6347
J. Phys. Chem. 1995, 99, 6347-6355
Application of Time-Dependent Raman Theory to Raman Excitation Profiles of Hexamethylbenzene-Tetracyanoethylene Electron Donor-Acceptor Complex B. Mark Britt and Jeanne L. McHale* Department of Chemistry, University of Idaho, Moscow, Idaho 83843
Donald M. Friedrich Environmental Molecular Science Laboratory, Pacific Northwest Laboratories, Richland, Washington 99352 Received: November 16, 1994; In Final Form: February 20, 1995@
Raman excitation and absorption profiles were obtained for the 1:l electron donor-acceptor complex of hexamethylbenzene with tetracyanoethylene in dichloromethane solution. The absorption and Raman profiles were analyzed using the time-dependent theory of Heller to obtain the displacements and non-Condon factors for the four strongest Raman modes, the electronic excitation energy, the transition dipole, and solvent linebroadening parameters. The results are compared to the data reported by Myers et al (J. Am. Chem. SOC. 1992, 114, 6208) for the same complex in carbon tetrachloride solution. Attempts to account for solvent effects on the normal-mode displacements in terms of the solvent local field lead are complicated by the effect of the solvent on the structure of the complex. We propose that in CH2C12 but not in CC4, the complex adopts a low-symmetry ground-state geometry which permits vibronic coupling of the charge-transfer and locally excited (TCNE) states.
TABLE 1: Physical Properties of CH2C12 and CC4
Introduction The weakly bound electron donor-acceptor (EDA) complex between hexamethylbenzene (HMB) and tetracyanoethylene (TCNE) has been previously studied in our laboratory using both experimental and theoretical One of the more interesting aspects of this system is its ability to form both 1:l (DA) and 2: 1 (DAD) complexes, depending on solvent. Our quantum mechanical calculations on 1:l complexes of TCNE with various aromatic donor^^-^ have interpreted the broad featureless absorption spectrum to be the result of the loosely bound ground-state potential surface. The energy and the transition strength of the charge transfer transition
DA
D+A-
depecd on the instantaneous configuration of the complex, and the shallow ground-state surface permits a large range of intermolecular geometries to contribute to the spectrum. Thus, even in the gas phase7,*and in jet-cooled sample^,^ absorption spectra of EDA complexes lack vibrational structure. The looseness of the ground-state complex allows solvent effects on the electronic spectra and on the complex itself to be especially important. Another common characteristic of many EDA complexes is the very low fluorescence yield for emission from the charge-transfer (CT) excited state,l0 an experimental observation that can be understood in terms of the large change in geometry on going from the ground to the CT electronic state. The unique features of EDA complexes present many challenges to the interpretation of resonance Raman excitation profiles. Anharmonicity, dependence of the transition moment on normal-coordinate (non-Condon terms), and the possibility of more than one resonant electronic state are some of the complications to consider. Interpretation of solvent-dependent spectral features must take into account not only the effect of the local field, but the possible influence of the solution on the structure of the complex as well. @
Abstract published in Advance ACS Abstracts, April 1, 1995.
0022-365419512099-6347$09.00/0
CHIC12
cc4
1.14 8.93 1.42 1.32
0 2.24 1.46 1.58
dipole moment, D dielectric constant refractive index density
TABLE 2: Properties of HMFkTCNE in CH2Cl2 and CC4 CH2C12
CCL
equilibrium constant, M-' 17 160 heat of formation, kJ/mol -35.3" -32.4b D-A stretch, VDA,cm-' 168 165 absorption max, cm-' 18 500 19 000 molar absorptivity, L mol-' cm-I 3300 4600 a Rossi, M.; Buser, U.; Haselbach, E. Helv. Chim. Acta 1976, 58, 1039. Briegleb, G. Elektronen-Donator-Acceptor-Komplexe; SpringerVerlag: Berlin, 1961. Recently, Myers et al." presented the results of using the time-dependent theory of Heller12-14 to model the absorption and Raman profiles of HMB:TCNE in CC4. In this work, we take advantage of the opportunity to investigate solvent effects by using the same time-dependent theory to analyze our Raman and absorption profiles of HMB:TCNE in CH2Cl2 solution. By adjusting parameters to get a best fit to the experimental profiles, we obtain a set of dimensionless displacements and non-Condon factors for the strongest Raman modes, the energy and transition moment for the CT transition, and the amplitude and frequency of solvent fluctuations which perturb the electronic transition. Previous experiments suggest some intriguing questions about the properties of HMB:TCNE in dichloromethane and carbon tetrachloride (see Tables 1 and 2 ) . The equilibrium constant for complex formation is much more favorable in cc14 than in CH2C12, yet the enthalpy of formation is more negative in CH2Cl2. (In our experience, however, we have found enthalpies of formation of EDA complexes to be quite unreliable, due to nonlinearity of In K versus lITplots, where K is the equilibrium constant determined from optical absorption.) To further confuse the question of complex strength in the two solutions, 0 1995 American Chemical Society
Britt et al.
