J . Phys. Chem. 1989, 93, 526-529
526
Low-Frequency Resonance Raman Spectra of Some T-T* Electron Donor-Acceptor Complexes Jeanne L. McHale* and Matthew J. Merriam Department of Chemistry, University of Idaho, Moscow, Idaho 83843 (Received: January 19, 1988; In Final Form: May 19, 1988)
The low-frequency resonance Raman spectra of the electron donor-acceptor complexes of hexamethylbenzene-h18and -d18 with the acceptors TCNE and TCNQ, and the complexes of p-xylene-hloand -dIowith TCNE, are reported. The previously observed Raman features of the hexamethylbenzene (HMB)/TCNE complex, assigned to the first and second overtones of the donor-acceptor stretch, are reinvestigated. The mode at about 220 cm-' in HMB-h18/TCNE is observed to shift to 200 cm-' in HMB-d18/TCNE, but the mode at 163 cm-' does not shift with isotopic substitution of the donor. The complexes HMB-h18/TCNQand HMB-d18/TCNQalso show low-frequency Raman bands at 150 and 200 cm-I, but no isotope shift is observed for either band. In light of the conflicting results of these isotopic substitution studies, we consider several alternative assignments of the low-frequencymodes, for example, that they are vibronically activated intramolecular modes. The validity of the pseudodiatomic approximation and the Morse and Lennard-Jones potentials, for the analysis of the donor-acceptor stretching vibration, is considered. On the basis of depolarization ratios and dependence of the low-frequency vibrations on the excitation wavelength and the strength of the complex, the assignment of the mode at 150-160 cm-' to an intermolecular vibration, in HMB/TCNE, HMB/TCNQ, and p-xylene/TCNE, is favored.
I. Introduction The formation of a binary complex from two nonlinear molecules is accompanied by the appearance of six new low-frequency vibrational modes. The investigation of intermolecular vibrations presents an opportunity to probe the intermolecular potential surface. Intermolecular vibrations have been observed in gas-phase van der Waals complexes,' in hydrogen-bonded complexes,2 and in a few n-a* charge-transfer c ~ m p l e x e s . ~We have previously observed4low-frequencyvibrations in the resonance Raman spectra of the a-a* complex of hexamethylbenzene with tetracyanoethylene. In this paper, we examine the effect of isotopic substitution on the low-frequency Raman spectra of a series of solution-phase a - ~ *complexes. The measurement of intermolecular vibrations in weakly bound solution-phase complexes presents a number of experimental difficulties. The totally symmetric donor-acceptor stretch of an electron donor-acceptor (EDA) complex is expected to be IR active, but attempts to observe this mode are hindered by the absorption of the s o l ~ e n t . ~In the Raman spectra of solution-phase complexes, low-frequency modes are easily obscured by the strong Rayleigh scattering. In mixed stack crystals of charge-transfer complexes, the donor-acceptor stretch, vDA, becomes an optical lattice phonon and has been observed in the far-IR spectra of complexes of TCNE with a series of aromatic donors.6 Intermolecular vibrations of crystalline a-a* complexes have been observed in Raman spectroscopy.' In our previous investigation4 of the EDA complex of hexamethylbenzene (HMB) with tetracyanoethylene (TCNE), we observed a mode at 160 cm-' which was assigned to the first overtone of the totally symmetric donor-acceptor stretch, 2vDA. In cyclohexane solution, where both 1:l and 2:l complexes of H M B with T C N E are present, an ad-
-
(1) (a) Robinson, R. L.; Ray, D.; Gwo, D.-H.; Saykally, R. J. J . Chem. Phys. 1987, 87, 5149. (b) Robinson, R. L.; Gwo, D.-H.; Saykally, R. J. J . Chem. Phys. 1987, 87, 5156. (2) (a) Novak, A. Struct. Bonding (Berlin) 1974,18, 177. (b) Marechal, Y. In Molecular Interactions; Ratajczak, H . , Orville-Thomas, W. J., Eds.; Wiley: Chichester, 1980; Vol. 1, p 231. (c) Thomas, R. K. Proc. R . SOC. London, A 1975, 325, 133. (3) (a) Gayles, J. N. J . Chem. Phys. 1968 49, 1840. (b) Klaboe, P. J . Am. Chem. SOC.1967, 89, 3667. (c) Yarwood, J.; Person, W. B. J . Am. Chem. SOC.1968, 90, 594. (d) Rosen, H.; Shen, Y. R.; Stenman, F. Mol. Phys. 1971, 22, 33. (4) Smith, M. L.; McHale, J. L. J . Phys. Chem. 1985, 89, 4002. ( 5 ) Person, W. B.; Yarwood, J. In Spectroscopy and Structure of Molecular Complexes; Yanvood, J., Ed.; Plenum: London, 1973; Chapters l and 2. (6) Rossi, M.; Haselbach, E. H. Helu. Chim. Acra 1979, 62, 140. (7) (a) Chen, F. P.; Prasad, P. N. J . Chem. Phys. 1977, 66, 4341. (b) Chen, F. P.; Prasad, P. N. Chem. Phys. 1976, 16, 175.
