postulated state E* (IV), which i s assumed to connect non-radiatively with the ground state, t h i s process being rapid compared with the fluoresc-ence l i f e t i m e . At room temperature, the r e l a t i v e l y rapid flow of energy into E* i s mostly one-way, and process IV competes strongly with r a d i a t i v e decay. The state E* may be a vibronic l e v e l whose v i b r a t i o n a l mode f a c i l i t a t e s the e f f i c i e n t transfer of e x c i t a t i o n energy to the l a t t i c e . On cooling the c r y s t a l to l i q u i d nitrogen temperature, there occurs a sudden, i r r e v e r s i b l e increase i n emission int e n s i t y , accompanied by a decrease i n the p o l a r i z a t i o n r a t i o . This may be due to the creation of a new state D, which i s assumed to l i e s l i g h t l y below E i n energy, so that 107 most, i f not a l l of the emission i s from t h i s state. The p a r t i a l depolarization and the other c h a r a c t e r i s t i c s of th i s state suggest that i t i s connected with the creation of de-fects i n the c r y s t a l l a t t i c e . These may be due to cracks or dislocations caused by the cooling process. In this connection, i t i s of in t e r e s t to note that Wallwork (86) found differences of a few tenths of an Angstrom i n some of the l a t t i c e constants of the anthracene-TNB c r y s t a l between room temperature and ca. -100 ° C , representing a maximum contraction approximately along the [103] c r y s t a l d i r e c t i o n on cooling. 108 VIII. OTHER COMPLEXES 9,10-Dimethylanthracene-TNB This complex was studied because the CT and lowest l o c a l i z e d t r a n s i t i o n s of the hydrocarbon could both be seen without overlap from TNB absorption. DMA has i t s f i r s t peak at 3980 A (25.1 kK) i n solution, but i t i s rather broad and extends out to 4200 A, imparting a yellow colour to the pure hydrocarbon. The absorption peak of the complex i n at carbon tetrachloride i s ^ 19.90 kK. The c r y s t a l l i n e complex i s red i n colour, and samples which have been c r y s t a l l i z e d between pressed disks are i n -tensely dichroic, appearing bluish-red i n one p o l a r i z a t i o n and pale yellow i n the other. Repeated attempts f a i l e d to produce a r e a l l y uniform single c r y s t a l , a l l samples appear-ing somewhat mottled between crossed polars, with each small region extinguishing over a range of 10°. No d i s t i n c t growth axes were apparent, and the interference figure was i n d i s t i n c t , but suggestive of the type given by a section normal to the optic a x i a l plane, with the b-axis i n the strongly-absorbing d i r e c t i o n . In most of the samples studied, small areas were noticed that had d i f f e r e n t o p t i c a l properties; e x t i n c t i o n was more complete and p a r a l l e l to d e f i n i t e cracks, and the dichroic 109 colours were orange-yellow. The red-yellow (most common) form i s referred to as ( I ) , the other by ( I I ) . Their ab-sorption spectra are shown together i n F i g 20. Considering f i r s t the most common modification ( I ) , the absorption spectrum c l e a r l y shows the separate CT and l o c a l -ized components which, as i n the anthracene-TNB complex, are oppositely polarized. The p o l a r i z a t i o n r a t i o s are quite high, being about 10:1 for the CT band and about half t h i s value i n the hydrocarbon absorption region. The absorption peaks i n the two polarizations are as follows: v e r t i c a l : 17.00 18.35 18.70 19.70 20.95 kK horiz: 16.60 (17.20) 18.30 - - 20.50 kK aromatic region ( h o r i z ) : 23.4, 24.5, 26.0, 27.3 kK. Assuming that the proper peaks are being compared, a rather large (ca. 400/cm) s p l i t t i n g i s present i n the CT region than was observed i n anthracene-TNB. The emission spectra excited by 3650 A and 5461 A l i g h t were i d e n t i c a l except for their i n t e n s i t y . No room-temper-ature emission spectra were run. emission: 15.42 14.27 13.20 (11.80) kK. The p r i n c i p a l i n t e r v a l appears to be around 1100/cm. The l a s t band, a very broad shoulder near 11.8 kK, may be re-lated to the hydrocarbon phosphorescence. 110 FIG. 21 FORM I (RED / YELLOW) FORM I 9, 10- D I M E T H Y L A N T H R A C E N E - TNB P O L A R I Z E D A B S O R P T I O N FIG 20 I l l O R A N G E - Y E L L O W (II) COMBINED CRYSTAL SPECTRA OF THE TWO 9,10-DIM ETHYL ANTHRACENE- TNB COMPLEXES FIG. 22 112 The other c r y s t a l (II) d i f f e r s l i t t l e from the f i r s t i n the general appearance of i t s spectra; the main d i f f e r -ence i s a b l u e - s h i f t of the e n t i r e emission and absorption: CT absorption: v e r t i c a l : 18.30 19.80 20.95 22.60 kK horiz: 17.75 19.25 20.60 21.90 kK aromatic (h o r i z ) : 25.0, 25.2, 26.25, 27.5 kK. The two forms (I) and (II) may be due to 1) an impurity i n the hydrocarbon that also forms a complex with TNB, 2) d i f f e r e n t c r y s t a l modifications of the same complex, or 3) complexes d i f f e r i n g i n r a t i o of TNB to hydrocarbon. The c r y s t a l emission spectrum of pure 9,10-dimethyl-anthracene ( p u r i f i e d by microsublimation i n nitrogen) con-s i s t s of a broad and nearly structureless band, having a maximum at 19.40 kK. This lack of structure, even at 78° K, suggests that i t e x i s t s as a dimer i n the c r y s t a l . Hexame thylbenzene-TNB The c r y s t a l structure being undetermined, only a b r i e f study of t h i s complex was made, using a p o l y c r y s t a l l i n e sample at 78° K. However, i t turned out to be of some i n t e r -est, as i t i s the only complex examined that gives d i f f e r e n t emission spectra on e x c i t a t i o n at d i f f e r e n t wavelengths. As F i g 23 shows, 3130 A e x c i t a t i o n r e s u l t s i n a peak near 113 FIG 23. HEXAMETHYLBENZENE-TNB:\ Emission spectra of single c r y s t a l at two d i f f e r e n t e x c i t a t i o n energies. FIG 24. FLUORENE-TNB c r y s t a l emission. 