10475
J . Phys. Chem. 1991, 95, 10475-10485 1-hydroxyanthraquinone were estimated to be 0 and 1.5 D, respectively. Using these values and a cavity radius of 3.4 A derived from the van der Waals volume of the molecule, the difference in solvent reorganization energies is calculated to be about 88 cm-’ for a moderately polar aprotic solvent such as acetonitrile ( e = 37.1, nD = 1.342). For the 1-(acy1amino)anthraquinones this value may well be somewhat larger. For comparison, kT is about 210 cm-I at room temperature. The important result of these estimates is, then, that the net solvent stabilization energy and the tunneling interaction are of the same order of magnitude. Depending on the specifics of dipole moment, cavity, and excited-state energetics, it is quite possible that there will be a subtle interplay between these two interactions. It is entirely conceivable that for one derivative the tunneling interaction would dominate, whereas for another derivative solvation effects may play an important role.
Conclusions The 1-(acylamino)anthraquinones have been established as a new class of ESIPT molecules, in which nitrogen acts as the proton donor. The electron density on the nitrogen can be adjusted by appropriate substitution of the acyl group, and the ground-state pK, of the amide hydrogen correlates with the ratio of tautomer emission intensities. These results can be interpreted in terms of an excited-state equilibrium constant (P= S,(T)/S,(N)), which is influenced by substitution. ESIPT is not always the dominant process; for weakly acidic amides, ISC from the S , ( N ) state is important. The solvent also has a significant influence on K*; in some cases, the effects are comparable to those observed for
changes in substitution. These results, along with semiempirical calculations, show that the asymmetry of the excited-state surface can be sensitively controlled by substituents, allowing the tautomer emission ratio to be varied by at least 2 orders of magnitude. The ESIPT process is extremely rapid ( '/I50 fs-'), which corresponds to S2 SI internal conversion and is much faster than solvation. The second, slow component (k,, = l / r s ) corresponds to an adiabatic ET on the S , surface. The latter process is closely analogous to Kang et al.'s model for the excited-state ET model of BA.9 In addition, we show that the dynamics of the slower E T component can be simulated by a stochastic model for the solvent coordinate employing empirical data on the solvation dynamics of the coumarins.lb ADMA is an interesting excited-state ET example because the change in charge distribution associated with the LE CT conversion is extraordinarily large (Le., pLE pso = 1.3 D and pcT is: 5.5 D)."'sJ Consequently, the solvent sensitivity of the -+
-
-
-
(14) Akesson, E.; Walker, G. C.;Barbara, P. F. J. Chem. Phys., submitted for publication.
fluorescence spectrum of this compound is great, as discussed in the pioneering work on this molecule by Mataga and co-workers and other groups." There are a number of reports on the ultrafast spectroscopy of ADMA.l'C*i" Some papers have reported the emission intensity dynamics a t particular emission wavelengths I(t,XOb,)and interpreted it as if it simply reflects the E T kinetics; i.e., [LE] 0: I(t,Xobs).lie'h'm'nDue to the complex photodynamics that are uncovered in this paper, the [LE] a I ( t , b b ) conjecture is in doubt. 1.4. Outline of This Paper. This paper is organized as follows. The experimental methods are described in section 2. Section 3 presents the basic equations of our application of Kang et al.'s9 empirical linear response theory model for the free energy profiles of the So, LE, and C T states (e.g., Figure 1). This is followed (section 4) by a qualitative discussion of the static absorption and fluorescence data on ADMA. In addition, new ultrafast transient fluorescence measurements on ADMA are presented in section 4. We introduce the adiabatic model and discuss the method for adjusting the parameters of the linear response theory model to yield a good fit of the potentials (Figure 1) to the static absorption and emission spectra. The dynamical application of the model to ADMA is discussed in section 6, including simulations based on the generalized diffusion equation, employing an empirically derived time-dependent diffusion coefficient (D(t)) from measurements on transient Stokes shift of coumarins.lb It is shown that the decay dynamics at a particular wavelength does not simply reflect the ET dynamics in the excited state, at least for ADMA. The remaining section summarizes the key results of this paper.
