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A spectroscopic study of the charge-transfer complex of anthracene and sym-trinitrobenzene Lower, Stephen Kent 1960-08-31

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A SPECTROSCOPIC STUDY OF THE CHARGE-TRANSFER COMPLEX OF ANTHRACENE AND SYM-TRIKITROBENZENE  by STEPHEN KENT LOWER B.A., University of C a l i f o r n i a , Berkeley, 1955  a thesis submitted i n p a r t i a l fulfilment of the requirements for the degree of M.Sc. i n the Department of CHEMISTRY  We accept t h i s Thesis as conforming to the required standard:  THE UNIVERSITY OF BRITISH COLUMBIA August, I960  In p r e s e n t i n g  this thesis i n p a r t i a l fulfilment of  the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l make it  freely  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  agree t h a t p e r m i s s i o n f o r e x t e n s i v e  I further  copying of t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood  that copying or p u b l i c a t i o n o f t h i s t h e s i s f o r g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  financial  permission.  Stephen K. Lower  Department o f  Chemistry  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada. Date  22 September, I960  ii ABSTRACT Complexes of aromatic hydrocarbons (donors) with electron acceptors such as 1,3,5-trinitrobenzene  (THB) are s t a b i l i z e d  principally by resonance between a dative and a "no-bond" wave function: $  N  = a  f  e  (DA) • b </f  (dV).  By means of second-order perturbation theory i t can be shown that, providing certain symmetry requirements are met,  the energy  corresponding to $> w i l l be less than that of the free separated M  donor and acceptor. i l i t y of 2-10  The resulting molecular complexes have a stab-  kcal, and usually possess a colour which i s associated  with a transition between the ground state V„  and an excited state  These charge-transfer spectra have previously been studied  only i n solution, and have been useful sources of thermodynamic data. In order to learn more of the t r a n s i t i o n i t s e l f , i t i s necessary to study the spectrum of the c r y s t a l , where the molecules are held i n fixed and (sometimes) known positions. The procedure by which the polarized c r y s t a l spectrum of the anthracene-THB complex was obtained i s b r i e f l y described. ison of the observed spectrum with the partially-known structure has shown  i  Compar-  crystal  r:  1) The supposition that the transition dipole moment i s perpendicular to the planes of the aromatic rings i s supported; 2) Vibrational structure can exist i n a charge-transfer band; t h i s i s the f i r s t reported observation of i t ; 3) The band i s s p l i t into two oppositely-polarized components, d i f f e r i n g i n energy by about 200/cm. An attempt i s made to explain t h i s s p l i t t i n g i n terms of Davydov's "weak-coupling" model of a c r y s t a l , i n which degenerate molecular states are presumed to become crystal states whose degeneracy depends on the symmetry of the associated u n i t - c e l l wave functions.  Some preliminary steps are described which should  eventually lead to the detailed calculation of t h i s effect i n the present case. Abstract Approved:  iii  TABLE OF CONTENTS  INTRODUCTION  .1  THEORY OF THE CHARGE-TRANSFER COMPLEX  3  PROPERTIES OF THE ANTHRACENE-TNB COMPLEX.IN SOLUTION .  9  THE POLARIZED CRYSTAL SPECTRUM OF ANTHRACENE-TNB  . . . 17  General Principles  1?  Experimental Procedure  19  Results  22  Discussion  28  BIBLIOGRAPHY  35  APPENDIX I  37  APPENDIX II  39  FIGURES Fig. 1  Correlation Diagram for the Anthracene-TNB Complex  . . . . . .  7  Fig. 2  Probable Orientation i n the Complex  7  Fig. 3  Absorption of Anthracene-TNB i n Solution  . . 13  Fig. 4  Absorption o f Anthracene-TNB i n Solution  . . 13  Fig. 5  Effect of Contact-Charge-Transfer  Fig. 6  AH plots for Anthracene-TNB i n Various Solvents 14  Fig. 7  Optical System f o r Polarized Crystal S pectra  21  Fig. 8  Anthracene-TNB, -180°C.  23  Fig. 9  Anthracene-TNB, 23°C. . . . . . . . . . . . .  24  14  F i g . 10 Anthracene-TNT, -180°C  26  Fig. 11  9,10-Dimethylanthracene-TNB, -180°C. . . . .  27  Fig. 12  The Space Group C2/c  30  Fig. 13 Projection of Unit C e l l i n (001).  31  iv  Fig. 14 Fig. 15 Fig. 16 Fig. 17  Orientation of Transition Dipole Moments . . 32 Transition Moments along (110); Projection on (100) 33 Projections of Transition Moments i n Unit C e l l ; Two P o s s i b i l i t i e s . . . . . . . . . . . . 34Graphical Determination of Equilibrium Constant of Anthracene-TNB . . . 3d  V  ACKNOWLEDGEMENT  "Res est arduissima vincere naturam.  - my attempt to merely observe i t would not have been possible without the valuable guidance of Dr. R.M. Hochstrasser, to whom I wish to express my gratitude and thanks* I am also indebted to Dr. C. Reid for stimulating my interest i n this f i e l d , and to the National Research Council for summer financial assistance.  1  I.  INTRODUCTION  Molecular compounds or complexes between aromatic hydrocarbons and 1,3,5-trinitrobenzene have been known for many years (3,34), and along with the more widely known p i c r i c acid adducts have played an important part i n the purification and characterization of a wide variety of aromatic compounds.  