1 1 1 1 1 1 1 1 1 ' 1 1 1 1 21 20 19 18 17 16 kK. 114 23.40 kK, while 3650 A and 4358 A l i g h t excites only the yellow emission centered at 17.10 kK. The two spectra i n F i g 23 are plotted to separate a r b i t r a r y i n t e n s i t y scales, since the r e l a t i v e i n t e n s i t i e s of the two e x c i t i n g l i n e s were not determined. Emission spectra were also run i n E.P. glass (Fig 23b). The spectrum obtained at 4000 A may be a superposition of donor phosphorescence (beginning near 22.0 kK) and CT f l u o r -escence, which begins below 18.0 kK. The absorption maximum i n carbon tetrachloride i s at 25.40 kK (16). Assuming that the c r y s t a l absorption i s centered i n t h i s region, i t i s cle a r that the bulk of the emission with 3130 A e x c i t a t i o n cannot be CT fluorescence, but must be fluorescence from the hexamethylbenzene. Fluorene-TNB. Non-oriented c r y s t a l l i n e samples were studied at two temperatures. As i s seen i n F i g 24, the low-temperature emission shows good structure, o r i g i n a t i n g at 20.8 kK. The room temperature emission i s structureless and i t s center i s red-shifted by about 800/cm. The c r y s t a l structure i s not known i n d e t a i l , but the r a t i o of fluorene to TNB i s 3:4. (43*) 115 Stilbene-TNB, Azobenzene-TNB. Stilbene forms a pale yellow complex containing two molecules of TNB per hydrocarbon. The c r y s t a l i s t r i c l i n i c , with two complexes per unit c e l l (43b). The room-temper-ature emission of the c r y s t a l i s broad and structureless, centered at 17.4 kK and polarized approximately 2:1 p a r a l l e l to the needle axis. At 78° K, the band retained i t s broad-ness and s h i f t e d to 16.8 kK; only a trace of structure appeared. An i r r e v e r s i b l e change i n p o l a r i z a t i o n r a t i o to 0.9:1 (needle axis: short axis) suggested that considerable disruption of the c r y s t a l l a t t i c e must occur on cooling. Phosphorescence from c r y s t a l l i n e stilbene has never been observed, and there i s no evidence of i t s appearance here, i n spite of the f a c t that the CT absorption band almost c e r t a i n l y overlaps the expected t r i p l e t l e v e l . Only the onset of the c r y s t a l absorption band was meas-ured. It climbs very steeply and has a shoulder at 22.7 kK. Comparison with the emission spectrum shows that the 0-0 frequency must be i n the neighborhood of 20 kK. The orange p l a t e l e t s obtained by evaporation of solvent from a solu t i o n containing both azobenzene and TNB have the same color as azobenzene i t s e l f , but they can be shown to contain TNB. Very c a r e f u l d i f f e r e n t i a l absorption studies 116 CT BANDS OF STILBENE- AND AZOBENZENE-TNB •OS TNB + C. STILBENE \AZOBENZENE X^+TNB 20 22 24 J 26 28 _L 1 ABSORPTION IN C C l 4 i * i i i i SINGLE C R Y S T A L N . 7 8 ° K. / V 19 18 17 16 15 14 kK. STILBENE - TNB EMISSION FIG. 25 117 on azobenzene and azobenzene-TNB solutions i n carbon t e t r a -c h loride revealed a weak band at 24.0 kK (Fig 25c) which i s presumably a CT band. Its location i s j u s t about where one would expect to f i n d the CT band of a simple hydro-carbon having i t s f i r s t excited state at 30 kK, but the n-7r* band of azobenzene (at 22.4 kK) o r d i n a r i l y obscures the very weak CT absorption. Unlike most of the other TNB complexes of N-substituted hydrocarbons (amines, e t c . ) , that of azobenzene shows no evidence of CT inte r a c t i o n involving the nonbonding electrons of the nitrogen atoms d i r e c t l y . No emission was detected, either from the s o l i d or from the r i g i d glass so l u t i o n of azobenzene-TNB. This i s i n accordance with the non-emitting property- of azobenzene i t s e l f . Azulene-TNB. The peculiar spectroscopic properties of azulene are wel l known; fluorescence i s from i t s second (3500 A) excited state (7); no emission from the lower (7000 A) state has been observed. From the i r studies of azulene i n naphthalene at 20° K, Sidman and McClure (78) assigned the f i r s t state at 14650/cm as short-axis polarized, H>b. The upper state i s 118 polarized p a r a l l e l to the long-axis, and assigned to * L a , 28050/cm. Transitions to both states are weak; the upper state absorption has an o s c i l l a t o r strength of f = 0.08, while the lower-state t r a n s i t i o n i s only a tenth as strong. The diffuseness of the 7000 A absorption, even at 4° K, has led (44) to the suggestion that r a d i a t i o n l e s s degradation of e x c i t a t i o n energy must occur through a succession of vibronic states with i n t e r s e c t i n g p o t e n t i a l energy surfaces. The s o l i d TNB complex i s black i n color, but appears brownish-red when viewed i n t h i n sections. Wallwork (86) has determined the c r y s t a l structure, but has been unable to r e f i n e i t completely, due possibly to a disorder of the same kind as i s present i n the pure azulene c r y s t a l . The space group of the complex i s P2^/C, and there are four D-A pairs per unit c e l l , The molecules are stacked along the b-axis, rather than along c, as i n anthracene-TNB. In solution, the absorption spectrum of pure azulene shows a wide gap between the f i r s t two absorption systems; thi s gap i s f i l l e d by the CT band upon addition of TNB. Thus the observed CT band i s related to the second, rather than to the f i r s t excited state of azulene. The absorption spectrum of the c r y s t a l l i n e complex i s shown i n F i g 26. C r y s t a l sections of d i f f e r e n t thickness 119 120 were used to bring out the and CT absorption peaks. The polar directions corresponded with the dichroic and e x t i n c t -ion axes, but the crystallographic directions were not de-termined. However, considering the reported c r y s t a l structure and the expected p o l a r i z a t i o n of the CT absorption, we are probably looking at the be or ab face. This would also account for the extremely weak absorption i n the 7000 A region, which should appear strongly only i n the ac_ face. I t was hoped that e x c i t a t i o n of the CT complex would r e s u l t i n t r i p l e t emission of azulene, as would be expected on the basis of the r e s u l t s with other hydrocarbons whose t r i p l e t l e v e l s are below t h e i r CT l e v e l s . However, no emission was observed out to 15 kK, either from the c r y s t a l or from the r i g i d glass. Chrysene-TNB. Only the beginning of the chrysene-TNB absorption spec-trum was obtained. The f i r s t d e f i n i t e peak i s at 21.2 KK (Fig 28)- the f i r s t weak peak near 19 kK i s probably a r e -f l e c t i o n e f f e c t . The emission spectrum at low temperatures i s moderately intense, showing well-developed peaks at 19.15, 17.82, and 16.58 kK. At room temperature, i t was too weak to record accurately. The emission spectrum bears some resemblance to the 1 2 1 / ^ \ b -K 7 8 ° \ ' " . 