6348 J. Phys. Chem., Vol. 99, No. 17, 1995
it should be noted that the C=C stretch of TCNE is found at the same frequency, 1550 cm-l, for HMB:TCNE in either solvent. Since this vibration in free TCNE undergoes a large red shift on formation of TCNE! anion,15 from about 1570 to 1390 cm-I, the C=C stretching frequency provides a marker for the degree of ground-state charge transfer. The putative donor-acceptor stretch YDA, found at 165 cm-' in CC4 and at 168 cm-' in CH2C12, could also indicate the strength of the ground-state complex. Unfortunately there is no way to know how much of this frequency difference is due to a solvent effect and how much to a difference in the strength of the complex. The increase in D-A frequency in CH2C12 could result from solvent repulsive forces or from increased complex stability. In CC4 solution, HMB and TCNE form both 1:1 and symmetric 2:l complexes, but in CHZC12 only 1:l complexes are appare n t . ' ~ (The ~ ~ experiments done by the Myers group employed concentrations for which the 2:l complex should have been small.) The maximum in the CT absorption spectrum is redshifted by about 500 cm-' in the polar solvent compared to the nonpolar one, which is reasonable in view of the ionic character of the excited state. Less easy to explain is the fact that the absorption cross section in CH2Cl2 is about 75% of the value in CC4 (see Table 2). Ordinarily, the intensity of the CT transition increases with the stability of the complex, but mixing of the CT and locally excited donor or acceptor states can disturb this trend.16 In addition, there may be a solvent effect on the intensity of any electronic transition. In simple approaches to calculating this local-field effect, the transition strength is a function of the solvent refractive index. As shown in Table 1, the refractive indexes of the two solvents are very similar, and it is unlikely that the difference in molar absorptivity can be attributed to the local field. And as will be revealed below, the magnitudes of the displacements along the shifted normal coordinates are smaller in C H F L than in CC4. One would expect these displacements to decrease as complex stability increases, as explained below. This collection of comparative data is difficult to rationalize without contradictions, in terms of either solvent effects on the strength of the complex or local field effects on the potential surfaces. We shall show that we are forced to consider the possibility of different complex structures in the two solutions. In our previous analysis of the Raman excitation profiles (REPs) of HMB:TCNE,3 we used transform theory to extract the dimensionless displacements and non-Condon terms (defined below) for two strong TCNE vibrational modes and a lowfrequency mode of the complex. The two TCNE modes at 1550 and 2223 cm-' are assigned to the C=C and CEN stretch, respectively, and we have assigned the 168 cm-' mode of the complex to the pseudodiatomic D-A stretch, though the concept of a normal mode is strained for motion on such a shallow and anharmonic potential surface. Using the results of a normalcoordinate analysis for TCNE, we resolved the dimensionless displacements along the symmetry coordinates and calculated bond length changes for the C=C, C-C, and C S N bonds. These bond length changes were found to agree fairly well with those calculated for the formation of TCNE anion." The dimensionless displacement of the D-A stretch was consistent with a change of 0.02 A in the equilibrium intermolecular donor-acceptor distance upon excitation. Although the analysis cannot determine the sign of the geometry change, we presume that the D-A distance decreases on going to the more polar excited state. A significant result from our transform theory analysis was the need to use fairly large, negative non-Condon terms to account for the experimentally observed blue shifts in the REPs with respect to the absorption profile. Physically,
the non-Condon terms represent the dependence of the electronic transition moment on the normal coordinate for the mode in question. Though it is not surprising to find the transition moment to be a strong function of the D-A distance, large nonCondon terms were also found for the C=C and C z N vibrations. The first-order approximation used to include nonCondon terms in transfom theory may be inadequate when the transition moment derivative is large.'* We undertook the present study for two reasons: to compare our previous results using transform theory to those from direct modeling (using the same data) of both absorption and Raman profiles using Heller theory, and to treat our data for HMB:TCNE in CHzC12 using the same approach as was used by the Myers group to analyze HMB:TCNE in CC4. Experimental Section The experimental details were presented in ref 3. In brief, measurements were performed on a 3.0 x M solution of HMB:TCNE in CHzC12. Raman spectra were excited at wavelengths from 457.9 to 637.6 nm using argon ion and dye laser excitation and laser powers below 50 mW. Raman cross sections were obtained by referencing Raman intensities of the complex to that of the solvent mode at 284 cm-'. The cross section for the solvent reference mode was determined from the ratio of the intensity of the 284 cm-' mode to that of the cyclohexane band at 800 cm-I, using the absolute cross sections for cyclohexane reported by Trulson and Mathies.lg Raman intensities, based on peak area, were determined by fitting the baseline-subtracted spectra to a suitable number of Gaussians. Intensities were corrected for self-absorbance and instrument response and are believed to be accurate to about *12%, based on replicate measurements. The computer program employed for the implementation of the time-dependent theory was kindly provided by Prof. Anne Myers of the University of Rochester. We modified it by writing an outer loop to vary the adjustable parameters and calculate the x2 error function. Theoretical Analysis (a) Quantum Mechanical Language for Discussing EDA Complexes. The Mulliken description of the structure and spectra of EDA complexes is well-known.20 It is reviewed briefly here in order to present a framework for considering how the solvent might influence the spectra and structure of the complex. The ground- and excited-state wave functions are taken to be superpositions of wave functions for the nonbonded (VO)and ionic (VI) states:
Yg= uWo(DA)
+ bW,(D+A-)
(1)
-
where a >> b and c >> d for a typical weak complex. The intensity of the CT transition, g e, as well as the binding of the complex in the ground electronic state, is due to the mixing of the nonbonded and ionic states. This mixing is roughly proportional to the ratio of the resonance integral to the energy difference of the zero order states: b
--oc
u
(VolHlVi) E, -Eo
(2)
For typical weak complexes such as HMEI:TCNE, the stability of the complex and the strength of the CT transition both increase as the mixing increases. (However see ref 16 for a discussion of how locally excited states can perturb this trend.)