I t i s only i n recent years that much  interest has been shown i n understanding their electronic structure, and although the past decade has seen considerable progress i n this direction, there i s s t i l l much that i s not understood about the spectroscopic properties of these complexes. The study of such donor-acceptor complexes i s important not only for i t s i n t r i n s i c interest, but also for i t s possible application to the general problem of i n t e r - and intramolecular energy transfer, which i s becoming of special concern to the b i o l o g i s t .  There i s i n -  creasing evidence that donor-acceptor complexes may play an important role i n certain biochemical processes.  Two recent examples of  speculation along these lines deal with two o f the most important energy-transfer steps i n the l i f e process, namely DPN-DPNH hydrogen transfer and photosynthesis. It i s known (36) that the transfer of hydrogen from substrate to DPN occurs d i r e c t l y at the 4-position of the nucleotide ring, and Chance (6) has given evidence for the existence of DPNH-enzyme and DPN-substrate complexes.  Kosower (19) has found that the course of  substitution of the 1-methylpyridinium ion i s influenced by the complexing a b i l i t y of the donor, and he discusses the significance  2  of t h i s result i n the l i g h t of Chance's findings. Piatt (35)  has suggested a new photosynthetic pathway involving  a complex of the type DONQR--(carotene) —ACCEPTOR as the "energy sink", the completing being responsible for placing the energy of the carotene below that of the chlorophyll.  He suggests  various ways i n which this or other similar complexes might act as active intermediates i n photosynthesis. The present investigation i s a prelude to what i s hoped w i l l be a f a i r l y detailed study of the polarized absorption and emission spectra of several polyacene-THB* complexes.  The immediate need  for this study arises from the question of the origin of the emission spectrum of the anthracene-TNB complex.  The e a r l i e r idea (38)  the emission i s from the t r i p l e t level of the hydrocarbon,  was that  and  i s thus r e a l l y donor phosphorescence, the T-*S forbiddeness rule being broken down by the strong f i e l d of the TNB.  Later work (9a)  suggested that the emission consists of a fluorescence component  >  (reverse of C-T absorption) and a superimposed polyacene phosphor-  ;  escence.  The current status of the problem, as summarized by  McGlynn (20, 20a) i s s t i l l one of some uncertainty. The f i r s t part of the present investigation consists of a study of the properties of the anthracene-TNB complex i n solution.  The  major part deals with the absorption spectrum of the anthracene-TNB crystal. *Abbreviations used here are as follows: TNB = 1,3,5-trinitrobenzene; C-T = charge-transfer; D= donor; A = acceptor; T= t r i p l e t ; S = singlet.  3  II.  THEORY OF THE CHARGE-TRANSFER COMPLEX  Molecular complex formation has long been thought due to the combination of an electron donor (D) with an acceptor (A),  Weitz  (42,43) and Weiss (40) suggested an ionic structure D A~ and +  predicted that a low ionization potential for the Lewis base D and a high electron a f f i n i t y for the Lewis acid A would lead to a stable complex.  Brackmann (3) came much closer t o the present concept by '  proposing resonance between a "no-bond" and a bonded structure i n which the color of the complex (assuming colorless components) i s due to the complex as a whole, and not localized to any one component. The presently accepted ideas on the nature of the donor-acceptor complex were set forth by Mulliken i n a series of papers (22-30) beginning i n 1950. His o r i g i n a l concern was with complexes of the benzene-iodine type (22), but he later (25) generalized his 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 and Boggus (20).  The following theoretical treatment  applies s p e c i f i c a l l y to the TNB-anthracene system. The wave function for a molecular compound DA i n i t s ground state can be written aft,(DA) + b ft (D A") + c - r i ( D V ) , +  (1)  where ro i s the "no-bond" wave function and includes the various c l a s s i c a l intermolecular forces such as dipole-dipole and dipoleinduced dipole interaction, hydrogen bonding, etc.  The dative-bond  wave functions ft and h. correspond to electron transfer from one member to another, resulting i n the establishment of a weak  4 covalent bond involving the odd electron remaining i n D and A* In the present treatment, a » b , and £ can be taken as zero. responding to ^  Cor-  , there i s also postulated an excited-state wave  function given by §  = a » ^  £  +  (2)  b»$£  where a ' ~ a, b ' ~ b. Starting with the ground-state wave function written as = a Hf + b K ,  (3)  we define S  12  jVfc  a  >  H  12  The energy i s given by  = /#V*4  < '5) 4  ^  JW¥77  E  (6>  Substituting with (3) and simplifying, we f i n d  a? H<if 2 k f U + b W n .  ( )  We wish to f i n d the coefficients which minimize the energy*  Taking  or  E(A.*S\,-»-  2at S  ( i  +  =  fc*S„.)  l  a  7 a  f i r s t the derivative with respect to a, and setting i t equal to zero, we obtain  3* v  .  '  .  .  (8)  and E i s a minimum when F(24S„t2lS, ) a 2aHa+2.kHix. z  (9)  Similarly, minimizing E with respect to Jb, we have E(4Sa+t5i ) t  =aHu+lH»i..  (10)  5 Equations (9)  and (10) can be rewritten  A ( H « - S „ E)+ (Hx, - S  E) +  lt  b (Hix-SaC) - O \> (Hti - S  l t  (9a)  E) = O  (10a)  which are s a t i s f i e d when the coefficients a and b are such that  = O  (11)  In the complex, the hamiltonian operator ~H° for the separated molecules i s perturbed by their interaction, giving r i s e to a new operator (12) and we seek the corresponding energies, given by  * §i » *i $i •  (13)  The secular equation (11) now becomes H:-(E>F,*)  HU-es  — o Ha-&s  where E has been replaced by H^  et-e".  <i4)  i n the second diagonal element, and  has been dropped ( i t i s small compared to E^ - fig )•  2  The  determinant i s evaluated by multiplying the second row by (H«  2  - ES)/(Eg - E ) and subtracting i t from' the f i r s t : x  Hi, - A £  -  = o  (Hi-  Ef») = O  (15)  6 and since the energies are non-degenerate,  Following the usual convention, we replace of the structure DA, and Eg by W^, and excited-state energies are W  n  by W,  the energy of D A~. +  and W,  respectively.  Q  the energy  Q  The groundThe relations  between these quantities are shown i n the s i m p l i f i e d correlation diagram of F i g . 1. Equation (16) now becomes -  o  E-Ejo = W „ - W n = Wo  •  (Hot  0  -VA^S)*"  w,-^c  '  (17)  Similarly, for the excited state deriving from eq. (2), we have  The r a t i o of the c o e f f i c i e n t s i s easily found.  or, again since E^W^  From (14),  i s close to tf , Q  i i ( w - W o ) -»-b  (H'^-lA/o'S)  t  -  O  ( 2 0 )  whence "  ~  '  In the above equations, W  Q  (21)  includes the energies of the  separated donor and acceptor molecules as well as a l l the various attractive and repulsive intermolecular  forces.  In addition,  also includes an attraction energy of covalent and ionic bonding. The difference between W, and W i s the sum of the donor ionization l o potential and acceptor electron a f f i n i t y . The ground-state resonance  D , A" +  50  0 0 0  30  000  W,  ENERGY, CM"  10  1  000  D.A W  N  CORRELATION FOR  Wo  DIAGRAM  THE A N T H R A C E N E - T N B FIG. I  COMPLEX OmO  PROBABLE IN  THE  ORIENTATIONS  COMPLEX FiG.2  8  energy i s the difference between tf and W^, and w i l l be-large i f Q  p (H  Q 1  - SWQ) i s large and  - W  i s small*  Q  In the case o f r e l -  atively weak complexes of the type under discussion, W be 0-10 kcal (20b).  Q  -  should  I t i s seen that $ h a s mostly no-bond charN  acter while $ i s mostly ionic; 6  the t r a n s i t i o n connecting the two '  states thus corresponds t o the p a r t i a l transfer of an electron from the donor (hydrocarbon) to the acceptor (TNB). If we assume that the resonance energy (W - W^) i s the primary G  s t a b i l i z i n g force i n the complex, then HQ and S must be non-zero, requiring that $ and $»be of the same symmetry species ( i n the point 0  group of the complex).  TNB most probably belongs to the point group  D^, and i t s ground state (considering only the tt -electrons) i s ...... (.aip W)\aQ ie )\ Z  2  n  1  A  while that of the anion TNB" i s  V  probably ... ( a j p ^ e ' O ^ C a j p ^ e " ^ ^ ) . B . Using the perimeter method of Mofitt (21), the symmetry species of the ground state of 1  2  n  p the anthracene cation has been assigned as Bgg (°2h^ (20a)•  T  n  e  molecular complex, having only one plane of symmetry, belongs to C £ or  (both usually called C ; g  see F i g . 2).  n  Inspection of the  appropriate character tables shows that Bgg transforms l i k e A" and  p E" l i k e A" + A', the l a t t e r being the only two representations of G . s Thus  T$ r*. T$ = A'A'A' = A ' A ^ o  by symmetry.  (  = A', and the transition i s allowed  9  III.  PROPERTIES OF THE ANTHRACENE-TNB-COMPLEX IN SOLUTION  Previous studies of molecular complexes have been carried out in solution, and since thermodynamic data so obtained are of importance i n understanding charge-transfer bonding, some consideration of the TNB-anthracene complex i n solution seems pertinent here. I t has been studied by Bier (2a) and Briegleb (5) i n carbon tetrachloride and benzene.  Their work has been repeated here using these solvents  and 1,3-dioxane and ethanol i n addition. The method of Benesi and Hildebrand (2) was used to determine the equilibrium constants.  This assumes the r e l a t i o n (for a 1:1 complex)  K =  (22)  x )(x .x ) G  A  c  to hold, where Xg i s the mole fraction of complex, and X^ and X^ are the i n i t i a l mole fractions of donor and acceptor, respectively. From the Beer-Lambert law,  (23)  D = log ( l / D = ( O i e 0  where D i s the optical density, (C) i s the concentration of complex; and € the extinction coefficient of the complex at the observed wavelength.  This method i s generally applicable to a 1:1 complex AB  where an absorption band exists which i s characteristic of the complex and outside the regions where A and B absorb separately.  Substituting  concentrations f o r mole fractions and making B>> A, (22) becomes K = or  C (B - C)(A)  C = KAB - KAC  (24) (24a)  10  Inserting (23)» D/16  + (D/16 )KA = KAB  (25)  which can be written I I f BL/D  Te *  e  =  T  *  ( 2 5 a )  i s now plotted as a function of 1/A,  straight l i n e of slope 1/K6  there should result a  and intercept 1/6  .  The TNB used was Eastman 639 "white l a b e l " and was r e c r y s t a l l i z e d from alcohol and water.  Neither a s o l i d melt nor a 0.1M  solution i n O  chloroform (1 cm c e l l ) showed any absorption above 4400A. of i t s higher s o l u b i l i t y and lower cost, i t was as "B" i n eq. 25a.  Because  ( i n most cases) used  The reagent grade anthracene was also r e c r y s t a l l -  ized from alcohol. The carbon tetrachloride, benzene, 95% ethanol,• and dioxane were a l l r e d i s t i l l e d prior to use.  