2. Experimental Methods ADMA was prepared according to the procedure published of Detzer et a1.l'' Spectroscopic samples were purified by column chromatography on silica with an eluent comprised of a 9:l hexane/ethyl acetate mixture. After three repeated chromatog raphy purifications, the compound was further recrystallized from toluene. Purity was verified by NMR, melting point measurement, thin-layer chromatography, and UV/visible absorption and fluorescence spectroscopy. The apparatus for the femtosecond up-conversion has been described e1~ewhere.l~Briefly, the second harmonic of a cw mode-locked Nd:YAG laser (76 MHz) synchronously pumps a two-jet (HITCI; saturable absorber and styryl 8; gain jet) dye laser which produces 70-fs fwhm pulses at 792 nm. After the amplification of the pulse through a gain dye jet (styryl8) pumped by copper vapor laser (8.2 kHz), the second harmonic is produced in 1-mm KDP crystal. A transient fluorescence signal of the compound excited by the UV light (396 nm) is monitored by detecting the light at the sum frequency produced by mixing of the residual fundamental laser with the fluorescence (up-conversion). By convoluting the transient data with the instrument response function and a multiexponential model for the decay, our apparatus is capable of resolving transients as short as 100 fs. The lifetime of the compound was measured by time-correlated single-photon counting. A mode-locked Ar ion laser (Spectra Physics 165) synchronously pumps a cavity-dumped dye laser (Spectra Physics 375) with DCM dye as gain medium. Emission photons are collected by a microchannel plate PMT (Hamamatsu R1564U-01) and amplified (Hewlett Packard 8447F amplifier). The observed instrument response function is about 150 ps.
3. A Solvent Coordinate Model for ADMA According to a linear response theory for the solvent coordinate, the nonequilibrium free energy dependences of the So, LE, and C T diabatic states are FS&) = f/2k,z2 (3-1) FLE(z) = 1/2k,z2+ Fo FCT(Z)= '/2k,(z - 1)' + Fo - AFO
(3-2)
(3-3)
(15) Kahlow, M. A.; Jarzeba, W.; DuBruil, T. P.; Barbara, P.F. Reu. So'. Insrrum. 1988, 59, 1098.
Tominaga et al.
10478 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
0
'.:..--
1
35 0
300
Figure 4. Observed (solid lines) and simulated (broken lines) static fluorescence spectra for ADMA in less po!nr (diethyl ether, 1). moderately polar (ethyl acetate, 2), and very pcbr (N,N-dimethylformamide, 3) solvents. The peak intensities are ricrnclized. The optimized free energy parameters are shown in Table il.
where k , is the solvent force constant. Eo is the energy of the spectroscopic transition between the So and LE states, and A P is the equilibrium free energy change for the LE C T charge separation. z is the solvent coordinate, which is defined as a certain integral of the orientational polarization of the solvent.I6 Figure 1 shows plots of these functions employing empirically determined k,, F,, and AFO; see section 5. In addition to the linear response theory assumption, in order for eqs 3-1-3-3 to be valid, it must be rurther assumed that the vibrational normal modes in each of the diabatic states do not change significantly as the solvent coordinate is varied. This is a common assumption in E T theory. Note further that, in our model, LE and So have perfectly %ested" energy curves versus z . This is based on the assumption that the transition between the diabatic states, So LE, has a very small change in charge distribution. This is reasonable, considering that this transition, in the nonadiabatic, LE limit, is a *A* band of the anthracene ring. Based on the diabatic model, there are two types of optical transitions: So LE ( T T * ) (3-4) So C T (charge-transfer absorption) (3-5) As stated, the former corresponds to a strongly allowed transition, IB2" of anthracene wifh typical emax i= lO4.Ila The e.g., IAl, latter band (eq 3-5) should be significantly weaker since it involves a transfer of charge between the two rings.
400
I
450
500
wavelength, /nm
Figure 5. Steady-state absorption spectra of ADMA in nonpolar (3methylpentane, solid line), moderately polar ( I .4-dioxane, broken-dotted line), and very polar (N,N-dimethylformamide, broken line) solvents.