3 0 0 ' - i » - r — i- - 1 1 _ J . . i " i - -i - i kK. 21 20 19 18 17 16 FIG 29. TRIPHENYLENE-TNB Emission from single c r y s t a l . 122 phosphorescence spectrum of chrysene (see Appendix C), par-t i c u l a r l y i n i t s general location, but the v i b r a t i o n a l i n t e r -v a l of the l a t t e r i s somewhat greater than i s observed i n the complex, and the CT emission shows the same p o l a r i z a t i o n and temperature-intensity r e l a t i o n s as does that of the anthracene-TNB complex. Triphenylene-TNB. With i t s extremely long phosphorescence l i f e t i m e (16 sec), triphenylene might be expected to form a complex with i n t e r e s t i n g emission properties, but examination of the CT emission shows that the CT state i s below the 23 kK phos-phorescence o r i g i n , and no t r i p l e t emission i s to be expected. The pale yellow complex emits only weakly, both i n the c r y s t a l and i n E.P. glass (Fig 29). The c r y s t a l emission contains very l i t t l e structure, even at low temperatures. Phenanthrene-TNB. According to Briegleb and Czekalla (17), the c r y s t a l l i n e complex has absorption and emission maxima at 25.5 and 18.3 kK, respectively. Phenanthrene phosphorescence was not re-ported i n the TNB complex, but was observed from complexes with tetrachlorophthalic anhydride, where i t appeared as a very broad band c o n s i s t i n g of three 1200/cm peaks, beginning J I • I 20 19 18 17 16 15 14 13 kK. 27c. S o l i d l i n e s : Emission spectra of a c r y s t a l of phenanthrene-TNB, containing anthracene-TNB as an impurity. For com-parison, spectra of pure phen-anthrene-TNB and anthracene-TNB are also shown. 124 at 19.5 kK. These workers suggest that t h i s 1200/cm v i b -r a t i o n corresponds to vibrations of 1320/cm and 1417/cm which are observed i n the phosphorescence component of the phenanthrene-TNB complex i n E.P. glass, and i n pure phen-anthrene phosphorescence, respectively. The spectrum of c r y s t a l l i n e phenanthrene-TNB i s shown i n F i g 27. It i s unusually broad at low temperature, but does have a trace of structure. It i s centered near 17.4 kK, and could include some phenanthrene phosphorescence, which would begin near 21.7 kK, about the same energy as the beginning of the CT emission. The broadness of the emission may be related to the fac t that two very close CT bands, separated by about 2 kK, have been observed i n solution (with tetracyanoethylene as the acceptor) (21), where the bands are also very broad. A phenanthrene-TNB c r y s t a l containing a small amount of anthracene-TNB was prepared by melting the two s o l i d s together between glass disks. The d i s t r i b u t i o n of the anthracene-TNB impurity was not uniform, but i t was orient-ed and the section extinguished between crossed polars. The emission i n t e n s i t y was very low, and no p o l a r i z i n g prism was used. As i s seen i n F i g 27c, the emission maximum corresponds roughly to that of anthracene-TNB, although i t i s s l i g h t l y 125 to the red of the centernof the anthracene-TNB emission spectrum. In general form, however, i t resembles the phenanthrene-TNB spectrum. Pyrene-TNB. Energetically, t h i s complex should resemble that of anthracene, since the two hydrocarbons have nearly the same io n i z a t i o n energies. From the spectrum i n F i g 30, we see that t h i s i s indeed the case, the f i r s t CT emission peak being s l i g h t l y lower i n energy than i n the anthracene-TNB complex. There i s a greater difference between the shapes of the oppositely polarized components than i s o r d i n a r i l y a seen i n CT spectra, and the room-temperature emission i s stronger and not as highly polarized as i n many of the other complexes. P a r t i c u l a r l y i n t e r e s t i n g i s the apparent s p l i t ? -t i n g of the three main peaks i n the ho r i z o n t a l l y polarized d i r e c t i o n (corresponding to weaker CT absorption and emission). The crystallographic directions i n the sample were not determined; l i t t l e i s known regarding the c r y s t a l structure, except that i t i s t r i c l i n i c with two complexes per u n i t c e l l (43c). The pyrene phosphorescence o r i g i n i s at 16.8 kK (23), and one might expect to f i n d a phosphorescence component beyond t h i s energy i n the CT spectrum. Aside from the long 126 t a i l on the red end of the CT emission at 78° K, there i s no clear evidence of phosphorescence here. Perylene-TNB. The deep red c r y s t a l s of the 1:1 complex are ortho-rhombic and form (001) faces from solution (43c). If the same face develops i n melts prepared between pressed disks, then the b d i r e c t i o n should be p a r a l l e l to the molecular planes and CT absorption should be stronger along a. The D and A pairs are not stacked i n i n f i n i t e columns as i n many other complexes, but are dist r i b u t e d i n layers con s i s t -ing e n t i r e l y of D or A molecules. These D and A layers are stacked a l t e r n a t e l y but i n such a way that the TNB mol-ecules are between spaces i n the perylene layers. It was d i f f i c u l t to prepare good single c r y s t a l s of this complex, because of i t s tendency to vaporize and decompose at i t s high (276° C) melting point. The absorption spectrum (Fig 31) shows a CT band with well defined peaks at 17.2, 18.5, and 19.7 kK. Absorption due to perylene i t s e l f i s polarized mainly i n the opposite d i r e c t i o n , but the two components of the perylene absorption d i f f e r considerably i n shape. The weaker component c l o s e l y resembles the b-axis component of the pure perylene c r y s t a l absorption, but the strong component i s much broader and Ui u s 6500 127 6000 5S00 -5600 cm 2 0 1.0 z UI o a o 5000 WAVELENGTH A 4500 4000 3500 FIG 31b. Absorption and fluorescence of perylene single c r y s t a l . (From R. Hochstrasser, r e f 83). 