The dioxane was  additionally purified by the procedure given in~Tfeissberger.(41) . Absorption measurements were made on a Gary model 14 recording spectrophotometer, i n 1- or 5-cm  c e l l s , with the hydrocarbon component  of the complex i n the reference beam at the same concentration as i n the complex i n the sample c e l l . temperatures, c e l l holders.  Runs were made at three or four  held constant (within 0.5° C  by means of thermostatted  In most cases f i v e concentrations of TNB were used,  as well as a blank containing only hydrocarbon.  The scanning  begun at a point well above the t a i l of the CT absorption, and  was was  continued at 20A/sec through the peak and into the aromatic bands. The absorption readings were made to three significant figures, but only the f i r s t two are r e a l l y dependable.  Details of the calculations  are presented i n tabular form i n the appendix, along with the graphic a l l analysis of a t y p i c a l run'.  As well be discussed below, there i s some  uncertainty i n the value of £ , and t h i s quantity was taken as constant  11  for a given complex-solvent  combination.  The equilibrium constants  obtained i n this way were used to calculate A H  values, by means of  the familiar relations -AP  = ST In K  (26) (27)  /  9JLK\  X JLO/r)  _ '  AH *  (28a)  Before considering the above results, i t i s perhaps pertinent to note some of the recent discussion (1, 20b) regarding the v a l i d i t y and meaning of data obtained by the Benessi-Hildebrand method. Especially noteworthy i s the contribution of Orgel and Mulliken (32) i n which they discuss the effects of formation of more than one  1:1  complex with different orientations, and of "contact" CT spectra.  1  They show f i r s t that the conventional Benessi-Hildebrand method applied to measurements made at One temperature does not permit one to distinguish between a system i n which one well-defined complex exists, and one i n which several (differently oriented) complexes: are present.  The observed properties of complexes are s t a t i s t i c a l  averages over a l l possible configurations i n thermal: equilibrium, and especially i n r e l a t i v e l y loose complexes l i k e these, there i s a strong likelyhood that the observed equilibrium constant K* i s made , up of several terms: K8 s  i  SK. 1  12  One cheek on this i s to plot values of log K* against 1/T.  The  resulting graph should be a straight l i n e only i f one complex i s present (or i f a l l the  are i d e n t i c a l ) .  Another indication of  multiple configurational complexes would be temperature dependence of the effective o s c i l l a t o r strength. The present results do not c l e a r l y show such an effect of any magnitude, although the small number of points taken, their scatter due to experimental error, and the r e l a t i v e l y narrow temperature range would obscure a small effect.  There i s some indication ( i n  two independent runs) that the apparent £ H of anthracene-TNB i n carbon tetrachloride i s higher at lower temperatures, but further discussion of the matter should await more detailed experimental work. One of the greatest drawbacks of the B-H method i s that values of e so determined for weakly absorbing complexes are-subject to considerable uncertainty. In a given system, considerable scatter of results (showing no trends) was noted for observations at different temperatures, and i t was decided to take an "average" or "most probable" value of €  for a given complex-solvent system.  no reason why i t should be constant with temperature  There i s r e a l l y and certainly  not with the solvent, but the present technique does not provide the accuracy required to discuss these effects even q u a l i t a t i v e l y . The second point made by Orgel and Mulliken i s that intermolecular charge-transfer spectra can occur as the result of s p e c i f i c interactions between donor and acceptor molecules through mere physical proximity, and that such interactions can exist- even i f the equilibrium constant for complex formation approaches zero.  13  4.8  4.0  3.2  LOG €  -180°  2.4  D A T A OF CZEKALLA  16  24  32  CM"'x  40  I0  48  FIG. 3  3  ABSORPTION OF ANTHRACENE-TNB IN  SOLUTION  looo i  800  600  400  200  FIG. 4  14  i A ACTUAL OBSERVED DUE  TO  CONTACT  EFFECT  OF  CONTACT  „HARGE-TRANSFER FIG.  5  3-0 25  O  CCl  20  ETHANOL  DIOXANE 3-6  &-H  PLOTS IN  FOR  VARIOUS  ANTHRACENE-TNB SOLVENTS  FIG.  6  15  Mulliken explains (30) contact charge-transfer spectra on the basis that the acceptor o r b i t a l of the anion may exceed the van der Waals size of the neutral acceptor molecule, permitting a donor molecule to interact with i t while s t i l l outside the van der Waals distance of approach.  Orgel and Mulliken discuss the effects of such  contact charge-transfer complexing i n terms of a simple s t a t i s t i c a l model.  The most significant result i s that such behavior would r e s u l t  i n a serious overestimation of 6 ; i f the equilibrium constant approaches zero and a l l absorption i s due to contact charge-transfer, the 1/ 6 intercept occurs at zero and the results lose their meaning, as shown i n Fig. 5* page 14. These points are mentioned here to bring out the fact that the interpretation of charge-transfer spectra i n solution i s even more uncertain than i n the case of "conventional" electronic spectra, and i t i s correspondingly more necessary to be cautious i n applying results of such studies to .other problems. A good example of t h i s i s the effect of the solvent on the heat of formation, as determined from the equilibrium constant' data and the graph of Fig. 6.  