9017
J. Phys. Chem. 1995, 99, 9017-9026
Absorption, Fluorescence, and Resonance Raman Spectroscopy of the Hexamethylbenzene/ Tetracyanoethylene Charge-Transfer Complex: Toward a Self-consistent Model Kristen Kulinowski? Ian R. Gould? and Anne B. Myers*,? Department of Chemistry and Center for Photoinduced Charge Transfer, University of Rochester, Rochester, New York 14627-0216, and Research Laboratories, Eastman Kodak Corporation, Rochester, New York 14560-2109 Received: March 1, 1995@
The weak, far-red fluorescence spectrum of the hexamethylbenzenehetracyanoethylenecharge-transfer complex has been measured in C C 4 and cyclohexane solvents. The total fluorescence quantum yield in C C 4 with 633 nm excitation is about 5 x The absorption spectrum, absolute resonance Raman excitation profiles, and fluorescence spectrum in C C 4 are simulated with a common model that explicitly includes the 11 most strongly Franck-Condon-active internal vibrations as well as the solvent, treated as an overdamped Brownian oscillator. The fits to the data require a large (2450 cm-I) “solvent” reorganization energy, which may involve a combination of true solvent motions and very low-frequency intermolecular complex vibrations. The same model is used to calculate the nonphotochemical return electron-transfer rate and compared with previous measurements of the ion-pair lifetime. This represents the first time, to our knowledge, that all four pieces of data (absorption, fluorescence, Raman, and electron-transfer rate) have been simulated with a common model and compared with experimental results.
Introduction Molecular electronic radiationless transitions in the weak coupling (nonadiabatic) limit are generally described by a Fermi Golden Rule expression that involves the product of an electronic matrix element and a Franck-Condon weighted density of states. Electron transfer in the highly exoergic “Marcus inverted region” (see Figure 1) is one such process. The usual expressions for electronic absorption and fluorescence spectra depend in a very similar way on a product of electronic and nuclear factors, and a number of workers have remarked on and/or attempted to utilize this analogy in the prediction or interpretation of electron-transfer rates.’-I5 In particular, it has been noted that the Franck-Condon part of the Golden Rule expression for electron transfer is identical to that for photoemission with a hypothetical “zero-frequency” photon. Both involve a product of vibrational overlap integrals between the initially populated levels of the upper electronic state and the possible acceptor levels of the lower state; in the radiationless transition the acceptor levels are those isoenergetic with the initial states, while in photoemission some of the exoergicity of the process appears in the emitted photon and the relevant Franck-Condon factors involve lower energy vibrational states. The analogy between one-photon electronic spectroscopy and radiationless transition rates has not, however, proved particularly useful for revealing the specific vibrational modes that are coupled to electron-transfer transitions, even in systems in which both spectroscopic and “dark” transitions coupling the same pair of electronic states can be observed. This is principally because electronic spectra involving a large degree of charge transfer are usually very diffuse and reveal little, if any, vibrational structure. Resonance Raman spectroscopy has long been recognized as a valuable technique for extracting the vibrational couplings
* To whom correspondence should be addressed.
’ University of Rochester and Center for Photoinduced Charge Transfer.
*
Eastman Kodak Corporation and Center for Photoinduced Charge Transfer. Abstract published in Advance ACS Abstracts, May 1, 1995. @
0022-365419512099-9017$09.0010
Nuclear Configuration
Figure 1. Relationship among the processes of absorption (a), resonance Raman (b), relaxed fluorescence (c), and nonradiative return electron transfer (d) for the charge-transfer complex DA in the Marcus inverted region.