Application of Time-Dependent Raman Theory
J. Phys. Chem., Vol. 99, No. 17, 1995 6349
One can well imagine how the solvent might perturb the stability equal vibrational frequencies in the ground and excited electronic and spectrum of a given complex through its effect on the states. The time-dependent overlaps can then be calculated with one adjustable parameter for each active mode, the displacement mixing of nonbonded and ionic states. The solvent could alter the overlap of the interacting wave functions (generally the A,, expressed as a dimensionless normal coordinate, of the excited-state potential surface. Going one step beyond the donor HOMO and the acceptor LUMO) through a cage effect that restricts the donor-acceptor separation. The importance Condon approximation, the transition moment is given by of the solvent cage effect has been invoked to explain the lack of correlation of CT absorption spectra with dielectric constant or refractive index.' Solvent polarity could perturb the mixing through a shift in the energies of the zeroth-order states, particularly that of the ionic state, El. where the sum is over the normal coordinates Qa for the active The maximum difference in ground- and excited-state gemodes. B-term Raman scattering is proportional to the product ometries would be achieved in the limit of no mixing; that is, of the zeroth-order transition moment and the first derivative. a purely "nonbonded" ground state and a purely "ionic" excited The working equations for the B-term contributions to the state. Thus increased mixing should cause the dimensionless absorption and Raman cross-section contain the terms (ilQali(t)) displacements of all normal modes to decrease. Also, in the and (ilQaHt)). As explained in ref 11, these are easily evaluated limit of no mixing, the difference in the ground- and excitedwith the help of recursion relations for harmonic oscillator wave state dipole moments would be maximal. As discussed below, functions. Relaxing the Condon approximation introduces an it is the normal-coordinate dependence of these dipole moments additional adjustable parameter for each mode, defined as which results in local-field effects on the displacements. (b) Modeling of Absorption and Raman Profiles. The c 1 'Mge working equations for applying Heller's t h e ~ r y , ' ~ - 'incor~,~~ (7) a aQa o porating the stochastic line broadening model of M ~ k a m e l , * ~ * ~ ~ are described in ref 11. We summarize them here briefly. The (This differs from the definition of C, used in ref 3.) absorption cross section OA is related to the Fourier transform Myers et al." were interested in obtaining the solvent (A,) of the overlap of the initial state at time t with the same state and internal (A,)reorganization energies, pertinent to theories at time t = 0: of electron-transfer rates, from their data. The former is found from the stochastic line-broadening parameter (A, = D2/2k~7') and the latter from the normal mode displacements (A; = '/2DwaA,2). They included in their analysis the displacements and non-Condon factors for 11 normal modes (6 HMB modes, The Raman cross section OR is related to the square of the 4 TCNE modes,,and the intermolecular mode). Due to solvent half-Fourier transform of the overlap of the initial state at time overlap or poor signal-to-noise, we did not attempt to model t with the final state at time zero: the REPS of all 11 modes. Instead, we modeled the profiles of the four most intense modes (one HMB mode at 1292 cm-', two TCNE modes at 1550 and 2223 cm-', and the donoracceptor stretch at 168, cm-'), but included the Aa's and Ca's for the next three strongest modes (those at 450, 540, and 970 cm-l) in the calculation. The displacements and non-Condon The states Ii) and If) are initial and final vibronic states, wo and factors for these three modes were taken from ref 11 and were not adjusted further. Though the neglect of additional vibraw , are the incident and scattered frequencies, Mge is the transition tional modes with small displacements may cause us to dipole moment in the Condon approximation, wi is the vibraoverestimate the solvent damping, we obtain a reasonable value tional energy of the initial state, and g(t) is a damping function. for the solvent reorganization energy. In contrast to the work The damping function is often taken to be of the form exp[of Myers, the non-Condon terms Caof the four strongest modes g(t)] = exp(-rltl). In this work, we followed Myers and were allowed to vary to get the best fit: we did not assume employed the stochastic line-broadening function given in refs them to be proportional to the corresponding A,'s. As in the 22 and 23. In brief there are two parameters needed to model work by the Myers group, we assumed no change in Vibrational g(t): the amplitude D and the rate A of the solvent induced frequency upon excitation. Thus, the displacement parameters flucutations in the energy of the electronic transition: (A,'s) that we obtain reflect the slope but not necessarily the shape of the upper potential energy surface. (5) (c) Effect of Local Field on _Normal-ModeDisplacements. Equations 3 and 4 are not the final forms of the expressions In the presence of a local field F , the ground- and excited-state used in this work. For the low-frequency mode at 168 cm-', potentials for each displaced normal mode can be written as thermal effects were included by summing over a Boltzmann distribution of initial states. Inhomogeneous broadening was accounted for by averaging the cross-section over a Gaussian distribution of electronic 0-0 energies, the mean energy EOand the standard deviation being adjustable parameters. Equations - A)2 (8b) V,(Q) = -ko(Q 3 and 4 are based on the Condon approximation, where Mge = 21 is taken as the transition dipole at the geometry of the Here p g and p e are the ground- and excited-state dipole ground electronic state. In the conventional approach to moments, Q = (uw/h)'/*qis the dimensionless normal coordiaccounting for A-term scattering of totally symmetric modes, the Condon approximation is made and the ground- and excitednate, 4 is the normal coordinate, and A is the dimensionless state surfaces are modeled as displaced harmonic oscillators with displacement of the excited-state potential surface in the absence
=-(-)
4e
+
@;F
(2);FQ
Britt et al.