In carbon tetrachloride, which should presumably  show the least interaction with the complex, i t i s 4.4 kcal.  In the  other three solvents the value i s between 2-3 kcal, and since i t i s known that TNB forms complexes with benzene (16,17), ethanol (20a), (and no doubt with dioxane), i t i s obvious that we are not looking at anything as simple as the 1:1 TNB-anthracene complex alone. The same effect was noted i n a similar series of experiments with the benzpyrene complex, i n which the heat of formation was' found t o be 6.2 kcal i n carbon tetrachloride and 3*3 kcal i n benzene.  Other  16  authors have noted similar effects, and Kosower (19) finds a c o r r e l ation between the heat of formation of the charge-transfer complex and the "Y-value" of the solvent.  17  IV.  THE POLARIZED CRYSTAL SPECTRUM OF TNB-ANTHRACENE  The study of c r y s t a l spectra affords one the opportunity of examining molecules which are held i n fixed positions, and i n favorable cases where the erystal structure i s known, the use of polarized l i g h t often permits one to find the d i r e c t i o n of the transition moment, t  and to make important decisions regarding the assignment of symmetry species to the electronic states involved.  However, the very forces  which hold the molecules i n position give r i s e themselves to effects which r a d i c a l l y change the appearance of the spectra from the vapor or l i q u i d states.  Besides a considerable shift (to the red) and  change i n intensity, other effects arise, such as mixing of nearby strong and weak transitions, and s p l i t t i n g of a f a i r l y intense t r a n s i t i o n into two components, d i f f e r i n g i n intensity and p o l a r i z ation (Davydov s p l i t t i n g ) . To understand these phenomena i t i s necessary to consider the entire crystal as a molecule, and to replace "molecular states" by "crystal states", where the symmetry properties of the unit c e l l assume primary importance'.  This view was f i r s t applied to ionic  crystals by Frenkel (14,15) with much success, and was later applied to molecular crystals by Davydov (12,13;  see Craig, 8).  The simplest view of a c r y s t a l which Davydov proposes i s the "oriented gas model" i n which there i s no interaction between the molecules.  More p r a c t i c a l for a l l but the weakest transitions i s  the "weak coupling" model i n which a small interaction occurs, which however i s not strong enough to perturb the electronic structure of the individual molecules.  Thus the crystal ground state can be  18  written as a product of the individual molecular wave functions -  <P, <2a. <Pj •'" ? N  (29)  while i n the excited state, any one of the molecules can he excited:  = <?, *et  • <p  (30)  w  Interaction of these results i n c r y s t a l states (unit c e l l wave functions) composed of linear combinations of the <§*  * vfe" ( 4t f  +  #3 +  :  " ')  i n which the combinations of molecular wave functions must transform l i k e representations of the unit c e l l symmetry group i f the transition i s allowed. Davydov considers the electrostatic interaction energy between two molecules (a) and (b) which arises from the coulombic interaction between the electrons  (e) and the nuclei (n). and which can be roughly  expressed as V  l,2 =  n  l 2 ' V l e  +  8  l l e  +  n  l 2 a  (  3  2  )  Further elaboration of the theory (8) results i n the summation of these terms over a l l atoms i n the molecule, the derivation of a crystal wave function, and f i n a l l y i n an expression for the s h i f t i n peak position from the gas to crystal state, and the s p l i t t i n g  19 between oppositely polarized components of corresponding peaks, which can be written dE°  M M  *  =  (constant)  H  +  I  j p  •  +  (33)  where the 1 ^ are interaction integrals between the j t h and kth molecules, p runs over a l l molecules translationally equivalent to it and the q, r , etc, run over a l l molecules related to 3 by the other symmetry operations of the unit c e l l group*  The summed interaction  integrals are taken i n linear combinations corresponding to those of eq* 31 which are allowed. The integrals I ^ are given by I  jk  " r "" l l  =  3  M  2  c  o  s  e  j l  c  o  s  Q  j2 ~  c  o  (34) s  e  j2  C 0 S  9  k2 "  c  o  s  Q  j3  c  o  s  ®k3  °2 i n which M i s the molecular transition moment ( i n A ) and r., i s the distance between their centers.  The angles 6^, 9^,  etc., are  angles made by the t r a n s i t i o n moment with an orthogonal set of axes erected at i t s center, with 6 ^ r e f e r r i n g to an axis along the l i n e connecting the centers of the two t r a n s i t i o n moments*  1  Experimental. Both the anthracene and' TNB were Eastman reagent grade*  The  former was r e c r y s t a l l l z e d twice from alcohol, and the l a t t e r from water.  The complex was prepared by combining a hot alcoholic solution  of anthracene with a hot concentrated solution of TNB, and allowing the mixture to c r y s t a l l i z e i n the dark;  The orange crystals were  removed by f i l t r a t i o n and r e c r y s t a l l l z e d from concentrated alcoholic TNB.  20  The samples were prepared by melting a small quantity of the s o l i d complex between two s i l i c a discs (or a s i l i c a disc and a microscope cover glass) and allowing the melt t o cool under pressure*  In  order to obtain large uniform areas, the sample was usually p a r t i a l l y remelted and cooled several times, the unmelted areas being used to seed the remelted ones.  