associated with spectrally diffuse electronic transition^.'^-*^ It has been used successfully in analyzing other fast photochemical processes such as dissociation and isomerization, but only recently has its applicability to unraveling the mode-specific details of electron transfer chemistry been r e a l i ~ e d . ~ . ~ . ~ - ’ The most detailed resonance Raman-based analyses have been carried out on the charge-transfer complex between hexamethylbenzene (HMB) and tetracyanoethylene (TCNE). Both our groupu and that of M ~ H a l recently e ~ ~ measured absolute Raman excitation profiles on resonance with the strong visible chargetransfer band and analyzed the intensities to derive the geometry changes between the ground (neutral) and excited (ion pair) electronic states. McHale’s group measured detailed profiles for only a few of the strongest Raman lines and analyzed their data via the “transform theory” approach which contains the 1924325
0 1995 American Chemical Society
9018 J. Phys. Chem., Vol. 99, No. 22, 1995 effect of the solvent implicitly through its contribution to the experimental absorption band shape. We measured less detailed profiles for all 11 main Raman-active vibrations and extracted the mode-specific geometry changes by directly simulating the absorption spectrum and Raman profiles with a model including 11 molecular modes plus the solvent, treated as a Brownian oscillator in the high-temperature, high-friction limit. While our analysis was quite successful at reproducing the available spectroscopic data, it remained unsatisfactory in two respects. First, the very fast electronic dephasing required to reproduce the absolute Raman cross sections led to a large solvent reorganization energy of 3930 cm-’, which did not seem reasonable in a nonpolar solvent (CCld), and a correspondingly low electronic zero-zero energy of 11 600 cm-’, much lower than expected based on the oxidation and reduction potentials of the donor and acceptor (see Discussion). Second, the report that perdeuteriation of the HMB substantially slows the rate of nonphotochemical return electron transfer in this system26 appeared inconsistent with the insensitivity to deuteriation of the resonance Raman spectra coupling the same electronic states. We have therefore sought further experimental and theoretical approaches that might aid in resolving these questions. In particular, it is evident that the relaxed fluorescence spectrum is a valuable piece of data, as the absorption and fluorescence together severely constrain the possible range of values for the total reorganization energy. Measurement of the complete fluorescence spectrum in this system is difficult due to the weakness of the emission and its location in the near-infrared, but we have now succeeded in making this measurement by employing laser excitation with three different detectors. The process of revising our spectral modeling to incorporate the fluorescence band shape also led us to reexamine the equilibrium constants and molar extinction coefficients for this complex, which must be known accurately in order to either measure or calculate the absolute Raman cross sections. This paper presents the new data on the normal (hlg-HMBITCNE) complex and our revised estimates of the mode-specific vibrational and solvent reorganization energies based on simultaneous modeling of all three pieces of experimental spectroscopic data. A separate paper” revisits the question of isotope effects on the spectra and electron-transfer kinetics.
Experimental Methods Hexamethylbenzene (HMB) and tetracyanoethylene (TCNE) were obtained from Aldrich and used without further purification. For the spectroscopic measurements in CC4, the donor and acceptor were dissolved in spectroscopic grade solvent (Fisher Scientific) at concentrations of approximately 6-7 mM HMB and 0.7-0.9 mM TCNE. An excess of HMB was employed to facilitate dissolution of the much less soluble TCNE. The resulting solutions were calculated using Liptay’s values for the equilibrium constants28to be 0.3-0.4 mM in the 1:l (DA) complex and 0.01-0.02 mM in the 2:l (DAD) complex. The small amount of 2:l complex was neglected in the spectroscopic analyses (Le., all absorption and Raman intensity was attributed to 1:1 complexes). For the absorption and fluorescence measurements in cyclohexane, the solutions were prepared in the same manner in spectroscopic grade solvent. The solutions were calculated using Smith and McHale’s values for the equilibrium constants29to be about 0.5 mM in the 1:l complex and 0.07 mM in the 2: 1 complex. Two less concentrated cyclohexane solutions having a smaller fraction of 2:l complexes (1:l to 2:l complex concentration ratios of 22 and 30, respectively) were found to have fluorescence band shapes indistinguishable from those of the original solutions.