6350 J. Phys. Chem., Vol. 99, No. 17, 1995 of a local field. We take the local field to be the same in the ground and excited states. The above equations can be rearranged to give V,(Q) a: '/,ho(Q - 6g)2- ,Z;F
TABLE 3: Comparison of Fitted Parameters for HMB:TCNE in CHzClz and CCL from Time-Dependent Theory and Parameters for HMB:TCNE in CHzCh from Transform Theory
(9a) theory
time-dependent theory
V,(Q)
=
+ '/,ho(Q
J?$,
- A - de)* - ,Z;F
(9b)
where the term proportional to the square of the field has been dropped and we have used the definitions
CH2C12, this work
CCh, ref 11
10,100 3.6 32 1580 250
11,600 4.2 127 1270
EO,cm-l Mie, Debye A, cm-I D, cm-I 2, cm-*
D
2223
c
A
1550
C
A
1292
C
Thus, the solvent dependent displacement can be expressed
A
168
as
C
Asol= A
+ 6, - 6,=
CHzC12, ref 3
Mode-Specific Parameters 0.41 0.48 -0.28 0.055 0.66 1.03 -0.35 0.08 0.62 0.73 -0.06 0.045 -3.1 -3.8 0.06 0.07
0.25 -0.094 0.45 -0.121 -3.99 0.056
o.ia
A
0.10
Whether the displacements should increase or decrease with solvent polarity depends on the normal coordinate dependence of the change in dipole moment, A& = - jig. If the local field is taken to be the reaction field due to the ground-state dipole moment of the complex, then it is parallel to Gg. The local field F could be expressed as the Onsager reaction field, which depends on the dipole moment, the solvent dielectric constant, and a cavity radius. We prefer to let the experiment tell us how the local field changes from one s21vent to the next. This is done through the knowledge of the 0-0 excitation energy EO,which depends on the local field and the ground- and excited-state dipole moments:
0.00
ze
0.06
0.M 0.00
ia
IS
ir
19
21
29
froquoncy, cm"
21 Zr 2s (Thouunds)
Figure 1. Absorption spectrum of HMB:TCNE in CH2C12, cross section in A2. In Figures 1-5, the triangles are experimental data and the lines are calculated. c
In using eq 12, we neglect any dependence of the dipole moment difference on solvent, which is probably not correct for our system. Nevertheless, we can estimate the difference between the local fields in carbon tetrachloride and dichloromethane. Results The best-fit parameters for modeling the absorption and four Raman profiles were found by minimizing the sum of the x2 error functions for the five spectra. The final parameters are displayed in Table 3, along with those obtained by Myers et al. in CC4, and the experimental and calculated profiles are displayed in Figures 1-5. There are several notable differences in the parameters for the two different solvents. The 0-0 energy for the charge-transfer (CT) transition is about 1500 cm-' less in the polar solvent. This is reasonable in view of the large dipole moment of the excited state. The smaller transition moment in CHZClZ is required by the smaller molar absorptivity in that solvent, which could imply that the mixing is greater (Le., the complex is more strongly bound) in C c 4 . We held the inhomogeneous broadening fixed at 250 cm-', while Myers used no inhomogeneous broadening. We did not find our results to be very sensitive to this aspect of the calculation. The larger amplitude (D)and slower rate (A) of solvent fluctuations in CHzClz could be a consequence of solvent polarity, but we could alter these somewhat and still get a reasonable fit. The most striking comparison is of the mode specific parameters Aa and C,. We find smaller values of the displacement Aa for all four
0 15
16
17
18
19
Frrqurncy, cm'
20
21 22 (Thouaanda)
Figure 2. Raman excitation profile of 2223 cm-' mode of HMB:TCNE in CH2C12. In Figures 2-5 the Raman cross section is in units of A2.
modes, and large negative non-Condon terms Cawere required to reproduce the blue shifts, with respect to the absorption spectrum, of the profiles for the two TCNE modes. We note that were the blue shifts the result of experimental error, for example, in correcting for self-absorption, they would be similar for all four modes. If viewed in terms of mixing of nonbonded and ionic states, the smaller displacements in CHPClz solution are hard to reconcile with the smaller transition moment in that solvent. Turning to the question of local field effects, we are faced with the problem of not knowing how the ground and excited
J. Phys. Chem., Vol. 99, No. 17, I995 6351
Application of Time-Dependent Raman Theory
I
9.00
2
*
A
7.50
6.00
c^
4.60 0
1
3.00
ll
5
1-10 16
16
17
16
19
20
21 22 (Thouomdo)
Froquonoy, om"
Figure 3. Raman excitation profile of 1550 cm-l mode of HMJ3:TCNE in CHZC12.
18
16
17
18
10
20
21 22 (Thou8rnd8)
Frrqurncy, cm"
Figure 4. Raman excitation profile of 1292 cm-' mode of HMJ3:TCNE in CHZC12.
involved in the charge transfer.26 These concepts are easiest to visualize for the low-frequency D-A stretch. To the extent that we can consider it a pseudodiatomic stretch, the normal coordinate for the mode is the donor-acceptor distance. The maximum possible value for the change in dipole moment, obtained in the limit of no mixing, would be &ge % eRDA, which for an intermolecular distance of 3.35 8, is 16 D. The measured dipole moment changes are much less than this, due to mixing. The change in &,, with increasing donor-acceptor distance would tend to be. positive if the distance term dominates, but negative if the overlap takes over. The sign of the nonCondon term for the 168 cm-' mode indicates that the transition moment Mge increases with RDA. The transition moment also depends on the distance and the overlap, so this tends to indicate that the distance term dominates. If this is also true for the dipole moment change, then the displacement of the intermolecular mode should increase (become less negative) as solvent polarity increases, in line with experimental results. The three intramolecular vibrations are in-plane motions. For the postulated structure of the complex, these motions would not perturb the donor-acceptor distance; however, they could result in nonzero values of faAp,$aQ) through the dependence of the overlap on normal coordinate. We can estimate the difference in the local field between the two solvents as follows. Assuming that the ground and excited state dipole moments for CC4 are the same in CHzC12, the difference in the local fields in the two solutions can be estimated from the difference in the energy EO obtained in the fits for the two solvents. Using the values
bge M 5.7D - 2 . 1 D = 3.6D
-
AE, = -A,iige(~cH2Cl, - Feel,) = - 1500 cm-'
L
the result is F c H ~-cF~C~Cx~0.25VIA. This is 1-2 orders of magnitude greater than the value that would be calculated for a dipole of 2.1 D in a cavity with a 5-2.5 8,radius, but it is an experimental result which we can use to estimate (a&&&) and thus the solvent effect on A for the 168 cm-' mode. We take the upper limit of the value for the change in dipole moment, eRDA, to obtain
= eQ(W,~)''* akge/aQ= 0.25 D
4Uge
15
16
17
18
10
20
21 22 (ThOUr8nd8)
Frrqurncy, cm"
Figure 5. Raman excitation profile of 168 cm-I mode of HMB:TCNE in CHZC12.