-
-
-
-
-
4. Experimental Results 4.1. Static Absorption and Emission Spectroscopy. The quantitative arguments of the previous section can be used to make crude assignments of the well-known static spectroscopy of ADMA. For example, static fluorescence spectra of ADMA are shown in Figure 4 by solid lines. These spectra reflect the relaxed excited state of ADMA since the excited-state photodynamics are over the order of picoseconds,IIC~m while the lifetime is many nanoseconds.lla The fluorescence bandwidth and fluorescence Stokes shift increase dramatically as the solvent polarity is increased. These are well-known manifestations of charge-transfer fluorescence bands. It is reasonable to assign the relaxed form of the excited state of ADMA to C T in polar solvents. The absorption spectra in various solvents are considerably more complex as shown in Figure 5. The X < 380 nm region is almost similar to the case of anthracene derivatives for which charge separation is not energetically feasible, except for a slight broadening in the vibronic structure which is more apparent in polar solvent. It will be shown that this broadening is due to an absorption from So to CT; see section 5. In contrast, the absorption spectrum in the 380-450-nm region has a very prominent and peculiar "red tail", which has been noted previously.""J Note that this spectral feature is more prominent (16) van der Zwan,
G.;Hynes, J. T. J. Phys. Chem. 1985, 89, 4181.
400
wavelength/ nm
700
Figure 6. Time-resolved emission srzctra of ADMA in N,N-dimethylformamide. The curves are log-normal function fits to the data (see Figure 7). The times in the figure represent the delay times after the laser excitation.
-
as the solvent polarity is increased. We will show below that the C T absorption. Thus, the red tail is a consequence of So absorption of ADMA involves an overlap of the two electronic transitions, So LE and So CT. This is treated quantitatively in section 5 . In summary, the qualitative features of the static spectroscopies are consistent with the basic model used to construct Figure 1. The relaxed emission spectrum in the polar solvent is assigned So transition. The relaxed absorption spectrum, to the C T which corresponds to a relaxed So species around z = 0 in Figure 1, involves two transitions. The lower frequency band is due to So CT. It is very broad and leads to the red tail in the spectrum. The higher frequency absorption component is sharper with resolved vibronic structure, which is assigned to So LE. 4.2. Ultrafast Spectroscopy. Figure 6 portrays time-dependent fluorescence spectra of ADMA in the polar solvent N,N'-dimethylformamide (DMF) in the time range 0.3-8 ps. The spectra (lines) are 10g-nor11-1al~~ fits to the individual fluorescence transients at various fluorescence wavelengths, as demonstrated in Figure 7. The dynamics at early times ( 0.3 ps have the appearance and dynamic behavior of a charge-transfer band undergoing the transient Stokes shift phenomenon. On Figure 1 this would correspond to an initially excited distribution of molecules in the CT state near z = 0. The transient Stokes shift we observe corresponds to the relaxation of the initially excited CT molecules toward the equilibrium position in CT, namely z = 1. Interestingly, there is no evidence of emission from the LE state as shown in Figure 6 on the t > 0.3 ps time scale. This can be demonstrated by considering the static emission spectra of ADMA in nonpolar solvents for which the emission has a substantial LE component. For example, see spectrum 1 in Figure 8, which is the static fluorescence spectrum of ADMA in 3-methylpentane. Note that this spectrum is considerably blue shifted from the observed transient spectrum in Figure 6 . There is strong evidence
that the transient emission spectra does not result from a substantial contribution of emission from the crude diabatic LE state of Figure 1. (In fact, the situation is more subtle because the LE and CT states are “adiabatically mixed”, but this will be discussed in section 5.) At times earlier than 0.3 ps we have had difficulty using the spectral reconstruction procedure to determine log-normal fits of the fluorescence transients of the type shown in Figures 6 and 7. The problem seems to be that the emission dynamics at the longer wavelength (A > 500 nm) are so complex involving multiple rise and decay components that the multiexponential fitting procedure for the transients fails to accurately mimic the early time ( t < 0.3 ps) dynamics. This is not so severe a problem for the transient data in the 400-500-nm range. However, the experiments do have limited time resolution (Le., valid for t > 100 fs). Due to the complications just mentioned we will limit our current discussion of the t > 0.1 ps dynamics to the blue edge of the spectrum, and specifically 433 nm. This wavelength corresponds to the peak position of the emission spectrum in 3MP, which has been assigned as pure LE fluorescence. Figure 9 shows the fluorescence dynamics of ADMA at 433 nm. The raw data are represented by points, and the line through the data is a best fit three-exponential decay, where the slowest of the three decays corresponds to the long (nanosecond) decay of the excited-state population. The faster decays have an average decay time of 0.27 ps. Analogous data for other solvents are shown in Table I together with the average solvation time. In the table one can see a correlation between the average decay time at 433 nm and the average solvation time, although the former are much smaller than the latter; with increase of the average solvation time, the average 433-nm decay time is increased. It should be noted that additional decay components with amplitudes as large as 50% and 7 d a a y < 50 fs would be difficult to detect in these measurements. In other words, emission measurements with shorter time resolution could, in principle, reveal additional faster decay components. A crude interpretation of the emission at 433 nm is that the LE emission must decay in times much shorter than ( T ~ )as , might be expected for E T in the inverted regime; see section 1. Our analysis suggests that a much more sophisticated analysis involving simulation is required to accurately interpret these dynamics; see section 6 and elsewhere.ls (18) Tominaga, K.; Walker, G . C.; Kang, T. J.; Barbara, P. F.; Fonseca, T. Following paper in this issue.