0022-3654/89/2093-0526$01 S O / O
ditional Raman mode at 220 cm-' was observed and attributed to the coincidence of the second overtone, 3VDA, and an a,, vibration of H M B involving out-of-plane motion of the methyl groups, I'(C-CH3). The latter is active in the 2:l complex. In this work, we reexamine these assignments in light of the results of isotopic substitution experiments and investigation of the related complexes p-xylene/TCNE and HMB/TCNQ. The observed isotope shifts being less than expected on the basis of the pseudodiatomic approximation, we consider the possibility that the modes in question are intramolecular modes made active in the resonance Raman spectra by vibronic coupling of the charge-transfer and locally excited (acceptor) electronic states. Except for the 220-cm-' mode in HMB/TCNE, which shifts to lower frequency in the presence of deuteriated donor and is attributed to an out-of-plane methyl group vibration, the analysis supports the previous assignment of the other low-frequency modes to intermolecular vibrations. The absence of measurable isotope shifts is attributed to the extreme anharmonicity of the intermolecular potential surface. 11. Experimental Section
HMB, TCNQ, and T C N E were purified by vacuum sublimation. All solvents used were spectrograde or HPLC grade and were used without further purification, except for drying over molecular sieves. TCNQ solutions were sensitive to air as well as water; solutions were prepared in an inert atmosphere and degassed by bubbling with argon. Solution concentrations were adjusted to give optimal absorbances for resonance Raman experiments (see ref 4), and the donor was present in great enough excess to ensure that virtually all of the acceptor was complexed. Raman spectra were recorded with a previously described4 computer-interfaced Raman spectrometer, with excitation provided either by a Spectra Physics 2025 argon ion laser or by a Spectra Physics 375B dye laser pumped by the argon ion laser. The samples were contained in a rotating quartz cell, and 90' scattering geometry was employed. Typical laser powers at the sample were 5-15 mW, and the spectra were recorded as averages as 15-30 scans. The low-frequency features were observed to be very weak and broad and were recorded only at wavelengths very near the maximum absorption in the charge-transfer band, due to the great difficulty in observing the low-frequency modes at excitation wavelengths not near resonance. 111. Results
In Figures 1-3 are shown the low-frequency resonance Raman spectra of HMB/TCNE, p-xylene/TCNE, and HMB/TCNQ, respectively. Spectra of complexes containing both the deuteriated 0 1989 American Chemical Society
T-A*
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 521
Electron Donor-Acceptor Complexes
h
200
I50
A
v , cm-'
Figure 1. Raman spectrum of (a) HMB-h18/TCNE and (b) HMBd18/TCNE in cyclohexane, excited at 514.5 nm.
I
120
I
I
I]
175
200
225
I
150
A V , cm-' Figure 3. Raman spectrum of (a) HMB-h18/TCNQ and (b) HMBd18/TCNQ in methylene chloride, excited at 590 nm.