20 18 17 16 15 14 EMISSION SPECTRA : PYRENE-TNB CRYSTAL 2.0 i 1.6 It \ 1.2 0.8 / ( / \ 78* K. 0.4 S \ a 0 16 18 20 22 24 26 ABSORPTION SPECTRUM OF PERYLENE-TNB CRYSTAL kK. FIO. 30 FIG. 31 127 t in 1 U » I u < cr 6500 • FLUORESCENCE 6000 5500 -5600 cm" 20 10 5000 WAVELENGTH A 4500 4000 3500 FIG 31b. Absorption and fluorescence of perylene single c r y s t a l . (From R. Hochstrasser, r e f 83). 128 the v i b r a t i o n a l peaks are less pronounced. This l a t t e r e f f e c t may be due to the high o p t i c a l density i n t h i s region; i . e . , i t may not be r e a l . No emission was detected from the c r y s t a l l i n e complex at wavelengths shorter than 10000A. Benzidine-TNB (p.p-diaminodiphenyl). This complex d i f f e r s from the others so far studied, i n that the donor's source of transferable charge i s not i t s 7T -electron system, but the nonbonding electrons l o c a l i z e d at the amino groups (21). Such (n,7r) complexes tend to be highly colored, often appearing dark red or black i n the s o l i d form. TNB complexes of benzidine and of 2-naphthyl-amine were studied, but th e i r properties are very s i m i l a r and only the spectrum of benzidine-TNB w i l l be discussed here. Neither of the complexes appear to emit i n the v i s -i b l e region to 10 kK, either from the c r y s t a l s or from r i g i d glass solutions. The c r y s t a l structure of benzidine-TNB has been p a r t l y determined by Wallwork (86). The space group i s ortho-rhombic Pbcn, and there are four complexes per unit c e l l . Films grown between pressed disks can be made very thin, and appear purple when viewed i n l i g h t polarized p a r a l l e l to the needle axis (the f a s t d i r e c t i o n ) , and yellow- to-brown i n 129 kK FIG 32 BENZIDINE- TNB C O M P L E X ABSORPTION SPECTRUM 130 the opposite p o l a r i z a t i o n . The broad CT band has i t s peak at 18.0 kK, and there i s a s l i g h t i n f l e c t i o n at 16.8 kK. The room temperature spectrum shows other d e t a i l s , including a weaker peak near 23 kK and strong oppositely-polarized absorption beyond 25 kK. The peak near 27 kK may be due to TNB absorption, but i t i s also i n the general region where a CT band corres-ponding to in t e r a c t i o n with the biphenyl moiety would be expected to occur, and this p o s s i b i l i t y should be considered i n future studies of this complex. Quinhydrone and phenoquinone. These complexes are somewhat outside the scope of this study, i n that they do not contain TNB, nor do they involve hydrocarbon donors. The work reported here i s preliminary to what i s intended to be a more detailed study of quinhyd-rone. This complex has been discussed i n some d e t a i l by others (21, pg 177). Nakamoto (66a) has noted the dichroism of the CT band, but the absorption spectrum has not been studied i n d e t a i l at low temperature. t h i n sections of the c r y s t a l l i n e complex prepared i n the usual manner are intensely dichroic, appearing deep purple to black i n one p o l a r i z a t i o n and colorless-to-brown i n the other. It was hot possible to obtain c r y s t a l s t h i n enough 131 14 F kK. 3 0 0 ° K. (DIRECT METHOD) ABSORPTION SPECTRA OF <JUINHYDR0NE CRYSTALS FIG. 132 to have measurable o p t i c a l densities i n the strongly-absorb-ing d i r e c t i o n ; the pairs of spectra i n Fig 33 therefore o o correspond to l i g h t polarized i n directions of 0 and 60 (rather than 90°) to the weakly-absorbing d i r e c t i o n . The spectrum i s seen to extend over an extremely broad region, and t h i s i s p a r t l y responsible for the metallic appearance of the c r y s t a l l i n e complex. The absorption spectrum of phenoquinone (Fig 34) i s more conventional i n that i t i s not as broad as that of quinhydrone. The o p t i c a l density r a t i o i s 14:1, and the center of the absorption band i s around 23.3 kK. The complex i s deep red and shows no evidence of the met a l l i c l u s t r e c h a r a c t e r i s t i c of quinhydrone. 3 0 0 ° — X 2 0 - (DIRECT) / 1 0 1 1 1 16 18 20 22 24 26 28 P H E N O Q U I N O N E C R Y S T A L 133 APPENDIX A Atomic coordinates and p r i n c i p a l directions i n the anthra-cene -TNB c r y s t a l . The coordinates x, y_, and z given i n Table IV r e f e r to the monoclinic axes a, b, and c, respectively, with b taken as the unique axis (second s e t t i n g ) . For computational pur-poses, i t i s necessary to know the atomic positions i n an orthogonal coordinate system whose axes are a, b, and c' , where c / i s at r i g h t angles to a. As shown i n the figure, a point at a=x, c=z w i l l have the orthogonal coordinates a = x = x-z s i n S , c = z = z cos £ , where S = (.$ -90 ). The coordinate z" was used i n constructing the pro-j e c t i o n on the (100) face (Fig 8). It i s related to the monoclinic axes i n the way shown i n the drawing, and i s given by z"= z-x s i n 5 . The l a s t column of Table IV gives values of a', the orthogonal coordinate at r i g h t angles to c. This was used i n c a l c u l a t i n g the po l a r i z a t i o n r a t i o s of the CT moment. 