10480 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
Tominaga et al.
TABLE I: Best Fit Decay Times for the Observed and Simulated Fluorescence Decay Dynamics at 433 nm in Various Solvents"
dimethyl suifoxide acetone propylene carbonate benzonitrile
0.29d,/ 0.28d./ 0.4ld.f 1 .60e
0.367dh 0.921d*'
1.2-1.4 0.67-0.83 2.4-3.4 4.5-4.7
Measurements were made at ambient temperature. * Time constants and preexponential factors for the normalized reaction coordinate time correlation function, A(f) (eq 6-7), were obtained from the independent dynamic solvation experiments using coumarin probes. See ref lb. 'The average solvation times obtained from the time-dependent fluorescence Stokes shift experiments with coumarin probes. See ref lb. d A single-exponential fit. 'A two-exponential fit. The average time is defined by the following equation: ( T ) = A , T , + A ~ T z , where A, and T , are the preexponential factor and time constant of the ith component. 'See ref 1 lm. gThe free energy parameters for the simulation are tabulated in Table 111. The relaxation times and preexponentials are as follows: 0.75 ps (55%) and 2.5 ps (45%). See ref 1b. The free energy parameters for DMF are used in the simulation. The relaxation times and preexponentials are as follows: 0.48 ps (50%) and 6.2 ps (50%). See ref lb. 'The free energy parameters for DMF are used in the simulation. The relaxation parameters and preexponentials are as follows: 2.1 ps (39%) and 6.1 ps (61%). See ref lb. TABLE II: Oscillator Strength of tbe Fluorescent State for ADMA in Various Solvents ET(~O)/ f(solvent)/ solvent kcal mol-' f(3-meth~lpentane)~
~~~~
diethyl ether ethyl acetate pyridine acetone acetonitrile
34.6 38.1 40.2 42.2 46.0
1.08 0.73 0.55 0.56 0.29
"Empirical solvent polarity scale, ET(30). See: Reichardt, C. In Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; Wiley: New York, 1982; Vol. 3. *The oscillator strength U, is approximately expressed asfa: k ~ /where ~ k;~ is the ~ radiative ~ , rate ~ of the fluoresce and is the frequency of the fluorescence maximum. The values off in various solvents are normalized by the value in 3methylpentane.
4.3. Evidence for LE/CT Configuration Mixing. The static and dynamic spectroscopy of ADMA gives clear evidence of strong mixing between the nonadiabatic L E and C T states. Consider the fluorescence spectra in Figure 8, where the abcissa is kig(X). Here, k i is the radiative rate constant, @ is the fluorescence quantum yield, and T , is~ the excited-state lifetime in each solvent. g(X) is a normalized fluorescence shape function."' The integral of each spectrum in Figure 8 can be related to the oscillator strength U, in each solvent as shown in Table 11. f can be approximately expressed as where Y:, is the frequency of the fluorescence maximum. In Table I1 the values offin several solvents are normalized by the nonpolar solvent (3MP) value. The oscillator strength decreases regularly as the solvent polarity is increased. This is due to an increase in the fraction of CT character in the excited state. It is important to note, however, that the increase in C T character is not simply due to a solvent-dependent equilibrium between two weakly coupled states, Le., LE and CT. If a weakly coupled model were correct, then a separate LE emission band would be apparent in Figure 8 in the various solvents. In fact, a L E band is only apparent in the least polar solvent, 3-methylpentane (curve 1). The variation infcan be explained by a strongly coupled (adiabatic) LE/CT model (section 5 ) . This model also explains the time-dependent decrease in integral emission intensity that is apparent in Figure 6. Incidently, this integrated emission intensity
iji -1
O
2
'
2
Figure 10. Theoretical estimates for the adiabatic free energies of the ground state (So) and the two excited states (SI and S,) of ADMA in Nfl-dimethylformamide as a function of the solvent coordinate. The free energy parameters were optimized to simulate the static absorption and fluorescence spectra simultaneously. The obtained values are k, = 13.0 = 0.8 kcal mol-'. kcal mol", hF0 = 10.5 kcal mol-', and HLE,CT
decrease as time increases is not due to the decay of the population of excited molecules, which occurs on a much slower time scale (several nanoseconds).