Examination through the polarizing micro-  scope located an area of sufficient size which showed uniformity and complete extinction.  The sample disc was then oriented on a brass >  disc so that the pinhole (# 60 d r i l l ) i n the l a t t e r corresponded with the area to be examined.  The brass disc and sample were then placed  in a Oewar c e l l i n such a manner that the direction of extinction corresponded to either the horizontal or v e r t i c a l axis of the o p t i c a l system.  '  The spectrograph was* a Hilger medium quartz prism instrument, equipped with a Hilger motor-driven scanning attachment containing a 1P28 photomultiplier which was operated at 800 volts from*a Gintel stabilized supply.  The detector was a Keithly Model 200 B electro-  meter equipped with a decade shunt.  The output of the meter was  connected to a standard Leeds & Northrup chart recorder.  The photo—8  tube currents varied from f u l l - s c a l e meter readings of 2x10* 2x10"^ amperes.  to  Ranges were changed by altering the shunt resistance.  The optical system i s shown diagramatieally i n F i g . 7.  The  light source was a six-volt, 18 ampere air-cooled projection lamp, operated from a s t a b i l i z e d ac supply.  A converging lens focussed  a spot of l i g h t onto the pinhole covering the sample.  The emerging  l i g h t was collected and made p a r a l l e l by a second lens, then passed through a Wollaston prism.  The resulting two beams were then  21  i t  TUNGSTEN p L  A  M  OPTICAL  DEWAR SAMPLE C E L L  SYSTEM  POLARIZED  WOLLASTON PRISM  SPECTROGRAPH S L I T  FOR  CRYSTAL  SPECTRA FIG. 7  22  focussed on the entrance s l i t of the spectrograph;  The polarization  to be used was selected by rotating the Wo1laston prism so that only the desired beam f e l l on the s l i t .  Before running a spectrum, the  optical system was adjusted so as to give equal i n t e n s i t i e s i n each polarization at a wavelength well separated from the C-T  absorption.  This adjustment was found to be very c r i t i c a l , and after making i t care was taken to avoid disturbing any part of the o p t i c a l system except the Wollaston prism.  After recording the two spectra, the  sample was replaced by a simple aperture and the spectrum of the l i g h t source and phot©multiplier response were determined.  Through-  out the process, care was taken to avoid d i f f r a c t i o n patterns and spurious effects due to chromatic aberrations of the simple lenses used. In interpreting the results, i t was assumed that the transmitted light at a wavelength outside the region of absorption was the same for both sample and reference beams.  The readings of sample  beam intensity were then corrected to zero o p t i c a l density at t h i s wavelength, and log I A Q  calculated.  Results. Several spectra were run, and the results are i n substantial agreement.  As expected (see following section on c r y s t a l structure), 7  the absorption i s more intense along the long axis.  The absorption  commences near 19000/cm and rises sharply to form a broad band, the most interesting feature of which i s the presence of a  1400/cm  vibrational interval, probably corresponding to an anthracene ring breathing vibration.  This i s the f i r s t reported observation of  vibrational structure i n a charge-transfer band.  A second point of  23  M I L L I M I C R O N S  275,  600 1  550 f  500  1  450 ,  _  400  360  ,  H  2-50  2-25  200  DENSITY  ANTHRACENE- TNB. -180°  FIG. 8  24  M I L L I M I C R O N S  tOPTICAL DENSITY  C M "  1  x  10  -3  ANTHRACENE-TNB. 23* c.  FIG. 9  25  interest i s that the peaks i n the short-axis polarized absorption are located 100-200 /cm to the red of the corresponding peaks of the other component.  These s h i f t s , though not much greater than the  accuracy and reproducibility of the method ( 100/cm), are always seen.  They appear to be quite sensitive to the nature of the c r y s t a l ;  preliminary experiments with a crystal of anthracene containing a small amount of complex show a reversal of the s h i f t . The spectrum shown i n F i g . 8 i s most representative.  The apparent  absorption to the red of 16000/cm i s attributed to r e f l e c t i o n losses, which are expected to change with wavelength.  Thus the apparent  optical density should be corrected by extrapolation of the r e f l e c t i o n loss.  Making such a rough extrapolation out to the center band  (21700/cm) and subtracting the r e f l e c t i o n from the o p t i c a l densities of the two peaks, at this wavelength, we arrive at a very approximate optical density r a t i o (not polarization ratio) of  3:1.  Fig. 9 shows the spectrum of the same sample at room temperature. The expected broadening obliterates the d e t a i l of the peaks, although some structure remains i n the strongly-absorbed  polarization.  The  optical density r a t i o i s approximately the same. Preliminary studies have been made on the 9,10-dimethylanthraceneTNB complex, and of anthracene-TNT (2,4-,6-trinitrotoluene), and their spectra are shown i n Figs. 10-11.  The apparently small optical <  density r a t i o i s probably a consequence of the rather thick crystals used, and further work on these complexes i s necessary.  