134 O ON r-l CO o CO m o CM r-l m CM CM CM fx. rH o o o o 00 <f o o co o 1 rH + CM + CM + rH + o r-l 1 rH + rH + o o CM + o rH O r-l o CM m o CM m CO vO CM vO <t co CM m CM O vO m CM vO ON 00 N O 1 ¥ O + o + o i o • O I CO + CO + CO + CO + CO + CO + co + CO + CO + r-l 00 CM m CO co o m CO O CO CO CO 00 CO o CO 00 CO CM CM rH m rH •rds, O 1 o + r-l + rH + o + o 1 I - l 1 CO + CO + CM + CM + <* + CM + CO + + + coc r-l ON m ON 00 m CM 00 CM vO o ON O O rH CO >> r-H + O + r-l + CN + CO + CM + O + CM + o + O i CM + orthogoi orthogoi X V© O O CM 00 O + CM vO r-l + 00 vO + o + m r-l O + m ON o i <t rH 1 00 <r rH 1 CM CM CM 1 CM CM CM 1 co CM i-l 00 CO m r-l r-l v© rH <t 00 m rH m CM m CM 00 00 m CM rH vO vO O • (0 m N O 1 r-l + CM + CM + o + o i r-l 1 + + CO + CO + m + CO + + m + + w LJ coo: s . r-l <f m m WN ON 00 m CM 00 CM vO o ON vO l>» o o vO O vO rH m CO rH >c linic r-l 1 o + r-l + CM + CO - L . CM + O + CM + o + o • CM o + + o 1 O + >c linic o vO CM r-l CO vO r-l rH r»» fx. vO o vO o o O o ON CO O o rH rH o CO o >uom X O rH + CO + CO + r-l + O 1 rH t rH + rH + o o CO + o rH + CO + + atom r-l CM U CO u o m o vO U u 00 u ON o rH £ CM O 33 rH z CM rH O CM O CO o TABLE IV. Atomic coordinates of anthracene-TNB. (See preceding page for explanation of symbols and other d e t a i l s ) . 135 Direction cosines of p r i n c i p a l axes i n anthracene-TNB. Axes L and M are the long and short axes, respectively, of anthracene. The CT vector i s assumed to l i e along the axis E, which i s drawn from the center of the donor to the center of the acceptor. In Table V, the upper signs ferer to the complex pairs in which the TNB molecules are located above, and to the r i g h t of an anthracene at the o r i g i n , as seen i n the (100) projection of F i g 8 (pg 71). x £ z L ± 0.364 ±0.891 ±0.289 M + 0.625 + 0.408 ±0.676 E + 0.633 ±0.373 £0.677 TABLE V. Direction cosines of axes corresponding to electronic t r a n s i t i o n dipole moments i n an thr ac ene-TNB. The cosines of the angles between the c-axis and the molecular axes are as follows: E/c =-1-0.927 L/c = - 0.037 M/c - +0.069 Cosines of angles between CT vector (E) and the anthracene molecular axes: E/L - + 0.198 E/M » + 0.152 136 APPENDIX B: CALCULATION OF INTERACTION INTEGRALS molecule -/L - /M /E r (A) 01 + .172 ' - .681! + .377 04.83 03 - .114 > .034 - .956 08.34 05 - . 991 - .111 + .426 08.64 07 - .642 - .104 - .467 15.1 09 + .721 + .023 + .447 12.4 11 + .906 \ - .060 - .676 10.64 13 + .441 j - .813 - .216 08.64 15 + .234 : - .504 - .833 15.1 17 - .347 ;+ .511 + .497 12.4 19 + .825 + .732 , - .062 10.64 02 - .897 . 118 + .152 10.25 04 + .889 ; + .136 - .170 10.25 06 - .451 + .732 - .710 10.25 08 + .393 - .714 + .692 10.25 10 — .086 + .050 + .895 11.6 TABLE VI. Angle cosines between lines-of-centers and vectors L, M, and E. Molecules are numbered according to diagram on following page, the even ones being trans l a t i o n a l l y equivalent to the reference molecule. molecule jEE jMM j L L j EM J EL 01 +1020 +1730 + 2260 2250 + 176 03 - 522 + 224 + 468 - 249 + 220 05 + 218 + 294 + 3280 - 224 - 231 07 - 040 + 054 + 451 - 042 + 092 09 + 077 + 079 - 320 - 067 + 158 11 - 176 + 096 - 755 - 087 - 272 13 - 094 + 836 560 + 256 - 498 15 - 073 + 102 - 027 + 032 - 066 17 + 085 - 039 + 570 + 066 - 152 19 - 010 - 137 + 1190 + 058 - 222 02 - 051 - 076 - 1810 - 110 - 133 04 - 146 - 083 + 815 - 096 - 150 06 - 292 - 148 - 1080 + 222 + 442 08 + 104 410 + 074 + 221 + 419 TABLE VII. Integral sums (see eqs. 28 and 32, Section IV). Values are i n wavenumbers. mol (p) ©8l e ^ P l 6 L 01 P 01 + .377 .172 .681 .172 + .129 + .623 03 - .956 - .114 + .034 - .035 - .027 - .024 05 + .426 - .991 - .111 + .991 + .112 + .144 07 - .467 - .642 - .104 + .641 + .104 + .127 09 + .447 + .721 + .023 - .721 + .023 - .049 11 - .676 + .906 - .060 - .907 - .061 - .090 13 - .216 + .441 - .813 - .541 + .814 + .786 15 - .813 + .234 - .504 - .397 + .496 + .493 17 .497 - .347 + .511 + .347 - .511 - .895 19 - .062 + .825 + .732 + .563 - .723 - .706 02 + .152 - .897 - .118 - .897 + .138 + .152 04 - .170 + .889 + .136 + .889 + .122 - .170 06 - .710 - .451 + .732 - .401 + .712 - .710 08 .692 + .393 - .714 + .383 - .728 + .692 10 .895 - .086 + .050 - - + .895 EFT Op ON O ON o e ETT Op CO ON CM OO ON CM ON o e LE 0p ON o 00 ON CM TABLE VIII. Cosines of angular terms of Eq (28) To obtain the t h e o r e t i c a l p o l a r i z a t i o n r a t i o s , the quantities given i n Table VII are summed appropriately (Table I I , pg 88) and substituted into Eq 31, pg 49: i r H e L H e M n A\ ? - .60 138 APPENDIX C: SUPPLEMENT POLARIZATION OF THE PHOSPHORESCENCE AND TRIPLET-TRIPLET ABSORPTION IN AROMATIC HYDROCARBONS Although twenty years have elapsed since Lewis and Kasha (48) i d e n t i f i e d the phosphorescence of organic mole-cules with r a d i a t i v e decay from the lowest t r i p l e t state, the experimental d i f f i c u l t i e s connected with the formation and maintainence of a s u f f i c i e n t concentration of t r i p l e t -excited molecules has caused our knowledge of the t r i p l e t manifold to l a g f a r behind our r e l a t i v e l y complete view of the s i n g l e t states of aromatic hydrocarbons. The spin-forbidden nature of the s i n g l e t - t r i p l e t i n t e r -combination makes the population of t r i p l e t l e v e l s by d i r e c t absorption from the ground state a highly i n e f f i c i e n t pro-cess; e x t i n c t i o n c o e f f i c i e n t s for T-^S absorption are ty p i c -a l l y of the order of 10 . On the other hand, the slow rate of t r i p l e t decay i n many systems allows one to bui l d up a useful concentration of t r i p l e t - e x c i t e d species i f s u f f i c -i e n t l y intense e x c i t i n g r a d i a t i o n i s employed. The moire common method of populating the t r i p l e t l e v e l i s by the i n d i r e c t route of non-radiative intersystem cross-ing from a higher s i n g l e t state. The high e x t i n c t i o n c o e f f -i c i e n t s f o r S<eSo absorption make thi s an extremely e f f i c i e n t means of introducing e x c i t a t i o n energy into a molecule. 