5. An Adiabatic LE/CT Model 5.1. Simulations of the Static Spectra. The energy profiles in Figure 1 for the diabatic states, So, LE, and CT result from a linear response model for the solutesolvent interactions (eqs 3- 1-3-3). The spectroscopic evidence in the previous sections suggests that the interaction between LE and C T is substantial. Independently, research on E T between organic donor and acceptor shows that electronic matrix elements, HSo,CT = (DAIqD'A-), are on the order of lo3 cm-' for donors and acceptors in contact.I2 The relevant matrix element for the LE/CT mixing is HLE,CT (= (DA*IqD+A-)), but a simple one-electron argument implies that HLE.CT % H%,cT." The electronic coupling between LE and C T can be treated a p p r ~ x i m a t e l yin ' ~ terms-of the two diagonalized states SI and S?
ISl(z)) = CLE(I)(z)lLE)+ CcT'I)(z)lCT) ISz(z)) = CLE(')(z)lLE)
+ CcT(2)(~))CT)
(5-1)
(5-2)
where CLEti) and are coefficients of the LE and C T diabatic states, respectively, and i signifies the adiabatic state ( i = 1 or 2).
The appropriate secular equation is (S-3)
where the diagonalized energies are given by eqs 3-2 and 3-3 and F is the adiabatic energy. The electronic matrix element HLE,cT is assumed to be independent of z (the Condon approximation) (19) (a) Kim, H. J.; Hynes, J. T.J. Phys. Chem. 1990,94,2736; J . Chem. Phys. 1990,93, 5194; Ibid 1990, 93,521 I . (b) By "approximately" we mean
that we do not include a self-consistent treatment of the solute electronic structure and the solvent electronic polarization, as discussed in these references.
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10481
Ultrafast Charge Separation in ADMA and is used as an adjustable parameter. Figure 10 portrays energy profiles for ADMA So, SI,and S2 in DMF. The parameters have been adjusted to optimize the agreement between simulated and observed spectra; see section 5.2. It is interesting to compare the adiabatic states (Figure 10) and the diabatic states (Figure 1). The avoided crossing (located at z = -0.3) alters the energy slightly from the diabatic level of the theory, especially near z = -0.3. In addition, the LE/CT mixing leads to spectral intensity borrowing effects that are essential in modeling the spectra of the compound; see sections 5.2. and 6.3. 5.2. Simulations and Comparison with Experiment. The potentials of Figure 10 can be used in the procedure of Kang et ah9 to predict the absorption and emission spectra Z(u) of chargetransfer compounds like ADMA in polar solvents. The approach is based on a classical model for the solvent coordinate. A more rigorous description of the approach is given in a separate paper.ls According to this theory the So SI absorption band can be expressed as follows.
-
W)g-s,
a
TABLE 111: Free Energy Parameters Obtained from the Simulation of the Static Absorption and Emission Spectra of ADMA in Various Solvents’ E T W,*
solvent kcal mol-’ diethyl ether 34.6 ethyl acetate 38.1 N,N-dimethylformamide 43.8
ks: kcal mol-I
kcal mol-I
4.0 7.0 13.0
3.0 6.0 10.5
AF,d
‘The electronic coupling ( H L E , c T ) is parameterized to be 0.8 kcal mol-’ so as to optimize the simulated absorption and emission spectra in all the solvents. 0.3 is used for the ratio r = ~LCT/WLE, where wcT and /LLE are the electronic transition moments between ground and Dt-Astates and between the ground and D-A* states, respectively. bThe force constant of the free energy of the diabatic states. ‘The free energy difference between the D+-A- (CT) and D-A* (LE) states in the equilibrium.