state dipole moments vary with normal coordinate. Electrooptical and dielectric data for HMB:TCNE have been reported by Liptay et al, who determined pg and pe for the 1:l and 2:l complexes in CCLZ4and for the 1 :1 complex in heptane.25In heptane, pg and pe are 1.3 and 9.5 D, respectively. In CC4, the values are pg = 2.1 D and pe= 5.7 D. The electrooptical experiments also revealed that the angle between the transition moment Mge and the dipole moment change &ge is zero. This is reasonable in view of the postulated structure of the complex, in which the centers of symmetry of the two molecules overlap, and the planes of the two molecules (neglecting the methyl groups) are parallel. Unfortunately, there are apparently no reports of electrooptical measurements on HMB:TCNE in CHzClz. The simple Mulliken theory approach to the estimate of Apge confirms intuitive expectation: the change in dipole moment on excitation is a function of the distance through which the charge is transferred, RDA,and the overlap of the orbitals
With the estimate of the local field difference given above, and using eq 11, the predicted solvent effect on the displacement for the donor-acceptor mode is ACH2C12
'CC14
+ o.62
which compares very favorably to the experimental result: ACH2C1,
= A c c 1 , + 0.70
Since we may have overestimated the derivative of the dipole moment change with respect to normal coordinate (including an overlap-dependent term would probably reduce the value), it is noteworthy that the predicted change in A is smaller than observed, but in the right direction. We have also neglected the change in Apge on going from CC4 to CHzClZ. If mixing is greater in CC4 than CHZC12, then the predicted change in displacement would be even greater if the increase in Apgein CH2C12were accounted for. Thus it would appear that the local field affect can account for the solvent effect on the displacement
6352 J. Phys. Chem., Vol. 99, No. 17, 1995 of the D-A stretch, provided we are willing to accept a much larger local field than would be predicted by continuum dielectric theory. Since this conclusion depends on the values for the parameters A, and EO,it is worthwhile to consider the sensitivity of the modeling procedure to these parameters. Our reduced magnitude of the fitted value of A, for the 168 cm-l mode, compared to that reported by the Myers group, is expected on the basis of the relative magnitudes of the experimental Raman crosssections. At 588 nm, we find OR to be about 17 x lo-" A*, which is approximately 40% of the value of 40 x lo-" A2 reported by Myers et al. at the same wavelength. The lowered value of A, accounts for 67% of this decrease, while the reduced transition moment (3.6 D in CHZC12 compared to 4.2 D in CC4) further decreases the Raman cross section by about 54% for a total reduction of 36% in the calculated cross section, in good agreement with experiment. The transition moment is determined quite well in the modeling because the absorption cross section is known quite accurately. A reasonable fit to our absorbance and Raman profiles could not have been obtained using the same A, as was reported in ref 11. The fitted profiles are also quite sensitive to the value of the 0-0 energy. Had we used a value of EO as large as that reported in ref 11, our calculated profiles would have been blue-shifted with respect to the experimental ones, unless we decreased the solvent damping (D of eq 5) to the point where the calculated absorbance profile would be too narrow and the Raman cross sections too small. Thus we feel that our analysis of the local field effect on A, for the 168 cm-' mode is based on fitting parameters that are fairly well determined. In the case of the three inGamolecular modes, it is difficult to predict even the direction of the change in A, with increasing solvent polarity. Referring to the Mulliken picture presented earlier, the solvent dependence of the displacement for an intramolecular mode should depend on whether the mixing of the nonbonding and ionic wave functions increases or decreases with normal coordinate. The sign of the normal coordinate is arbitrary, but we have taken the displacements for the two TCNE modes to be positive in order to reproduce the expected increase in C=C and CN ' bond distances in the CT state. Once the sign of A, is fixed as positive, one concludes that if mixing happens to increase as the bond stretches, then (aAp,JaQ) should be negative and the displacement for that mode should decrease as the local field increases. However, if mixing increases as the C=C and CEN bond lengths increase, then the transition moment derivative (aMg&3Q) should be positive, in disagreement with the significant negative non-Condon terms observed for these two modes in dichloromethane solution. Clearly, the simple two state picture of Mulliken and the local field approach cannot both be correct in this situation, as they would predict a relationship between the solvent dependence of A, and the sign of C , opposite to that which is observed. The local-field analysis does not take into account inherent differences in the complex in the two different solvents. Given that all four displacements shown in Table 3 are smaller in magnitude in CH2Clz than in ccl4, we might conclude that mixing is stronger when the complex is dissolved in the former solvent. This appears to contradict the conclusion reached on the basis of the transition moment being smaller in CHzC12. If the smaller transition moment reflects less mixing, then we would also expect the change in dipole moment to be greater in CH2C12. This would further amplify the solvent shifts in the A,'s, perhaps to the extent that the observed decreased values in dichloromethane might not reflect the mixing in the complex. The most troubling difference in the two sets of parameters is
Britt et al. TABLE 4: Depolarization Ratios of HMB:TCNE in CHzClz assignment VDA
HMB TCNE TCNE TCNE
freq, cm-I 165 1292 1530 1550 2223
e 0.34 0.34 0.37 0.35 0.44