139 The r e s u l t i n g s i n g l e t excited states can be depopulated by a number of routes, including (46) intersystem crossing and radiationless decay to the lowest t r i p l e t l e v e l . The rate of i n t e r n a l conversion between states of i d e n t i c a l 11 m u l t i p l i c i t y i s around 10 /sec (74); t h i s may be reduced ; 8/ ' to 10 /sec i f the process involves a change of spin- s t i l l a rapid enough rate to compete e f f e c t i v e l y with d i r e c t S->SQ fluorescence i n many systems. In th i s way, Craig and Ross (26) have been able to build up t r i p l e t state concen-trations greater than 10 molar. In order to maintain a molecule i n a t r i p l e t - e x c i t e d state for any length of time, i t i s necessary that i t be embedded i n a r i g i d medium; i n f l u i d systems the pertur-bations induced by c o l l i s i o n a l encounter with other mol-g ecules r e s u l t s i n rapid (10 /sec) r a d i a t i o n l e s s deactivation of the excited species. Most studies involving t r i p l e t states have therefore been made i n r i g i d glasses- usually a mixture such as ethanol, isopentane and ether ("EPA") which has been cooled to 78° K without c r y s t a l l i z i n g . In pure c r y s t a l s , the phosphorescence i s generally weaker than i n solution, and sometimes of much shorter h a l f -l i f e . The approximate reversal of the fluorescence-phos-phorescence r a t i o i n c r y s t a l l i n e and dissolved triphenylene 140 (42) i s e s p e c i a l l y s t r i k i n g . These e f f e c t s have recently been discussed (42) i n terms of the exciton theory, and i t has been suggested that intersystem crossing,is generally less probable i n c r y s t a l s than i n solution, and this i s largely responsible for the decreased r a t i o of phosphor-escence to fluorescence observed i n many c r y s t a l s . Exceptions to these general trends are found i n c r y s t a l s of c e r t a i n aromatic ketones and other molecules, and p a r t i c -u l a r l y in benzophenone, which phosphoresces at high e f f i c -iency i n both the pure c r y s t a l and i n solution. When aromatic hydrocarbon impurities are dissolved i n benzophenone -4 to a concentration of about 10 molar, the benzophenone phosphorescence i s quenched by about 50%, and replaced by phosphorescence from the hydrocarbon, i f the lowest t r i p l e t state of the impurity l i e s below that of benzophenone (43). 16 17 18 19 20 21 22 23 24 WAVENUMBER xlO' 3 25 FIG 34. E f f e c t of added naphthalene on the phosphorescence of benzophenone (43). 141 impurity benzophenone impurity S* s* T cu S T o — T S S* Phosphorescence from the hydrocarbon impurity i s observed even i f i t s f i r s t excited s i n g l e t state i s above that of benzophenone (and only the l a t t e r i s absorbing an appreciable amount of the l i g h t ) , i n d i c a t i n g that the energy transfer i s from the t r i p l e t l e v e l of the host to that of the guest. When the impurity s i n g l e t states are below the t r i p l e t l e v e l of benzophenone, no impurity fluorescence i s seen, so the energy transfer must be predominantly by t r i p l e t excitons. This provides a very useful method of populating t r i p l e t levels i n hydrocarbons whose elec t r o n i c states are su i t a b l y located with respect to those of benzophenone. It i s then possible to observe the spectra associated with the t r i p l e t state while the molecules are oriented i n a c r y s t a l l a t t i c e . 142 The systematic study of the lowest t r i p l e t states of aromatic molecules began with the phosphorescence studies of Lewis and Kasha (48), which have since been supplemented by many workers. Weak absorption corresponding to T<-SQ t r a n s i t i o n s have been found i n a number of molecules, and in t e r e s t i n locating higher t r i p l e t l e v e l s soon developed. Absorption to these upper states d i r e c t l y from the ground state cannot normally be observed, as i t i s not only weak, but i s obscured by the much more intense s i n g l e t - s i n g l e t absorption bands. It was therefore necessary to study T->T absorption, which, being spin-allowed, should have an i n -te n s i t y comparable to that of the S-^S absorption bands. This requires the b u i l d i n g up of a s u f f i c i e n t concentration of t r i p l e t - e x c i t e d molecules by means of intense cross-illumination. This was done by McClure (50,51), Craig and Ross (26), and by Porter and Windsor (73), the l a t t e r em-ploying f l a s h methods. A l l these workers used r i g i d - g l a s s solutions of the hydrocarbons, and together they have located upper t r i p l e t levels i n a number of hydrocarbons, and i n some cases have estimated the e x t i n c t i o n c o e f f i c i e n t s of tr a n s i t i o n s to these states. Important as p o l a r i z a t i o n studies are i n assigning symmetries to ele c t r o n i c states, r e l a t i v e l y l i t t l e work has been done on the p o l a r i z a t i o n of t r a n s i t i o n s involving 143 t r i p l e t states. Williams (91) observed the r e l a t i v e pol-a r i z a t i o n of naphthalene and phenanthrene phosphorescence, and Azumi and McGlynn (3) have studied the po l a r i z a t i o n of in d i v i d u a l vibronic bands of phenanthrene phosphorescence. Dorr and coworkers (38b) have made p o l a r i z a t i o n measure-ments on a number of hydrocarbons and heterocycles. A l l these studies have been made i n r i g i d glass solutions of randomly oriented molecules; no absolute p o l a r i z a t i o n r a t i o s have yet been reported. Work was therefore begun (and i s currentl y i n progress) on measuring the absolute p o l a r i z a t i o n r a t i o s of both the phosphorescence and the t r i p l e t - t r i p l e t absorption i n several aromatic hydrocarbons. The f i r s t part of thi s pro-j e c t makes use of the e f f i c i e n t triplet-energy transfer properties of benzophenone, to which the hydrocarbons were added as impurities. The usefulness of benzophenone for this purpose i s somewhat limited by the lack of information regarding i t s c r y s t a l structure. I t i s known to be ortho-rhombic, and several metastable modifications e x i s t , with t r a n s i t i o n temperatures j u s t above the melting point of the low-temperature form. An approximate idea of the molecular orientation with respect to the external morphology of the c r y s t a l has been drawn from i n