I t i s very  d i f f i c u l t to obtain good single crystals of either of them.  26  M I L L I M I C R O N S  2-75  2-50  2-25  200  1-73 1-50  1*00 0*75 0-50  0-25  O P T I C A L  C M  -  1  x  |0~  3  D E N S I T Y  ANTHRACENE-TNT. -ISO*  FIG. 10  27  M I L L I M I C R O N S  2-75  2-50  2-25  200  1-75  1-50  1-25  1-00 0*75  0-50  0-25  O P T I C A L  C M "  D E N S I T Y  1  x  10 - 3  FIG.  9,10- DIMETHYL ANTHRACENE - T.N.B. -180*  FIG. II  28  Discussion. The orange acicular prisms of anthracene-TNB complex (as obtained) by c r y s t a l l i z a t i o n from solvents) shov a strong dichroism when examined in polarized l i g h t , the orange color being most intense when the l i g h t i s polarized along the long axis of the c r y s t a l . Similar examination of a thin section of the needle (looking down the long axis) f a i l s to reveal any dichroism.  Since the C-T t r a n s i t i o n presumably occurs  with a moment perpendicular  to the planes of the anthracene and TNB  molecules, these results suggest that the crystal i s made up of such units stacked up along the long (c) axis. of absorption  The r e l a t i v e i n t e n s i t i e s  i n the two polarizations also indicate such a structure.  Detailed interpretation of the energy s p l i t t i n g s cannot yet be given, as the c r y s t a l structure of the complex i s not completely known, and certain questions regarding Davydov s p l i t t i n g calculations and the effect of permanent dipoles (as i n TNB) on the s p l i t t i n g s are currently being studied and discussed.  The calculations summarized  below are to be regarded purely as preliminary steps toward the explanation of the observed effects. The c r y s t a l structure of the complex has been p a r t i a l l y determined by Wallwork (39) # who states that the crystals are monoclinic,  = 1331& .  and belong t o the space group C2/c (Cg^)* with eight molecules ( i . e . , four complexes) per unit c e l l .  The molecules are stacked alternately  i n a staggared manner i n columns p a r a l l e l t o the c_-axis, but t i l t e d by about 6° from the position i n which they would be perpendicular to that axis. and C  Q  The unit c e l l dimensions are a = 11.69 A, b = 16.36 A, o o = 13.23 A. The special positions are assigned as follows:  0  29  Anthracene:  0,0,0;  0,0,%;  TNB:  0,y,%; 0,y,%;  %%0i %  KM. fc*y %i t  Fig. 12 shows the general point positions and symmetry operations of the space group c2/c, and Figs. 13 and 15 show projections of the unit c e l l s (as deduced from Wallwork's data) i n the ab and be planes, respectively. Without knowing the value of "y", the exact locations of the TNB molecules cannot be known;  i n the present calculations i t has  been assumed to be 0.17 A, which would be the distance required to t i l t the line connecting the centers of the anthracene and molecules by 6°.  TNB  I t i s further assumed that the molecules are  inclined along the b axis, and that the transition moments are perpendicular to the planes of the aromatic rings. There i s some question as to just what constitutes a complex "molecule" i n t h i s c r y s t a l , and i t i s defined f o r the purposes of the present discussion as the pair of centers between which the charge-transfer process i s taking place.  I f we assume that t h i s  process w i l l occur between p a r a l l e l molecules i n preference to , those inclined 12° with respect to each other, then a knowledge of the relative directions of i n c l i n a t i o n of the TNB and  anthracene  would f i x the location of the complex "molecules" i n the c r y s t a l . Thus i n F i g . 16 (pg 33)»  the transition moments are drawn i n two  different ways, using the same locations of the individual molecules. The calculations summarized i n Appendix I I . are based on the relation ships of Figs. 16a, 14 and 15  t  and on a t r a n s i t i o n moment length of  0.88A as estimated from the absorption spectrum of Fig. 4 and the  30  O Oi-  i +  O o I 4'  1 3 4 ' 4  THE  SPACE  GROUP  3 4  C2c-Cl  H  FIG. 12  31  PROJECTION  IN  (OOI)  (UNIT CELL SHADED)  FIG. 13  32  ORIENTATION DIPOLE ( N O T O F  T O  OF  MOMENTS  E X A C T  M O M E N T S  TRANSITION  S C A L E ;  I N C L I N A T I O N  E X A G G E R A T E D )  FIG.14  33  TRANSITION  MOMENTS ALONG (110);  PROJECTION L A R G E  C I R C L E S  R E P R E S E N T  ON  (100)  A N T H R A C E N E  UNIT CELL SCALE  L O C A T I O N S  FIG. 15  34  equilibrium constant data.  The values of the interaction integrals  between molecule "0" ( F i g . 14) and the other fourteen adjacent molecules are calculated and given i n Appendix I I . The integrals between molecules related to each other by the same space group operations are summed i n the table below: molecule "0" transformed into no.: 3,4;  operation  XT 1 ^ , cm~*  translation  + ?60  £ screw axis  - 2440  11,12. 1,7. 2,6,8,5; 10, 13. 14, 9.  a  +  c  /  2  s  l  i  d  e  +  1  2  3  0  Further interpretation o f the s p l i t t i n g awaits the completion of work now i n progress.  I t should be mentioned that there i s reason  to f e e l that the relations shown i n F i g . 16b may be more l i k e l y , and i t i s hoped to confirm t h i s shortly.  Y -\ A  v L-^t  8  /  F i g . 16. PROJECTION OF TRANSITION MOMENTS IN A UNIT CELL ON (100). Two p o s s i b i l i t i e s are shown; part A i s i d e n t i c a l with F i g . 15* TNB molecules are at heads of arrows.  35 BIBLIOGRAPHY 1.  