Kulinowski et al. The fluorescence spectrum in CC4 was collected with two different basic experimental setups and three different detectors. This was necessary because no single detector available to us is sensitive over the entire frequency region spanned by the emission spectrum. Excitation was provided by either the 527 nm frequency-doubled output of a mode-locked Nd:YLF laser or the 633 nm output of a CW helium-neon laser illuminating a stationary 1 cm path length cuvette having a volume of about 3 mL. In the first setup, a laser power of 15-25 mW (YLF) or about 5 mW (He-Ne) was focused into the sample with a 50 mm focal length lens, and the emission was collected in a backscattering geometry, focused into a Spex 1870 0.5-m single spectrograph with a 150 groove/mm ruled grating blazed at 800 nm, and detected by a liquid nitrogen-cooled charge-coupled device (CCD) multichannel detector from Princeton Instruments (EEV 1192 x 296 pixel array). Ten exposures of 30 s each were averaged, after which the averaged pure solvent spectrum (essentially a dark base line in the spectral region of interest, where the solvent’s Raman scattering is negligible) was subtracted. Uncomplexed HMB and TCNE each exhibited no detectable emission in the region of the complex’s fluorescence spectrum. The second detection setup employed a Spex Fluorolog-2 fluorimeter with a 0.34-m single spectrograph and either an R928 multialkali photomultiplier or a North Coast Scientific liquid nitrogen-cooled germanium detector. The laser power was about 200 mW unfocused (YLF) or about 5 mW focused (He-Ne), and the emission was collected in a 90” geometry. No degradation of the sample was observed during the course of data collection, and in both experimental configurations the signal amplitude was found to depend linearly on laser power. The fluorescence spectra in cyclohexane were measured only with He-Ne laser excitation and CCD detection. All spectra were intensity corrected using an Optronic Laboratories halogen-tungsten filament lamp. The lamp’s output was reflected into the optical system by a glass slide located at the sample position and coated with Eastman Kodak White Reflectance Coating. The lamp spectrum obtained in this manner was divided into the lamp’s calibrated output, and this ratio was multiplied by each spectrum obtained with that apparatus. This eliminated the wavelength dependence of all optical components the signal encountered in each experimental setup. Due to the large Stokes shift between absorption and fluorescence and the relatively low complex concentrations, reabsorption of the emitted light was negligible, and no reabsorption corrections were made. The corrected spectra from the CCD and germanium detectors were then examined for regions of overlap. Each spectrum had a region where the detector response was so low that correction for wavelength dependence was not sufficient to restore the true band shape. This region began just to the red of the observed fluorescence maximum for the CCD-detected spectrum and just to the blue of the maximum for the germanium-detected spectrum. After these regions were cropped, there was still enough overlap between the two spectra to splice them together with confidence. The photomultiplier data were not used in assembling the final fluorescence spectrum but served as verification of the band shape in the visible region as detected with the CCD. In order to estimate the fluorescence quantum yield in CC4, a higher resolution piece of the total emission spectrum (Raman plus fluorescence) at 633 nm was obtained by using the 5 mW He-Ne laser, focused with a 30 cm focal length lens into the sample in a stirred 3 mL cuvette. The emission was collected in a backscattering geometry, focused into a Spex 500M 0.5-m single spectrograph with a 1200 groove/mm grating blazed at
J. Phys. Chem., Vol. 99, No. 22, 1995 9019
HMB/TCNE Charge-Transfer Complex
500 nm, and detected with the CCD detector. The Raman and fluorescence spectra were measured from about 645 nm (300 cm-l Raman shift) to about 930 nm by using several different spectrograph settings. After sensitivity correction, the Raman cross section for the 2222 cm-' complex band was determined by reference to the cc14 solvent intensities as described p r e v i ~ u s l y ,and ~ ~ the integrated intensity of the part of the fluorescence observable at the same spectrograph setting as the 2222 cm-' Raman line (about 730-775 nm) was determined relative to the Raman intensity: dOF(UL,Us)/dms = a2222(wL){zF(mL,mS)/lz2222(mL,mS)duS}
(
where 02222 is the 2222 cm-' band's resonance Raman cross and ws section, CTF is the fluorescence cross section, and iz~ are the incident and emitted frequencies in cm-'. The total fluorescence cross section was then estimated by ratioing the part of the emission below 900 nm to the total integrated fluorescence spectrum measured with 527 nm excitation as described above. The differences in the fluorescence band shapes between 527 and 633 nm excitation are fairly small (see below). The fluorescence yield is given by
&(wL)= { l d q [ do,(mL,ms)/dmsl}/a,(wL)
(2)
calculated from the "time-dependent" expressions recently summarized in ref 13. The optical absorption cross section at frequency w , UA(O), is given by