d i r e c t evidence, p r i n c i p a l l y the diamagnetic anisotropy studies of Bannerjee and 144 Haque (4), and the polarized absorption and emission spectra of McClure (51). When c r y s t a l l i z e d between quartz disks, benzophenone forms f l a t needles showing p a r a l l e l e x t i n c t i o n (usually not to complete darkness), the fa s t d i r e c t i o n being para-l l e l to the needle axis. From the c r y s t a l studies, i t can be concluded that the planes of the two rings are i n c l i n e d to one another and are approximately perpendicular to the c-axis, which i s probably the axis of minimum r e f r a c t i v e indix and thus p a r a l l e l to the needle axis. Although d i s -solved hydrocarbons may not form s t r i c t l y " s u b s t i t u t i o n a l " s o l i d solutions (with the impurity oriented i n exactly the same way as the molecule i t replaces), i t i s reasonable to suppose that the r i n g planes of such molecules are approximately perpendicular to the c-axis; thus out-of-plane hydrocarbon t r a n s i t i o n s should be polarized c h i e f l y along the needle axis, while in-plane t r a n s i t i o n s should have most of their i n t e n s i t y perpendicular to this d i r e c t i o n . However, knowing as l i t t l e as we do about the exact mol-ecular positions i n benzophenone, i t i s not possible to i d e n t i f y in-plane t r a n s i t i o n s which are polarized i n d i f f e r e n t d i r e c t i o n s , e.g., short- and long-axis t r a n s i t i o n s i n naphthalene, phenanthrene, etc. 145 Most of the samples were prepared by melting a weighed quantity of the hydrocarbon with p u r i f i e d benzophenone, and allowing the melt to s o l i d i f y . A portion of t h i s was then remelted and annealed between a quartz disk and a cover glass. In t h i s way i t was possible to prepare thick c r y s t a l s (about 0.5 mm) suitable for T-T absorption studies. Polarized phosphorescence spectra are shown i n Figs 35 and 36 f o r solutions of chrysene, phenanthrene, acenaphthene, and naphthalene i n benzophenone. These spectra were a l l corrected f o r photomultiplier response. E x c i t a t i o n was by 3650 A l i g h t , which i s j u s t on the edge of the absorption band of benzophenone. The spectra shown here are a l l for samples at 78° K; however, very s i m i l a r r e s u l t s were ob-tained at room temperature. A summary of the phosphoresc-ence spectra i s given i n Table IX. The bands at energies hydrocarbon p o l a r i z a t i o n p r i n c i p a l maxima acenaphthene phenanthrene chrysene naphthalene in-plane in-plane out-plane (out) 17. (in) 19.45, 20.3, 20.9 kK 18.1, 19.3, 20.2, 20.8 16.25, 17.85, 19.2 ), 18.4, 19.9, 20.8, 21.3 17.9, 19.4, 20.2 FIG IX. Phosphorescence of hydrocarbons i n benzophenone. above 21 kK are probably mostly due to benzophenone phos-phorescence; they are polarized i n the molecular plane, - * 1 I I > I 1 1——J L . I _ 1 1 | • 24 22 20 18 16 22 21 20 19 18 FIG. 35. POLARIZED PHOSPHORESCENCE SPECTRA OF CHRYSENE AND PHENANTHRENE IN BENZOPHENONE. Samples at 78°K. Intensities are corrected for photomultiplier response. NAPHTHALENE ,« . OUT-OF-PLANE 20 19 18 17 16 ACENAPHTHENE 22 20 19 18 FIG. 36. POLARIZED PHOSPHORESCENCE SPECTRA OF NAPHTHALENE AND ACENAPHTHENE IN BENZOPHENONE, 78° K. 4> 148 as McClure found (51). The r e s u l t s obtained for phenanthrene by Azumi and McGlynn (3) and also by Williams (91) indicated that the phosphorescence i s primarily out-of-plane polarized, with in-plane components contributing to c e r t a i n vibronic bands. Work i n progress using phenanthrene i n biphenyl appears to bear this out, and so the present r e s u l t s with benzophenone seem to stand i n disagreement with work on other systems. The f i v e bands observed (they are s h i f t e d to the red by about 300/cm from the values of Azumi and McGlynn) do vary i n p o l a r i z a t i o n r a t i o , but are a l l in-plane polarized. The benzophenone phosphorescence (not shown i n F i g 35) i s s i m i l -a r l y polarized, as i t should be, i n d i c a t i n g that the two spectral components are i d e n t i f i e d c o r r e c t l y . It i s hoped that further work with phenanthrene dissolved i n other suitable c r y s t a l s w i l l help to cl e a r up the apparent anomaly encountered with benzophenone. The phosphorescence of naphthalene i n benzophenone i s almost depolarized; how meaningful the s l i g h t polarizations observed are, w i l l only be c l e a r when assignmentscof the separate vibronic components are made, and comparison spectra of naphthalene i n other c r y s t a l s are av a i l a b l e . The out-of-plane p o l a r i z a t i o n of the chrysene phosphor-escence i s i n agreement with the work of Dorr and Gropper (38b). 149 In three hydrocarbon-benzophenone systems, i t was possible to observe t r i p l e t - t r i p l e t absorption. Absorp-tion spectra were measured over the appropriate wavelength range with- and without 3130 A i r r a d i a t i o n of the c r y s t a l , and the o p t i c a l densities of the T-T absorption were com-uted from the two sets of i n t e n s i t y values. The maximum o p t i c a l density measured amounted to only 0.06, and hydro-carbon fluorescence, probably excited by d i r e c t absorption of the 3130 A l i g h t , masked out the T-T absorption i n sev-e r a l hydrocarbons that are known to give spectra i n EPA. The spectra shown i n F i g 37 include only the stronger components, polarized perpendicular to the benzophenone needle axis, and thus predominantly i n the planes of the hydrocarbons. In naphthalene, the r a t i o of the o p t i c a l densities p a r a l l e l to the two directions i s about 5:1, and i s probably comparable i n anthracene and chrysene. Compar-ison of these spectra with the ones obtained i n EPA (26,50) hydrocarbon lowest T T-T, benzoph. T-T, EPA (a) chrysene 19.2 kK 17.6 kK 17.12 kK naphthalene 21.30 23.48, 24.82 24.00, 25.46, 26.95 (b) anthracene < 14.80 22.77, 24.20 23.42, 24.75 TABLE X. T r i p l e t - t r i p l e t absorption spectra. Comparison of r e s u l t s for hydrocarbons i n benzophenone, and i n r i g i d glass, (a): McClure (50), (b) Craig & Ross (26). 