In the pseudodiatomic approximation," the reduced mass for the donor-acceptor stretch of the 1:l complex is simply calculated from the masses of the donor and acceptor molecules k =
MDMA MD
IO0
120
I40
160
A V , cm
180
200
-1
Figure 2. Raman spectrum of (a) p-xylene-hlo/TCNE and (b) p-xylene-dlo/TCNE in methylene chloride, excited at 476.5 nm.
and undeuteriated donors are shown. For HMB/TCNE the solvent used was cyclohexane, and for the other systems the solvent used was CH2C12. From previous analysis4 of concentration-dependent visible absorption data, we have determined that both 1:l and 2:l complexes of H M B with T C N E are present in cyclohexane solution but that CH2C12solutions of either H M B or p-xylene8 with TCNE contain only 1:l complexes. We have also recently determined that HMB/TCNQ forms only a 1:l complex in CH2Clz s o l ~ t i o n . ~The expected isotope shifts and the experimental results for the three systems are discussed separately below. ( a ) HMBITCNE. In previous work, we interpreted the mode a t 163 cm-' in HMB/TCNE to be the first overtone of an intermolecular mode involving the donor-acceptor distance as the normal coordinate, Using the fundamental frequency of 89 cm-' reported by Rossi and Haselbach,6 we deduced the spectroscopic parameters to be v, = 103 cm-l and x,v, = 7.2 cm-I, where the vibrational energy level of the anharmonic donor-acceptor stretch is given by
E, = (U
+ X)hvc - (U + %)'X,hv,
(1)
On the basis of the above estimates of the frequency and the anharmonicity, the second overtone, 3vDA, would be expected at about 220 cm-l, in good agreement with experimental observation. However, in earlier work we found the relative intensity of the 220-cm-' mode to increase with the concentration of 2:l complexes and suggested therefore that 3vDA might overlap the a', out-ofplane methyl deformation, I'(C-CH3), observed in the hexamethylbenzene infrared spectrumlo at 220 cm-I and active in the 2:l complex. (8) Hoferkamp, L. A.; McHale, J. L., unpublished work.
(9) McHale, J. L.; Merriam, M. J., to be submitted for publication. (IO) Bougeard, V. D.; Bleckmann, P.; Schrader, B. Eer. Eutuen-Ges. Phys. Chem. 1973, 77, 1059.
+ MA
(2)
With this approximation, taking account of the dependence of both v, and x,u, on reduced mass,I2 the first overtone is predicted to shift from 163 to 159 cm-', and the second overtone from 223 to 217 cm-', upon substitution of HMB-h18 with HMB-d18. If we approximate the methyl groups of H M B as point masses, the isotopic shift of the intramolecular I'(C-CH3) mode can be easily calculated from the Teller-Redlich product rule.'* This gives the rough estimate that the I'(C-CH3) mode should shift from 220 to 21 1 cm-l on deuteriation of HMB. In the resonance Raman spectra of HMB/TCNE in cyclohexane, excited at 514.5 nm, we observe the 163-cm-' mode to shift not at all and the 220-cm-' mode to shift to 200 cm-' on deuteriation of the donor, as shown in Figure 1. On the basis of reported studies of isotope shifts in the intermolecular vibrations of van der WaalsI3 and hydrogenbonded c ~ m p l e x e s , it' ~ is not expected that the donor-acceptor stretching vibration have the same reduced mass dependence as a true diatomic stretch. In section IV, we will consider some alternative assignments for the unshifted 163-cm-I mode and discuss qualitatively why isotope shifts of intermolecular vibrations might be anomalous. Nevertheless, the large isotope shift of the mode at about 200 cm-" suggests that it is indeed an intramolecular vibration of HMB due to out-of-plane motion of the methyl groups. In the DZhsymmetry of the D-A-D complex, a totally symmetric combination of the I'(C-CH3) modes on different donors of the same complex could become active by A-term (Franck-Condon) enhancement, provided that the methyl groups are distorted out of plane in the excited state of the 2:l complex. We have shown'5 that the excited state of the HMB/TCNE/HMB complex is distorted away from the symmetry of the ground-state complex by having one short donor-acceptor distance, associated with localized charge transfer. It may be that the methyl groups on one or both of the HMB molecules are also distorted out-of-plane in the excited state of the 2:l complex. We have failed to observe the 220-cm-' mode in solvents where only the 1:1 complex of HMB with TCNE exists. (1 1) (a) Legon, A. C.; Millen, D.J. Faraday Discuss. Chem. Soc. 1982, 73,71. (b) Read, W. G.; Campbell, E. J.; Henderson, G. J. Chem. Phys. 1983, 78, 3501. (12) Herzberg, G. Specrra ofDiaromic Molecules; Van Nostrand Reinhold: New York, 1950. (1 3) Balk, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. J. Chem. Phys. 1979, 71, 2723. (14) (a) LeBue, J. M.; Rice, J. K.; Blake, T. A.; Novick, S.E.J. Chem. Phys. 1986,85, 4261. (b) Georgion, K.; Legon, A. C.; Millen, D. J.; North, H. M.; Willoughby, L. C. Proc. R. Soc. tondon, A 1984, 394, 387. (15) Merriam, M. J.; Rodriguez, R.; McHale, J. L. J . Phys. Chem. 1987, 91, 1058.