the large negative non-Condon factors obtained for the TCNE vibrations in CH2C12 but not in CC4. Lacking a simple theory, such as the local field approach used for the solvent dependent displacements, it is difficult to account for this result. It is significant that the Raman band in the vicinity of the CEN stretch has a pronounced asymmetry. We found it was best fit by two Gaussians, one centered at 2223 cm-' and a less intense one at 2230 cm-'. The area of the former was used to generate the REP for the totally symmetric C F N stretch, because the weaker scattering at 2230 cm-I is believed to be due to the nontotally symmetric CEN stretch. Also of note is the small deviation of the depolarization ratio of this band from the value of '/3, as shown in Table 4. The value e = '13 is characteristic of totally symmetric vibrations deriving resonance enhancement from a single nondegenerate electronic state. (Since the depolarization ratio of the two components of the band due to CEN stretching would be subject to errors in numerically separating the two components, we report e for the entire band.) To attempt to understand these puzzles, we present some of the qualitative features of our results on the semiempirical (INDO) quantum mechanical calculations of the spectra and potential energy surfaces of HMB:TCNE.6 Of interest to the present study is the calculation of the ground- and excited-state potential energy surfaces as a function of relative translational motion of the two molecules in a plane perpendicular to the line connecting the centers of symmetry in the symmetric (C2") form. Figure 6a,b defines the coordinate system and depicts the relative angular orientation of the two minimum energy configurations obtained by rotating one molecule with respect to the other about the z axis, which is perpendicular to the planes of the two molecules. The ground-state surface was found to have a shallow minimum at the symmetric configuration as well as minima at displaced geometries. For the orientation shown in Figure 6a, there are minima at the two equivalent positions x = 2 A, y = -0.5 8,, and x = -2 A, y = 0.5 A, in addition to the minimum at x = 0, y = 0. (The x, y coordinates locate the center of the TCNE molecule relative to the origin fixed in the HMB center of symmetry. The equivalence of the two displaced minima is a consequence of the gearing of the methyl groups.) The difference in energy of these two minima is only about 2 cm-', and the barrier between them about 200 cm-'. In the orientation shown in Figure 6b, which is calculated to be 100 cm-' lower in energy than the form shown in Figure 6a, the symmetric geometry is only a local minimum on the xy potential energy surface. The minima at x = 1 A, y = 1.75 A, and x = - 1 A, y = - 1.75 8, are 164 cm-' lower than the energy at x = 0, y = 0. We found the excited-state surface of HMB: TCNE to have a maximum at the symmetric configuration and minima at displaced geometries. The well depths and barriers to different configurations on the excited state surface are much larger than those on the ground-state surface. There are actually two closely spaced CT transitions which carry oscillator strength. The splitting of the two excited states varies with relative position of the two molecules, up to about 2000 cm-I. This can be viewed as a consequence of the splitting of the otherwise doubly degenerate donor HOMO by the presence of the TCNE molecule. The oscillator strength of these two transitions is a strong function of the relative position of the two molecules.
Application of Time-Dependent Raman Theory
a
J, Phys. Chem., Vol. 99, No. 17, 1995 6353
a
Figure 6. Symmetric (C2J structures for the HMB:TCNE complex.
Figure 7. Distorted (C,) structures for the HMB:TCNE complex.
For example, at an intermolecular separation of 3.1 A, and at x = y = 0, the oscillator strengths for the first and second CT transitions are zero and 0.26, respectively. At the displaced geometry, x = y = 0.5, and for the same intermolecular distance, the oscillator strengths for the first and second CT transitions are 0.04, and 0.15 respectively. In the orientation shown in Figure 6a, the first CT transition carries zero oscillator strength and the second CT transition carries maximal oscillator strength. The results of the quantum mechanical calculations lead us to consider the possibility that the differences in the HMB:TCNE complex in the two solutions go beyond mere differences in stability (i.e., “mixing”). Given the fluxional relative geometry of the two molecules permitted by the shallow ground state surface, could solvent interactions favor two different equilibrium geometries in the two solutions? As previously mentioned, experimental evidence suggests that in CCb, HMB:TCNE assumes a symmetric configuration, for example, one of the CzVsymmetry forms shown in Figure 6. If the complex assumes a less symmetrical form in CHZClz, such as one of the C,forms shown in Figure 7, one consequence would be that the transition moments for the TCNE locally excited (LE) z-z* and CT transitions would no longer be perpendicular, as they are in the symmetric form. The LE and CT excited states could then couple and lead to B-term Raman activity. Vibronic coupling of the LE and CT states will result in off-diagonal elements of the polarizability tensor for vibronicly active modes, resulting in depolarization ratios which differ from ‘/3. The apparent blue shifts of the REPS for the TCNE C=C and C S N vibrations could be considered to result from the resonance effect of the TCNE LE state. Though it would appear that such a contribu-
tion would require modeling the Raman and absorption profiles with additional parameters for the LE state, we show in the next section that the non-Condon factors do the job of accounting for this coupling and provide clues about the geometry of the complex. The large difference in the absorption cross section of the complex in the two solvents could be a consequence of LE-CT intensity borrowing and the dependence of the transition moment on the ground-state equilibrium geometry rather than just due to a difference in complex stability. As our calculations have shown, the oscillator strength is a sharply varying function of complex geometry, so even a slight distortion could greatly perturb the transition strength.