150 P O L A R I Z E D T R I P L E T - T R I P L E T A B S O R P T I O N S P E C T R A .06 r .04-.02-N A P H T H A L E N E in B E N Z O P H E N O N E (polarized in-plane) .04 .03 .02 .0 A N T H R A C E N E in BENZOPHENONE (polarized in-plane) 25 24 23 22 cm-'xIO"3 FIG. 37 151 shows that the naphthalene T-T bands are of si m i l a r appear-ance i n both cases, but there i s a rather s t r i k i n g difference i n the r e l a t i v e i n t e n s i t i e s of the f i r s t two bands of the anthracene T-T absorption. In EPA, the f i r s t (lowest energy) band i s 2-3 times as intense as the second, whereas i n benzo-phenone, the two bands have nearly i d e n t i c a l i n t e n s i t i e s . The explanation of t h i s e f f e c t must await further studies of T-T absorption by anthracene i n other c r y s t a l s , possibly biphenyl, and more detailed data regarding the p o l a r i z a t i o n r a t i o s . The symmetry of these upper t r i p l e t l e v e l s has been 3 discussed by McClure (50), who has suggested C b as a reasonable p o s s i b i l i t y . In molecules belonging to the point-group C2 V» th i s would transform according to A^ ( t o t a l l y 3 symmetric). Transition to this l e v e l from L a (which i s presumably the symmetry of the lowest t r i p l e t ) i s allowed for an in-plane polarized moment; thus the observed p o l a r i z -ation i s compatable with these tentative assignments. More detailed study of these spectra, p a r t i c u l a r l y i n other systems where more quantitative p o l a r i z a t i o n data can be ob-tained, should prove extremely useful i n characterizing these upper t r i p l e t levelss 152 BIBLIOGRAPHY Journal t i t l e s are abbreviated i n the standard CODAN form, except where indicated by an astarisk; i n these cases, the abbreviation i s explained i n the footnote. A key to CODAN i s found i n the inside covers of each issue of CHEMICAL TITLES. Order of l i s t i n g of each entry i s journal t i t l e , volume number, page number of beginning of a r t i c l e , and l a s t two d i g i t s of year of publication. 01 ANDREWS L CHRE 54 713 54 02 ANDREWS L, R KEEFER JACS 74 4500 52 03 AZUMI T, S McGLYNN JCPS 37 2413 62 04 BANNERJEE K, A HAQUE LJPH* 12 87 39 05 BAYLISS N NATU 163 764 49 06 BAYLISS N JCPS 18 292 50 07 BEER M, H LONGUET-HIGGENS JCPS 23 1390 55 08 BENESI H, J HILDEBRAND JACS 71 2703 49 09 BIER A RTCP 75 866 56 10 BIER A, J KETELAAR RTCP 73 264 54 11 B0WEN E JCPS 13 306 45 12 BRACKMAN W RTCP 68 147 49 13 BREE A, S KATAGIRI (private communication) 13a BREE A, L LYONS JCSO 2658 56 14 BRIEGLEB G: Zwischenmoleculare Krafte. Enke, 1937 Stuttgart: 15 BRIEGLEB G, J CZEKALLA ZEEL 58 249 54 153 16 BRIEGLEB G ZEEL 59 184 55 17 BRIEGLEB G, J CZEKALLA ZEEL 63 6 59 18 BRIEGLEB G, J CZEKALLA ANCE 72 401 60 19 BRIEGLEB G, J CZEKALLA ZEEL 24 37 60 20 briegleb g, H DELLE ZEEL 24 359 60 21 BRIEGLEB G: Elektronen-Donator-Acceptorkomplexe. Springer, Heidelberg, 1961 22 BRIEGLEB G, J CZEKALLA, G REUSS ZEEL (i n press) 23 CLAR E, M ZANDER CHBE 89 749 56 24 CRAIG D, P HOBBINS JCSO 539 55 25 CRAIG D JCSO 2302 55 26 CRAIG D, I ROSS JCSO 1589 54 27 CRAIG D, P HOBBINS JCSO 2309 55 28 CZEKALLA J NATW i ,40 467 56 29 CZEKALLA J , G BRIEGLEB, W HERRE, R GLIER ZEEL 61 537 57 30 CZEKALLA J , J SCHMILLEN , K MAGER ZEEL 61 1053 57 31 CZEKALLA J , J SCHMILLEN , K MAGER ZEEL 63 623 59 31a CZEKALLA J ZEEL 63 712 59 32 CZEKALLA J ZEEL 63 1157 59 33 CZEKALLA J ZEEL 64 1221 60 34 CZEKALLA J CHIM 15 26 61 35 CZEKALLA J , K MEYER ZEEL 27 185 61 36 DAVYDOV A ZETF 18 210 48 37 DAVYDOV A: Theory of Molecular Excitons , translated by M. Kasha. McGraw-Hill, N.Y., 1962 154 38 DEWAR M, A LEPLEY JACS 83 4560 61 38a FORSTER Th DFSO* 27 7 59 38b DORR F ZEEL 67 193 62 39 FRENKEL J PHRV 17 1276 31 39a GESCHWENDTNER H, H WOLF NATW 48 42 61 40 HAM J JACS 76 3881 54 41 HAMMICK D, H HUTCHISON JCSO 1 89 55 42 HOCHSTRASSER R RMPH 34 531 62 43 HOCHSTRASSER R (in press) 43a HERTEL E, G ROMER ZPCF 11 77 31 43b HERTEL E, K SCHNEIDER ZPCF 15 79 32 44 HUNT G, I ROSS PCSL 11 61 45 ISENBERG, A SZENT-GYORGI PNAS 44 857 58 43c HERTEL E, H BERGK ZPCF 33 329 36 46 KASHA M DFSO* 9 14 50 46a KOSOWER E JACS 80 3467 58 47 KROSS R, K NAKAMOTO, V FASSEL SEAC 8 142 56 48 LEWIS G, M KASHA JACS 66 2100 44 49 LIVINGSTON R, A PUGH DFSO* 27 144 59 50 McCLURE D JCPS 19 670 51 51 McCLURE D, P HANST JCPS 23 10 55 52 McGLYNN S CHRE 58 113 58 53 McGLYNNS, J BOGGUS JACS 80 5096 58 54 McGLYNN S, J BOGGUS, E ELDER JCPS 32 357 60 155 55 MOODIE M, C REID JCPS 22 252 54 56 MULLIKEN R JACS 72 600 50 57 MULLIKEN R JACS 72 4493 50 58 MULLIKEN R JCPS 19 514 51 59 MULLIKEN R JACS 74 811 52 60 MULLIKEN R JPCH 56 801 52 61 MULLIKEN R JCPQ 51 341 54 62 MULLIKEN R JCPS 23 397 55 63 mulliken R RTCP 75 845 56 64 MURAKAMI H SPOU* 18 18 49 65 MURRELL J JACS 81 5037 59 66 NAKAMOTO K JACS 74 390 52 66a NAKAMOTO K BCSJ 26 70 53 67 OBREIMOV I, K SHABALDAS JPUS* 7 168 43 68 OKSENGORN B JPRA 20 572 59 69 0R6EL L, R MULLIKEN JACS 79 4839 57 70 ORGEL L JCPS 23 1352 55 71 PARISER R JCPS 25 1112 56 72 PLATT J SCIE 129 373 59 73 PORTER G, H WINDSOR JCPS 21 2088 53 74 PORTER G, M WRIGHT DFSO* 27 18 59 75 PRIKHOTKO A JPUS* 8 87 44 76 REID C JCPS 20 1212 52 77 ROSS S, M LABES JACS 77 4916 55 156 78 SIDMAN J, D McCLURE JCPS 24 757 56 79 SIMPSON W, D PETERSON JCPS 26 588 57 80 SKRAUP S, M EISEMANN ACJL 449 1 26 81 STEPHENS D, H DRICKAMER JCPS 30 1518 59 82 SUZUKI K, S SEKI BCSJ 28 417 55 83 TROTTER J (private communication) 84 WALLWORK S ACCR 7 648 54 85 WALLWORK S JCSO 61 494 61 86 WALLWORK S (private communication) 87 WALLWORK S ACCR (in press) 88 WEISS J JCSO 42 245 42 89 WEITZ-HALLE E ZPCF 34 538 28 90 WEITZ-HALLE E ANCE 66 658 54 91 WILLIAMS R JCPS 30 23 59 92 WINSTON H JCPS 19 156 51 * Journals not yet assigned CODAN abbreviations: LJPH Indian J. Physics DFSO Disc. Faraday Soc. JPUS J. Phys. USSR SPOU Sci. Papers Osaka Univ. Note: Z. Elektrochemis (ZEEL) is Ber. Bunsengesell. fur Physikalische Chemie since January 1963. 

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