528
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989
(b) p-Xylene/ TCNE. Compared to the donor HMB, p-xylene forms a more weakly bound complex with TCNE.16 Linear regression of concentration-dependent optical absorption data8 confirms that, as in the HMB/TCNE system, the dominant stoichiometry in CH2C12solution is 1:1. In Figure 2 is shown the low-frequency Raman spectra, excited at 476.5 nm, of T C N E complexes of p-xylene-hlo and -dloin CH2C12solution. A mode at 159 f 2 cm-I is observed, and no significant isotope shift can be detected. Again, on the basis of the assumption that this band is due to 2VDA, and by use of Y, and xeue for HMB/TCNE to estimate the isotope shift of p-xylene/TCNE, the overtone would be predicted to be red-shifted by about 3 cm-' on deuteriation of the donor. For this weak, broad Raman band, a shift this small would be difficult to measure. In section IV, we weigh the alternative assignment that the band in question is due to an intramolecular mode of the acceptor TCNE versus the possibility that the mode in question is an intermolecular mode with an anomalous isotope shift. ( c ) HMBITCNQ. We have recently investigated the EDA complex of HMB with TCNQ using optical and resonance Raman spectros~opy.~ The X-ray structure of the HMB/TCNQI7 complex reveals that this system is analogous to the HMB/TCNEI8 complex, in that the projection of the H M B onto the plane to TCNQ results in overlap of the donor with the exocyclic double bond of the acceptor. The bond lengths and angles of the C= C-(CN)2 part of TCNQI9 are very similar to those of TCNE.20 The Mulliken a and b coefficients, describing the contribution of the ionic and no-bond wave functions to the wave function of the complex, are essentially the same for HMB/TCNE2' and HMB/TCNQ.22 We therefore expect the interaction of H M B with TCNQ to be similar to that of HMB with TCNE, although the equilibrium constants for association are different.9 Assuming that the force constant of the donor-acceptor stretching mode of HMB/TCNE is the same for HMB/TCNQ, the frequencies of 2vDA and 3vDA are predicted to be 150 and 208 cm-I, respectively, for HMB-h,,/TCNQ. In the pseudodiatomic, anharmonic oscillator model, these vibrational frequencies would shift to 146 and 203 cm-' in HMB-d,,/TCNQ. Figure 3 shows the low-frequency Raman spectra of the HMB-h,, and -dl8 complexes of TCNQ in CH2CI2,excited at 590 nm, the wavelength of maximum absorption in the charge-transfer absorption band. The observed Raman frequencies of 150 and 204 cm-I are in good agreement with the prediction obtained by assuming that the force constant for HMB/TCNE can be transferred to HMB/TCNQ. However, neither band shows an isotope shift, in contrast to the case of the HMB/TCNE system in cyclohexane, where the higher frequency band is red-shifted on deuteriation. Thus, it does not appear, in the T C N Q complex, that the 200-cm-' mode is an intramolecular mode of hexamethylbenzene. In other work,9 we have determined that HMB forms only 1:l complexes with TCNQ in CH2C1, solution. This would tend to confirm our earlier conclusion that the r(C-CH3) vibration of HMB is active only in the 2:l complex with HMB. Unfortunately, the solubility of T C N Q in cyclohexane is too low to enable similar studies of HMB/TCNQ. In the next section, we consider some alternative assignments of the low-frequency modes in these three systems. IV. Discussion
In order to reconsider our previous assignments of the lowfrequency modes of HMB/TCNE, a brief review of the reasons (16) In CH2C12, the equilibrium constants for p-xylene/TCNE and HMB/TCNE are 0.5 and 17 M-I, respectively. See: Michaelian, K. H.; Rieckhoff, K. H.; Voigt, E.-M. J . Phys. Chem. 1977, 81, 1489. (17) Colton, R. H.; Hem, D. E. J . Chem. Sot. B 1970, 1532. (18) Saheki, M.; Yamada, H.; Yoshioka, H.; Nakatsu, K. Acta Crystallogr., Sect. B 1976, 32, 662. (19) Long, R. E.; Sparks, R. A,; Trueblwd, K. N. Acta Crysfallogr. 1965, 18, 932. (20) Little, R. G.; Pautler, D.; Coppens, P. Acta Crystallogr. 1971, 27, 1493. (21) Holm, R. D.; Carper, W. R.; Blancher, J. A. J . Phys. Chem. 1967, 71, 3960. (22) Flurry, R. L. J . Phys. Chem. 1965, 69, 1927.