(5-4)
I d ’ IMS,(4l2 g(vo(z),v-~o(z))ps,(z,t)
Here g(uo(z),lruo(z)) is the normalized vibrational shape, IMs,(z)12 is the square of the electronic transition moment expectation value between So and SI,p%(z,t) is the classical probability distribution function on the So surface, and uo(z) is the frequency that corresponds to the energy gap; e.g., uo(z) = (Fs,(z) - Fs,(z))/h. The electronic transition moment for the band So Si or S, So is given as follows
-
-
Msj(z) = (Sol#$)
(5-5)
Ms,(z) = (SOIH~[CLE(’’(Z)~LE) + Cc~(‘’(z)lCT)l (5-6) MSj(z) = CLE(i)(z)pLE + CCT(’)(Z)pCT
(5-7)
where FLE and are the transition moments of the diabatic states with So. The former quantity can be estimated by measuring k: in 3-methylpentane where the relaxed emission is apparently predominantly due to LE character. In turn, the k: in the very polar solvent D M F gives an estimate for pcT. Actually, for computational simplicity we use the ratio r of the quantity r = pCT/pLEfor the simulation in this paper, where r = 0.3. The corresponding equation to (5-4) for S, So fluorescence, where i = 1 or 2, is given by
-
I(vJ)s,-so
a
Jdz IMs,(z)I2 g(vo(z),Vvo(z)) p s , ( z , t ) ~ ~ (5-8)
where the symbols are analogous to those in eq 5-4. The function g ( u o , ~ u 0 is ) the vibrational shape of the emission or absorption band. It corresponds to the contribution of the band shape that is not due to the solvent coordinate. In other words, g(uo,v-vo) corresponds to the Franck-Condon factors for the various vibrational sequences and progressions in the spectrum, including local phonon interactions with the medium that are not included in the polar solvent coordinate. We make the crude approximation that g(uo,ruo) is not significantly different for LE and CT, both of which involve a excitations of the anthracene ring. This approximation, which seems to be experimentally justified (see below) corresponds to assuming that solvent variation in the spectral shape due to the solvent coordinate is much larger than the variation due to the intrinsic vibrational shape. We obtain an estimate for g(v,,,lruo) by simply recording the ADMA absorption and fluorescence spectra in the nonpolar solvent 3-methylpentane, where the solvent broadening is very small since the emitting state is predominantly LE. The probability distribution function for the static spectra corresponds to the equilibrium distribution. For the static absorption spectrum p(z,t=m)
a
exp(-F&)/RT)
(5-9)
For the relaxed emission spectrum P(zJ=-)
a
exp(-Fs,(z)/RT)
(5-10)
Figure 11. Simulated static absorption spectrum of ADMA in ethyl acetate. The broken line is the observed spectrum. ‘‘SO-S,” and ‘S0-S2” correspond to the transitions from So to SI and So to S2, respectively. “total” signifies the sum of the two absorption bands.
Here, only the S1 state is important since Fs,(z) - Fs,(z) >> R T in the relaxed region of the solvent coordinate, Le., z = 1. Figure 4 compares observed emission (solid lines) spectra of ADMA in various solvents to simulated spectra employing eq 5-8 and a set of best fit parameters (Table 111). A fixed value of r, 0.3, is used for all the simulations. The electronic coupling HLE,CT is set at 0.8 kcal mol-’ for all the solvents as a parameter used to simulate the absorption and emission spectra in all the solvents. Thus, in the simulation for each solvent PFO and k, are the parameters adjusted to simultaneously fit the absorption and emission spectra of ADMA, as shown in Figure 11. The simulated spectrum (“total” solid line) is compared to the observed spectrum (dashed line). Note that the simulated absorption spectrum is the sum of two components, So S, and So Sz transitions, which are largely So CT like and So LE like, respectively. The simulated spectra agree reasonably well with the observed spectra. This seems to indicate that the basic concepts of the Kang et al. model? a classical solvent coordinate and an adiabatic model for the LE/CT interactions, are valid. Apparently, the approximation that g(vo(z),v-vo(z)) is not strongly dependent on z is justified, at least on a semiquantitative level. It is interesting that the simulation in Figure 11 agrees with the experiment in both the structured and the red tail regions of the spectrum. The different components of the spectrum (So S, and So S2)reveal that optical excitation near the maximum of the spectrum (in fact, the laser-induced absorption region, -396 nm) excites both adiabatic excited states. This is an important issue when understanding the ET and observed photodynamics of ADMA, which we discuss in the following section.
- - - -
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6. Dynamical Simulations and the Photodynamics 6.1. General Issues. The results of the previous two sections have important implications for understanding of photodynamics of ADMA and related molecules. Foremost, the analysis of the absorption spectrum reveals that optical excitation at the wavelength of our femtosecond laser produces both S1 and S2popu-
10482 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
400
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Tominaga et al.