ANDREWS, L.J.: Ghent. Revs. 5 ^ . 713 (1954).  2.  BENESI, H.A., and J.H. HILDEBRAND:  J . Am. Chem. Soc. 7JL,  2703 (1949). 3.  BRACKMAN, W.:  Rec. trav. chim. 68, 14? (1949).  4.  BRIEGLEB, G.:  Zwischenmolekulare Krafte:  G. Braun,  Karlesruhe, 1949. 5.  BRIEGLEB, G., and T. SGHACHOWSKOY: Z. Physik. Ch. B19., 255 (1949).  6.  CHANGE, B.: Mechanism of Enzyme Action: Baltimore, Md., 1954.  Johns Hopkins Press,  Ppg 433-452.  7.  COULSON, C.A.: Valence: Oxford, 1952.  Ppg 58-6?.  8.  CRAIG, D;P.: J . Chem. Soc. 1955. 539.  9.  CZEKALLA, J . : Die Naturwissenschaften 20, 467 (1956).  10.  CZEKALLA, J . : Z. Elektrochemie 61, 537 (1957)*  11.  CZEKALLA, J . : Z. Elektrochemie 63_, 1157 (1959).  12.  DAVYDOV, A.S.: Zhurn. Eksp. Teor. Fyz. 18, 210 (1948).  13.  DAVYDOV, A.S.: Theory of Molecular Excitons, trans. M. Kasha: McGraw-Hill, N.Y. ( i n press).  14.  FRENKEL, J . : Phys. Rev. 3JL, 17 (1931).  15.  FRENKEL, J . : Fyz. Zhurnal Sovjet. 9., 958 (1936).  16.  HAMMICK, D., G. HILLS and J . HOWARD: J . Chem. Soc. 1932. 1530.  17.  HEPP, P. Annalen 215. 344 (1882).  18.  KETELAAR, J.A.A., et a l . :  19.  KOSOWER, E.M.:  20.  McGLYNN, S.P., and J.D. BOGGUS:  Rec. trav. chim. 2k* H 0 4 (1952).  J . Am. Chem. Soc. 80, 3^6? (1958). J . Am. Chem. Soc. 80, 5096 (1958).  20a.  McGLYNN, S.P..: Chem. Revs. 5 8 , 1113 (1958).  20b.  McGLYNN, S.P., J.D. BOGGUS, and E. ELDER: J . Chem. Phys.  21.  2 2 , 357 (I960). MOFITT, W. J . Chem. Phys. 22, 320 (1954-).  36  22.  MULLIKEN, R.S.:  J . Am. Chem. Soc. 2 2 , 600 (1950).  23.  MULLIKEN, R.S.:  J . Am. Chem. Soc. £ 2 , 4493 (1950).  24.  MULLIKEN, R.S.:  J . Chem. Phys. 19., 514 (1951).  25.  MULLIKEN, R.S.:  J . Am. Chem. Soc. £ 4 , 811 (1952).  26.  MULLIKEN, R.S.:  J . Phys. Chem. £ 6 , 801 (1952).  27.  MULLIKEN, R.S.  Symposium on Molecular Physics.  Nikko,  Japan, 1953. 28.  MULLIKEN, R.S.:  J . chim. phys. 52, 341 (1954).  29.  MULLIKEN, R.S.:  J . Chem. Phys. 23., 397 (1955).  30.  MULLIKEN, R.S.:  Rec. trav. chim. 21* 845 (1956).  3L  NAKAM0T0, K.: J . Am. Chem. Soc. 24, 390 (1952).  32.  ORGEL, L.E., and R.S. MULLIKEN:  34.  PFEIFFER, P.: Organisehe Molekulverbindungen, 2nd. ed.  J . Am. Chem. Soc. 22, 4839 (1957).  F. Enke, Stuttgart, 1927. 35.  PLATT, J.R.: Science 129. 372 (1959).  36.  PULLMAN, M., A. SAN PIETRO, and S.P. COLOWICK: J . B i o l . Chem. 206. 129 (1954).  37.  REID, C.: Excited States i n Chemistry and Biology: Butterworth's, London, 1957.  Ppg 113-118.  38.  REID, C.: J . Chem. Phys. 20, 1212 (1952).  39.  WALLWORK, F.: Acta Cryst. £ , 648 (1954).  40.  WEISS, J . : J . Chem. Soc. 1942. 245.  41.  WEISSBERGER, ed.: Technique of Organic Chemistry, V o l . IV: Organic Solvents:  Interscience, Nev York, 1955.  42*  WEITZ-HALLE, E.: Z. Elektrochem. 3jt. 538 (1928).  43.  WEITZ-HALLE, E.: Angew. Chem. 66, 658 (1954).  44.  WOODWARD, R.B.: J . Am. Chem. Soc. 64, 3058 (1942).  Pg* 371.  37 APPENDIX  I  DETERMINATION OF THE EQUILIBRIUM CONSTANT OF THE TNB-ANTHRACENE COMPLEX BY THE METHOD OF BENESI AND HILDEBRAND. Solvent:  carbon tetrachloride,  Stock solutions: concentration  C e l l s , 1 cm.  Anthracene ("B"), 0.0337 M;  TNB ("A"), 0.0119 M;  of TNB i n each sample was 0.953 mM. 296°K D B/D  2?8°K D B/D  D  331°K B/D  ml "A"  A  1/A  10  .0135  74.0  .168  5.6?  .266  3.58  12  .0162  62.7  .193  4.94  .309  3.08  .460  10.35  14  .0189  52.9  .211  4.51  .348  2.74  .533  8.94  16  .0216  46.3  .241  3.96  .392  2.43  .599  7.95  18  .0243  41.1  .270  3.53  .420  2.27  .664  .7.18  20  .0270  37.0  .294  3.24  .453  2.10  .733  6.50  22  .0297  33.7  .320  2.98  .484  1.97  .800  5.95  These results are plotted i n F i g . 15 on the following page. The average intercept i s taken as 1/ = (0.70 _+ .05) x 10~^ or t  = 1430 + 100.  ,  278°K:  slope = 1/K = .0485 x l o " ;  296°K:  K = .70/.0775 = 2*0.  \ i' 331°K: s:  The equilibrium constants are calculated below. 3  K = .70/.0485 = 14.5.  K = .70/. 119 = 5.9.  ~ The values for l:H of TNB-Anthracene i n various solvents are  calculated to be the following (see F i g . 6 ) : Benzene  2.7  Ethanol  2.5  Carbon Tetrachloride  4.4  Dioxane  2.3  kcal  38  39 APPENDIX II. NOTES ON THE CALCULATION OF THE ENERGY SPLITTING The direction cosine between two lines J, and k in terms of the orthogonal coordinates (1,2,3) is given by cos J P j = cos 8ji ®iji cos  +  c o s 9  k  j2  k2  e o s  9  c o s 9  +  j3 ^ c  8  ®k3 *  By the use of this relation we can simplify Eq. 34-: e 3k = * r jk *" W 2  I  5  3  c  o  s e  jl  c  o  s 6  kl "  c  o  s  *jk*  ( 3 4 a )  Thus we must calculate the angle between the two transition moments, and the angles between each moment and the line connecting their centers.  This problem is in general quite laborious, but is consid-  erably simplified when we assume (as we do here) that a l l the transition moments lie in the same plane or in parallel planes.  The calculation of 1^. for the various interactions (j =0, k s 1-14; see table 14 for numbering of adjacent moments) is summarized in the following table. k * cosOjk 3. 11 -.232 4, 12 +.232 +.999 1. 7 2* 10 -.009 6, 13 +.540 8> 1* +.280 -.472 5, 9  The transition dipole moment is estimated at 0.88A. cos Otj 3ab 3ab-eos +.232 -.161 -1.16 -.161 -1.16 -.232 +1.98 +.999 +.987 -.006 -0.98 -.009 +.540 -.572 -1.55 -.280 -.384 -1.36 -.472 -.395 -1.37  * value of k in I^ , with j = 0. k  r xlO 1090 1090  289 810 3370  985 3500  jk + 190 + 190 -1220 + 216 + 82 + 246 r  + 70  


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