McHale and Merriam for our original assignments is in order. The depolarization ratios of the 163- and 223-cm-l modes of HMB/TCNE were previouslf observed to be approximately / 3 , suggesting totally symmetric vibrations resonance enhanced via a single excited electronic state. Since the donor-acceptor distance probably decreases upon excitation to the charge-transfer excited state, it is possible for the totally symmetric donor-acceptor vibration and its overtones to be active via Franck-Condon (A term) type e n h a n ~ e m e n t .The ~~ 15&160-cm-' vibration of a series of solution complexes of TCNE with aromatic donors has been previously observed, in resonance Raman, by Voigt et al.,24who assigned it to a totally symmetric vibration, us, of TCNE. In that study, and in this work, the mode in question was found to increase in frequency with the strength of the complex, as would be expected for a donor-acceptor stretch or its overtone. These facts, along with the data on the fundamental frequency vDA reported in ref 6, led us to the assignments of ref 4. Since the isotope shifts are not in apparent agreement with these conclusions, we consider here some alternative assignments: (a) The Mode at 150-160 em-' Is a Totally Symmetric Vibration of TCNE or TCNQ. The a l gscissoring mode of TCNE, us, has been observed and assigned by normal-coordinate calcul a t i o n ~ . ~ The ~ , ~ frequency ~ of this mode, 120-130 crn-l, is somewhat lower than the frequency of the mode of interest. The analogous scissoring vibration of TCNQ, vlo(alg),has been observed2' at about 145 cm-'. We have recently investigated9 the Raman spectra of TCNQ in CHzC12solution and found all totally symmetric vibrations except ulo to be strongly enhanced by the locally excited TCNQ electronic state at 400 nm. Although no low-frequency vibration was observed in solutions of free TCNQ, a mode at 150 cm-I was observed in the Raman spectra of HMB/TCNQ solutions, but only when excitation wavelengths very near the maximum in the charge-transfer spectrum of the complex, 590 nm, were used. It is possible that the scissoring vibration of T C N E or TCNQ is simply resonance enhanced in the complex, but such enhancement would depend upon a change in the NC-C-CN bond angle or a large change in vibrational frequency of the scissoring mode in the excited state of the complex. The frequency of vs(alg)of T C N E has been found not to change much upon addition of an electron;26aneither does the frequency of ulo(alg)of TCNQ.27b The relevant bond angle in TCNQ does not change greatly upon ionization.28 It is therefore not likely that these totally symmetric acceptor modes are enhanced by excitation within the charge-transfer absorption band. (b) The 150-160-cm-' Vibration Is a Nontotally Symmetric Vibration of TCNE or TCNQ Made Active in the Complex by Vibronic Coupling. The b,, vibrational mode of T C N E at 165 cm-' is very close in frequency to the mode in question; similarly, TCNQ has a b,, vibration at 146 cm-l. Assuming that the symmetry of the HMB/TCNE complex in solution is CZu,the charge-transfer excited state would have A I symmetry ( z polarized), and the b,, vibration of T C N E would go over to b2 symmetry. The long axis polarized T-T* excited state of TCNE would also have B2 symmetry in the complex. Thus, vibronic coupling of the charge-transfer (CT) and locally excited (LE) states, via a b,, vibration of TCNE, is allowed. Furthermore, the LE and C T states can be approximated by configurations that differ in M O occupancy by only one electron; thus, they are allowed to interact ~ i b r o n i c a l l y . ~However, ~ there is no overlap of the (23) Albrecht, A. J . Chem. Phys. 1961, 34, 1476. (24) Michaelian, K. H.; Rieckhoff, K. E.; Voigt, E.-M. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 4196. Chem. Phys. Lett. 1973, 23, 5; 1976, 39, 521. (25) Miller, F. A,; Sala, 0.;Devlin, P.; Overend, J.; Lippert, E.; M o m , H.; Varchmin, J. Spectrochim. Acta 1964, 20, 1233. (26) (a) Hinkel, J. J.; Devlin, J. P. J . Chem. Phys. 1973, 58, 4750. (b) Yokoyama, K.; Maeda, S. J. Chem. Phys. 1973,58,4750. ( c ) Takenaka, T.; Hayashi, S. Bull. Chem. SOC.Jpn. 1964, 37, 1216. (d) Rosenberg, A,; Devlin, J. P. Spectrochim. Acta 1965, 21, 1613. (27) (a) Bozio, R.; Girlando, A,; Pecile, C. J . Chem. Sot., Faraday Trans. 2 1975, 71, 1237. (b) Bozio, R.; Girlando, A,; Pecile, C . J . Chem. Sot.., Faraday Trans. 2 1978, 74, 235. (28) Hoekstra, A,; Spoelder, T.; Vos, A. Acta Crystallogr. Secr. B 1962, 28, 14.