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wavelengthhm
Figure 12. Simulation of S2 So fluorescence spectrum for ADMA in N,N-dimethylformamide using the instantaneous probability distribution function just after short pulse laser excitation.
lations, in a roughly 1/2 ratio (seeFigure 11). This provides novel access to the mechanistic understanding of excited-state intramolecular ET reactions. It is interesting that, for BA, the only other molecule that has been analyzed by the Kang et ale9model, the S2state was of much higher energy (and more weakly absorbing). Consequently, S2 is not populated by laser excitation near the maximum. The major factor that distinguishes BA and ADMA is the magnitude of the driving force A P . For BA the ET reaction in polar solvent is in the normal regime. The SI state at z = 0 is L E like, and S2 (z = 0) is much higher in energy and C T like, similar to the normal regime of Figure 2. Thus, the reaction in BA occurs entirely on the SI surface. The situation for the ADMA reaction is different, because it is in the inverted regime. Laser excitation near the spectral maximum populates both SI and S2 for ADMA. It follows from these arguments that there are two distinct ET processes that should be considered, namely
which is diabatic with respect to the SI/S2representation and S,(zzO)
k,(SI adiabatic)
’S1(z=l)
which is an adiabatic ET process on the SI surface. The latter process resembles the Kang et al. model for the ET in BA.9 From the standpoint of contemporary t h e ~ r i e s ’on ~ ,quantum ~~ rate processes in liquids, the model implicated by eqs 6- 1 and 6-2, which partitions the dynamics into the two processes, should only be appropriate when certain approximations are valid. In particular, it is important that the S,/S2energy gap be much larger than RT, which is induced by the case in the relevant region of the potential (z > 0). In addition, the Ycoherence” between SI and S2created by the laser excitation pulse must decay (dephase) before eqs 6-1 and 6-2 can be described as steady-state rate process. Unfortunately, we do not have any specific information on the appropriate dephasing dynamics, although estimates in the literatures for large molecules in solution suggest that dephasing times in the range of 10-150 fs are reasonable.21 This is much shorter than our measurements of the kinetics of the process represented by eq 6-2. In contrast, we estimate that the nonadiabatic ET component (e.g., eq 6-1) is complete within 100 fs and may be influenced by coherent effects; see below. 6.2. Simulation of the S2 So Fluorescence and ket(S2-Sl). Figure 12 portrays a simulation of S2 So fluorescence spectrum
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(20) Hanggi, P.; Talkner, P.; Borkevec, M. Rev. Mod. Phys. 1990,62,251. Borgis, D.;Hynes, J. T. J . Chem. Phys. 1991, 94, 3619. Voth, G. A.; Chandler, D.; Miller, W. H. J . Chem. Phys. 1989, 91, 7749. (21) Shank, C. V.; Becker, P. C.; Fragnito, H. L.; Fork, R. L. In Ufrrufusr Phenomenu VII; Yagima, T., Ycshihara, K., Harris, C. B., Shionoya, S., Fds.; Springer-Verlag: Berlin, 1988.
Figure 13. Simulation of S2 So fluorescence spectrum for ADMA in N,N-dimethylformamideusing the thermally equilibrated probability distribution function in the S2 state.
in DMF according to eq 5-8 using the instantaneous z probability distribution that is prepared by the laser pulse. Figure 13 portrays a simulated spectrum for the S2 So emission in the presence of a relaxed solvent distribution of S2, 1.e.