where pgeis the electronic transition dipole moment at the ground state equilibrium geometry, n is the solvent refractive index, we, is the electronic zero-zero transition frequency, Bi is the Boltzmann population of vibrational level li) of the ground electronic state, wi is its vibrational energy, Ixi) = @(q)/,~gelIi) is the multidimensional ground vibrational wave function multiplied by the coordinate dependence of the electronic transition moment, Ixi(t)) = exp(-iHet/h)Ixi) is this initial state propagated for time t by the excited state vibrational Hamiltonian, He, and g ( t ) is a solvent broadening function discussed below. The corresponding expression for the fluorescence band shape, ZF(W), is
W
weg+ w,>t - gftA (7)
Here Iw) is a vibrational eigenstate of the excited electronic surface, and Ixw(r)) = exp(-iH,t/h)IX,) where H, is the ground state vibrational Hamiltonian. Since we modeled only the band shape of the fluorescence and not its absolute intensity, t = { Jdms [doR+,(mL,ms)/dms]/ms3}/8nn2cAooA(mL) (3) frequency-independent multiplicative constants in eq 7 are where OR+F is the total cross section for all emission (Raman omitted. Finally, the apparent resonance Raman cross section and fluorescence), c is the speed of light, n is the solvent at excitation and scattered frequencies of W L and ws, respecrefractive index, and tively, is where o ~ ( mis~the ) absorption cross section. The lifetime of the ion-pair state is also estimated as30
A, = S d m L [ o * ( @ q l
(4)
is proportional to the square of the transition dipole moment. The molar extinction coefficient E and equilibrium constant K for the HMB/TCNE complex in CC4, although reported several times in the l i t e r a t ~ r e , ~ ~were % ~ redetermined '-~~ by us independently through the Benesi-Hildebrand method.34 Stock solutions of Hh4B (6 mh4) and TCNE (1.4 mM) were prepared by dissolving each solid in CC4. Experimental solutions were made by mixing between 0.5 and 5 mL of HMB stock solution with 5 mL of TCNE solution and bringing the solution to a total volume of 10 mL by addition of CCL. The absorbance of each solution in a 1 cm path length cell thermostated at 25 "C was measured on a Perkin-Elmer Lambda-9 W / v i s spectrophotometer. In the concentration regime where only 1:1 complexes are important, the Benesi-Hildebrand equation takes the form
where [A], and [D]Oare the initial (stoichiometric) concentrations of acceptor and donor and A is the measured absorbance. (The [A]& term is often dropped, but under our conditions it is not negligible compared with 1.) The extinction coefficient and equilibrium constant were then obtained by plotting [A]d A versus l/[D]o and using eq 5 to obtain (1 [A]olY)/& and l/e from the slope and intercept, respectively.
+
Computational Methods The absorption and fluorescence spectra and resonance Raman excitation profiles for the Hh4BRCNE system were
where L,f(w~- OS)is the line shape of the Raman transition between vibrational levels li) and If) on the ground state surface, and air(w~,ws)is the resonance Raman cross section for this transition, given by
where the symbols are as defined following eq 6. Equation 8 simply indicates that when several different transitions are nearly degenerate (Le., those that start from different thermally populated initial states but involve the same quantum number changes), they appear to contribute to the same experimental Raman band, and their calculated intensities must be summed for comparison with experiment. The algorithms used to calculate the time-dependent overlaps kilxi(t)), hwlxW(t)),and mxi(t)), including thermal population of initial states (li) f IO)), frequency changes between the two electronic surfaces, and nonzero coordinate dependence of the electronic transition moment, have been given e l s e ~ h e r e . ' ~ ~The * ~only . ~ ~ essential difference between the calculations required for absorption/ Raman and for fluorescence is that the roles of the ground and excited electronic states are reversed. The quantity g(t) in eqs 6, 7, and 9 represents electronic pure dephasing due to the solvent. Coupling of the charge-transfer transition to low-frequency motions of the solvent causes broadening and shifting (Stokes shift) of the electronic spectra and damping of the resonance Raman cross sections as long as
9020 J. Phys. Chem., Vol. 99, No. 22, 1995
Kulinowski et al.
the relevant time scale for fluctuations in the solvent-solute interaction is fast enough for the interactions to appear "homogeneous" on the Raman time scale, Le., faster than the ground state vibrational d e p h a ~ i n g .In~ ~principle, g(t) should also include the excited state lifetime decay, but the measured lifetime of '10 ps37 is negligible compared with the pure dephasing. The solvent coordinate was modeled as a single Brownian o s ~ i l l a t o r ' ~ in ~ ~the ~ - overdamped, ~' low-frequency, high-friction limit, where it contributes a Gaussian line shape and a Stokes shift to the electronic spectra. Although the expressions given p r e v i o ~ s l y ~ are * - ~valid ~ in this limit, in the present work we have used the following more general expressions which assume that the oscillator's motion is frictionally overdamped but allow it to have an arbitrary frequency, not necessarily low compared with kT:14,41
gr(t) = -(A/A)[exp(-At) gR(t) = @/A)cot(hpN2)[exp(-At)
- I]
(lob)
+ A t - 11 +
0000
12000
16000
20000
24000
Wavenumber (cm-')
V,
= (2~dtip)n
(1 0 4
where M is the solvent contribution to the reorganization energy, A-' is the characteristic time scale for solvent fluctuations, and p = l/kT. In the high-temperature and slow modulation limits, defined as kT >> fiA and K = N(2;lkr)1'2