n-n*
Electron Donor-Acceptor Complexes
mismatched orbitals, the donor and acceptor HOMOS, based on symmetries from an I N D O c a l c ~ l a t i o n . ~This ~ last fact spoils an otherwise strong argument for vibronic activation of bl, TCNE modes, following the rules of ref 23. Similar arguments apply to HMB/TCNQ, where only a single plane of symmetry exists in the solid-state c0mp1ex.I~ Assuming the solution-phase complex also belongs to the C, point group, vibronic mixing of the LE and CT states via the bl, normal modes is allowed by symmetry. However, the overlap of the mismatched orbitals in the interacting configurations is not zero by symmetry.30 Thus, vibronic activation of bl, vibrations of T C N Q is allowed in the complex. If the modes in question are bl, vibrations of the acceptor, however, then such vibronic coupling would result in a nonzero off-diagonal element of the polarizability tensor. This would lead to a predicted depolarization ratio31p of 3/4, whereas the measured values are close to I / j . Depolarization ratios of 1/3 are observed for totally symmetric modes enhanced by resonance with a single nondegenerate electronic state. (c) The 150-160-cm-' Vibration Is an Infrared-Active Acceptor Vibration Which Becomes Allowed in the Lower Symmetry Environment of the Complex. Again, the likely candidates for this mechanism would be the bl, vibrations of TCNE and TCNQ. In C2, HMB/TCNE, the T C N E vibration takes on b2 symmetry. This is still a nontotally symmetric vibration and would have to be activated by vibronic coupling, which we have ruled out above. In the C, symmetry of the HMB/TCNQ complex, the b,, TCNQ mode is totally symmetric and could be allowed by Franck-Condon enhancement. However, this would depend on a displacement in the normal coordinate for the bl, vibration in the charge-transfer state. As mentioned previously, the NC-C-CN bond angle of TCNQ does not change much on going to TCNQ-, so we do not expect A term enhancement for this vibration. ( d ) The 150-160-~m-~ Vibration Is the Result of Coupling between Inter- and Intramolecular Modes. There has been a great deal of theoretical interest32in the coupling of intra- and intermolecular vibrational modes. In the case of Fermi resonance between a low-frequency intramolecular vibration and uDA, two coupled Raman bands would be expected at similar frequencies. We have not found any evidence for such coupling. V. Conclusions The above considerations lead us to return to our original assignment; the mode at 150-160 cm-I is the first overtone of the totally symmetric donor-acceptor stretch. Certainly one way to rule out the possibility that it is due to TCNQ or TCNE is to try isotopic substitution of the acceptor. Unfortunately, deuteriation of TCNQ leads to a negligible isotope shift2' of the ul0 mode at 144 cm-l. TCNE has no protons and the exotic I3C, 15N derivative would be difficult and expensive to obtain, and it is not certain that there would be a large isotope shift of us anyway. In addition, the unshifted 200-cm-l mode in HMB/TCNQ does not seem to have a likely interpretation in terms of an acceptor or donor vibration, so it would appear that it is probably the overtone 3vDA but that there is no isotope shift. (29) Edwards, W. D.; McHale, J. L., to be submitted for publication. (30) Lipari, N . 0.;Rice, M. J.; Duke, C. B.; Bozio, R.; Girlando, A.; Pecile, C. Inr. J . Quantum Chem., Quantum Chem. Symp. 1977, 11, 583. (31) Sonnich Mortensen, 0.;Hassing, S. In Advances in Infrared Raman Spectroscopy; Clarke, R. J. H., Hester, R. E., a s . ; Heyden: London, 1980; Vol. 6, Chapter 1. (32) (a) Sage, M. L.; Jortner, J. J . Chem. Phys. 1985, 82, 5437. (b) Ewing, G. E. Annu. Rev. Phys. Chem. 1976, 27, 553.