Conclusions The difference in fitting parameters for absorption and Raman spectra of HMB:TCNE in two different solvents cannot be accounted for simply in terms of differences in the solvent local field or solvent dependence of Mulliken-type mixing. Clearly, the surprising difference in the electronic transition moment, which is unexpectedly less in CH2C12 than in CC4, hints at structural differences in the complex in the two different solvents. The fact that the 1:l complex can bind a second donor to form the 2:1 species in CCb but not in CHzClz also suggests that the structure of the 1:l complex is different in the two solvents. We speculate that the complex assumes a less symmetrical form in the polar solvent compared to the nonpolar one and that the lowered symmetry permits coupling of the CT and TCNE LE transition moments. The contribution of the LE state to the TCNE resonance Raman intensity is responsible for the apparent blue shifts of the TCNE profiles.
6354 .I. Phys. Chem., Vol. 99, No. 17, 1995
Non-Condon contributions to the intensity are equivalent to intensity borrowing via vibronic coupling.z9 Though Albrechtderived expressions for B-term Raman scattering using a Herzberg-Teller expansion of the non-Bom-Oppenheimer states?O B-term scattering can also be viewed to result from coordinate dependence of the transition moment. The two views are compared by equating the following:
Aes e
where = - l$ is the zero-order energy of the two vibronically coupled states, and the matrix element in the numerator, h:, = (VII &!Z/8QalYs) vanishes unless the direct product of the irreducible representations (ir reps) to which electronic states e and s belong contains the ir rep of normal coordinate Qa. In either of the CzVgeometries shown in Figure 6, the z-polarized CT state is totally symmetric, as is any TCNE vibration which is totally symmetric in the free molecule. The LE state is x-polarized in the geometry of Figure 6a, so vibronic activity of totally symmetric TCNE vibrations is forbidden by symmetry. (The localization of the LE state on TCNE allows us to neglect vibronic activity of HMB modes.) If the complex is distorted as shown in Figure 7a, the only remaining symmetry element is the ~ ( x zreflection ) plane, which contains the C=C bond of TCNE. The CT transition moment is parallel to this plane, so both the x-polarized LE state and the CT state belong to the totally symmetric representation, permitting vibronic activity of totally symmetric modes. Altematively, we could envision a distorted .structure which preserves the symmetry plane perpendicular to the C=C bond (Figure 7b). In this form the LE state would correspond to the A’ ir rep, while the CT state remains totally symmetric, A‘. In this geometry totally symmetric vibrations would be inactive, but nontotally symmetric C Z N vibrations such as the mode at 2247 cm-’ in free TCNE>1,32which transforms as A’ in this geometry, would become allowed. An even lower symmetry complex would of course permit vibronic activity of both types of TCNE modes, in agreement with our observations and the calculated ground state potential energy surface. Is the fairly large magnitude of the fitted non-Condon terms for TCNE normal modes reasonably explained by vibronic coupling? The LE transition of TCNE has an oscillator strength f0,, vgs\Mgsl2 on the order of one and peaks at about 50 000 cm-l, while the CT transition has an oscillator strength on the order of 0.1 and a peak frequency of about 20 000 cm-’. Thus the unperturbed LE transition moment is about twice that of the CT transition. For the LE-CT energy level separation of 30000 cm-’, the coupling strength would have to be on the order of h:, x 4500 cm-’ to get a non-Condon term Cawith an absolute value on the order of 0.3. (Though the energy denominator A@, is negative, we cannot predict the sign of the coupling strength.) The energy of the perturbed CT transition would then be red-shifted by about (h,“J2(Q)/AESe % 350 cm-’. Thus part of the red-shift we observe for the complex in CH2Cl2 complared to C C 4 could be due to LE-CT coupling being present in the polar solvent. (The reduced value of the transition moment in CH2C12 is not due to this coupling, as it is the transition moment for the equilibrium geometry. Instead, it reflects the dependence of the CT transition moment on the equilibrium geometry, which is different in the two solutions.) Thus a fairly large non-Condon term can result from vibronic coupling which exerts only a small perturbation on the absorbance spectrum. 0~
Britt et al. We can use our fitted value of D from the stochastic solvent broadening model to estimate the solvent reorganization energy A, to be about 6200 cm-l. This compares to the value of about 4000 cm-I obtained by the Myers group in CC4. These values are much larger than what would be predicted by modeling the solvent as a dielectric continuum:27
Here EO is the static dielectric constant and n is the refracti!e index. Assuming Apgeis 3.6 D and the cavity radius a is 5 A, the solvent reorganization energy given by eq 14 would be about 115 cm-I in CH2C12, and nearly zero in CC4. Even if the excited-state dipole moment were as large as 16 D, the predicted value of A, would only be about 2300 cm-’ in CH2Cl2. Solvent reorganization energies determined from fitting the line shapes of CT emission have been found to be in the range 4000-8000 cm-1.27,28Failure to account for all the internal modes coupled to the transition may account in part for a value of A, which is too large, but the similarity of the magnitudes obtained in this work and that of Myers to those obtained with the assumption of one or two internal mode^^',^^ suggests a physical basis for the failure of dielectric continuum theories to account for the solvent reorganization energy. Since our attempt to account for the solvent effect on the D-A displacement also requires local fields large compared to the Onsager reaction field, the underlying basis for these discrepancies may be the local solvent structure. Recent photochemical hole-buming studies of octatetraene in an n-hexane crystal have observed surprisingly large local fields, about 0.01 V/A, for a nonpolar host molecule.33 We speculate that part of the “anomalously” large reorganization energy we observe in our polar solvent merely reflects the fact that the local field is much larger than that predicted by continuum dielectric theory. The conclusion reached here that the solvent actually decides the equilibrium geometry of the complex indicates that the solvent is strongly coupled to the CT interaction and thus to the CT electronic transition. The apparent success of either time-dependent or transform theory in modeling Raman excitation profiles of this weakly bound complex is somewhat surprising, given that the usual “standard assumptions” are probably not valid for this system. The observed absorption spectrum is no doubt the result of two closely spaced CT transitions, polarized in the same direction. The low-frequency mode is probably quite anharmonic, though no overtones are observed (or expected) that would reveal the degree of anharmonicity. If the complex goes from a symmetric form to a distorted form on excitation (in CCL), as our calculations suggest, then Duchinsky rotation should be considered, although it would probably not affect the intramolecular vibrations. For the case of the D-A and C=C stretches, it is probably inaccurate to neglect the change in vibrational frequency in the excited state. In addition to the D-A stretch which is observed, it may be that some of the remaining five intermolecular modes are also coupled to the electronic transition. Though they are not observed, due to the inherently weak resonance Raman intensity of low-frequency vibrations, they may have significant displacements in the excited state. Part of our large solvent reorganization energy could be compensating for the neglect of these modes and of other weak intramolecular vibrations. Perhaps it is the failure of the system to adhere to the standard assumptions which causes the results of transform theory and time-dependent theory to differ. Going beyond the standard assumptions could quickly lead to a proliferation of parameters and would not be prudent in view of the limited quality and quantity of data.