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 529 If the vibration at 150-160 cm-' is a pseudodiatomic stretch, then it might be possible to correlate the spectroscopic parameters u, and xeu, with the experimentally determined dissociation energy of the complex. AH for the 1:l complex of H M B with T C N E has been determined to be -35.3 kJ/mol in CH2Clz solution.33 The dissociation energy De can be roughly approximated by De = -AH R T = 38 kJ/mol or about 3200 cm-'. For the Lennard-Jones potential, this dissociation energy (usually called t) can be related to the force constant, k, for the donor-acceptor stretch, according to De = kr2/72, where re is the equilibrium internuclear (intermolecular) distance. If we estimate re to be 3.5 A, and use the experimentally determined force constant k = 34.2 N/m for HMB/TCNE, the Lennard-Jones expression for De results in an estimate of 35 kJ/mol for the dissociation energy, in good agreement with the experimentally determined value of 38 kJ/mol. For any anharmonic potential, it is simple to calculate the dissociation energy from the spectroscopically determined frequency and anharmonicity. For the Morse oscillator, the wellknown expression is
+
De = u ~ / 4 x e u e (Morse oscillator) (3) The analogous expression for the Lennard-Jones potential is 0.790, = u,2/4x,ue (Lennard-Jones) (4) If one uses the values of u, and xeu, determined in this work, for HMB/TCNE, the above two equations predict De = 370 and 465 cm-I for the Morse and Lennard-Jones potentials, respectively. These values are much smaller than the thermodynamically determined value of about 3200 cm-'. Thus, it appears that the Morse and Lennard-Jones potentials would underestimate the anharmonicity of the donor-acceptor stretch. The large anharmonicity of uDA is probably related to the lack of observed isotope shift of the mode. The intermolecular potential surface for these weakly bound sandwich complexes is expected to be very shallow, and the low-frequency "normal modes" may be strongly mixed. Although the Lennard-Jones potential adequately relates the force constant to the dissociation energy, it fails to account for the anharmonicity that results from this mode mixing. Anomalous isotope shifts of intermolecular vibrations have been reported for other types of weakly bound systems. In hydrogen-bonded complexes, double-minimum potentials and mode mixing can lead to unusual isotope shiftse2 In van der Waals complexes, the isotope dependence of the indirectly determined stretching frequency is not in accord with the pseudodiatomic p r e d i ~ t i o n s . ' ~Previous J~ reports in isotopic substitution in vibrational studies of other charge-transfer complexes have found shifts that are less than e ~ p e c t e d . ~It~not , ~ clear ~ why, in this work, no isotope shift is measured; however, it does not seem possible to assign the unshifted mode to a vibration of the acceptor or donor. In order to better understand these low-frequency vibrations, further theoretical studies of the full intermolecular potential surface of the complexes are in progress.
Acknowledgment. The support of this work through N S F Grant CHE-8605079 is gratefully acknowledged. Registry No. HMB-h18/TCNE ( l : l ) , 2605-01-8; HMB-h18/TCNE (2:1), 16012-18-3; HMB-d,E/TCNE (lzl), 117581-18-7; HMB-dl,/ TCNE (2:1), 117559-34-9; HMB-h,,/TCNQ (lzl), 1171-14-8; HMBd18/TCNQ ( l : l ) , 117559-32-7; p-xylene-hlo/TCNE ( l : l ) , 2590-63-8; p-xylene-dlo/TCNE ( l : l ) , 117559-33-8. ( 3 3 ) Rossi, M.; Buser, U.; Haselbach, E. Helv. Chim. Acta 1976, 59, 1039.