Application of Time-Dependent Raman Theory
Acknowledgment. The support of the National Science Foundation for this work is gratefully acknowledged. We thank Anne Myers for helpful conversations and for providing us with a copy of her computer program. References and Notes (1) Smith, M. L.; McHale, J. L. J. Phys. Chem. 1985,89, 4002. (2) McHale, J. L.; Memam, M. J. J. Phys. Chem. 1989,93, 526. (3) Britt, B. M.; Lueck, H. B.; McHale, J. L. Chem. Phys. Left. 1992, 190, 528. (4) Emery, L. C.; Sheldon, J. M.; Edwards, W. D.; McHale, J. L. Specfrochim. Acta 1992,48A, 715. ( 5 ) Edwards, W. D.; Du, M.; Royal, J. S.; McHale, J. L. J. Phys. Chem. 1990,94, 5748. (6) Emery, L. C.; Edwards, W. D., to be submitted. (7) Hanazaki, I. J. Phys. Chem. 1972,76, 1982. (8) Prochorow, J.; Tramer, A. J. Chem. Phys. 1967,44, 4545. (9) Russel, T. D.; Levy, D. H. J. Phys. Chem. 1982,92, 2718. (10) Prochorow, J.; Tramer, A. J. Chem. Phys. 1966,47, 775. (1 1) Markel, F.; Ferris, N. S.; Gould, I. R.; Myers, A. B. J. Am. Chem. SOC.1992. 114, 6208. (12) Heller, E. J.; Sundberg, R. L.; Tannor, D. J. Phys. Chem. 1982, 86,1822. (13) Lee, S.-Y.; Heller, E. J. J. Chem. Phys. 1979,71, 4777. (14) Tannor, D. J.; Heller, E. J. J. Chem. Phys. 1982,77, 202. (15) Moore., J. C.:, Smith., D.:, Youhne., Y.:, Devlin. J. P. J. Phvs. Chem. lgl,75,325. (16) Murrell, J. N. J. Am. Chem. SOC.1959,81, 5037.
J. Phys. Chem., Vol. 99, No. 17, 1995 6355 (17) Lyons, L. E.; Palmer, L. D. Aust. J. Chem. 1976,29, 1919. (18) Chan, C. K. J. Chem. Phys. 1984,81, 1614. (19) Tmlson, M. 0.; Mathies, R. A. J. Chem. Phys. 1986,84, 2068. (20) Mulliken, R. S.; Person, W. B. Molecular Complexes; Wiley: New York, 1969. (21) Myers, A. B.; Mathies, R. A. In Biological Applications of Raman Spectroscopy; Spiro, T. G., Ed.; Wiley: New York, 1987; Vol. 2, p 1. (22) Sue, J.; Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1986,85, 462. (23) Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1987,86,6085. (24) Liptay, W.; Rehm, T.; Wehning, D.; Schanne, L.; Baumann, W.; Lang, W.; 2. Naturforsch. 1982,37a, 1427. (25) Liptay, W. In Excited States; Lim, E. C., Ed.; Academic: New York, 1975; Vol. 1, p 129. (26) Merriam, M. J.; Rodriguez, R.; McHale, J. L. J. Phys. Chem. 1987, 91, 1058. (27) Cortes, J.; Heitele, H.; Jortner, J. J. Phys. Chem. 1994,98, 2529. (28) Gould, I. R.; Noukakis, D.; Goodman, J. L.; Young, R. H.; Farid, S . J. Am. Chem. SOC. 1993,115, 3830. (29) Warshel, A,; Dauber, P. J. Chem. Phys. 1977,66,5477. (30) Albrecht, A. J. Chem. Phys. 1961,34, 1476. (31) The non-totally-symmetric stretch of TCNE, at about 2247 cm-' in the free molecule, has b~~symmetry in a coordinate system having the y axis along the C-C bond and the x axis perpendicular to the plane of the molecule. (32) Hinkel, J. J.; Devlin, J. P. J. Chem. Phys. 1973,58, 4750. (33) Gradl, G.; Kohler, B. E.; Westerfteld, C. J. Chem. Phys. 1992,97, 6064. JP9430901