-
P S ~ ( Z J = ~exP(-&,(z)/RT) )
(6-3)
Note that the spectra in Figures 12 and 13 are very similar since 0) of the initial probability distribution (ps,the peak (z,,, (z,f=O)) prepared by the laser pulse is close to the peak of equilibrated distribution. This implies that the contribution to the total fluorescence of ADMA from the S2state should have the same spectral shape in these figures at all times. In other words, the S2 So band is not expected to undergo a dramatic change due to the solvent dynamics, since the S2potential, which is similar to the zero-order LE state for z > 0.1, is not significantly displaced along the solvent coordinate from the So potential. In contrast, simulation of the SI band (see below) shows a dramatic transient Stokes shift. An qualitative examination of the transient fluorescence experimental data on ADMA (Figure 6) reveals that the fluorescence band shape at times as early as 0.3 ps shows no evidence of S2 fluorescence emission. The simulation presented below is based in part on the assumption that k,,(S2+Sl) is too rapid fs-I) to be observed by our apparatus. We will show that the transient emission data of Figure 6 and the individual transients at 433 nm (Table I; Figure 9) are in agreement with simulation based on this assumption. The rapid rate of the S2 SI ET process is extraordinary! It exceeds the average solvation time of D M F (( T ~ =) 1.O-1.5 ps) by over 1 order of magnitude. It is less surprising when one takes the point of view that this ET process resembles an internal conversion in a large polyatomic molecule with a small S2/S1gap. In the presence of a stationary configuration of the polar solvent molecules around ADMA (which is appropriate at very short times), the S2/S, energy gap is =1400 cm-I, for z = 0, the most probable value of z immediately after excitation by the laser pulse, and for an internal conversion process with such a gap the rapid rate is reasonable. We discuss ket(S2-Sl) in a separate paper1*where we consider the formal definition of ket(S2-S1) in terms of the Kang et aL9 model. The remaining portion of section 6 deals with simulations of the transient fluorescence of ADMA in terms of the instantaneous S2 SI conversion and subsequent adiabatic process on the SI surface. 6.3. Simulation of the SI Probability and Fluorescence Dynamics: Methodology. We now consider a quantitative model for predicting the transient emission of ADMA. The model is based on the adiabatic potentials of Figure 10. Employing the spectroscopic model of section 5 , we can predict easily the initial probability distribution of SI (psl(z,t=O)) and S2(ps,(z,t=O)). The next stage in the simulation is to add the S2population to the SI, which is based on the assumption that k,,(S2-Sl) is unresolvably
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The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10483
Ultrafast Charge Separation in ADMA
5
Figure 14. Time-dependent probability distribution function, p(z,t), for the excited-state electron transfer on the S , surface of ADMA in N,N-
dimethylformamideobtained from a generalized Smoluchowskiequation. A two-exponential function of A ( t ) (eq 6-7) with A , = 0.55, A2 = 0.45, T ] = 0.75 ps, and T~ = 2.5 ps was used for the solvation dynamics. The S, potential surface is also shown in the figure.
Figure 15. Coefficients of the LE state character in the adiabatic (i = 1, 2) states as a function of the solvent coordinate.
A
t /ps
rapid on the time scale of our measurements. In particular, we use the relationship Ps,(z,t=T)
= ps,(z,t=O) + PS*(Z,t=O)
(6-4)
where 7 is a time much shorter than our time resolution. The next stage in the simulation is to calculate the evolution of ps (z,t) due to “polarization diffusion”I6 along the reaction coordinate. The results of this simulation are shown in Figure 14 along with an expanded region of the SI potential. The evolution of ps,(z,t) is calculated using the generalized Smoluchowski equation (GSE).” The GSE describes how the distribution probability on the potential surface diffuses with time and spatial coordinate and is expressed as dp(z,t)/dt = D ( t ) d / d z [ d / d z
+ d(G/RT)/dz]p
(6-5)
with a generalized diffusion coefficient ( D ( t ) ) . G is a potential acting on the system. In our case, G = Fs,(z). According to Hynes2 and Okuyama and O ~ t o b yD(t) , ~ ~ is expressed as D(t) = -((6z)’)h(t)/A(t)
(6-6)
U t ) = (6z 6 z ( r ) ) / ( ( 6 z ) ’ )
(6-7)
with 6z = z - zq (zq = 1 for the CT well). A(t) is the normalized reaction coordinate time correlation function. Experimentally, A(t) can be estimated by the time-dependent fluorescence Stokes shift method using a polar solvation fluorescent probe A(?) = C(t)
(6-8)
where C(t) is defined by eq 4-1. For the simulation in D M F we used the data of Jarzeba et al.lbfor coumarin 153. These authors made biexponential fit of the experimental C(t),i.e., C(t) = A , exp(-t/Tl) A2 exp(-t/r2), where A , = 0.55, 7 , = 0.75 ps, A2 = 0.45, and 7’ = 2.5 ps, giving the average solvation time ( 7 , ) of 1.5 ps. 6.4. Simulation of the SIProbability and Fluorescence Dynamics: Results. The predicted evolution of the probability distribution ps,(z,t) is represented in Figure 14 superimposed on a plot of the S, potential, Fs,(z). The initial coefficient for the simulation is p ( z , t = T ) (eq 6-4), which corresponds to the instantaneous distribution after the unresolvably rapid ket(S2+S1) process. Note that the probability evolves smoothly, as in an ordinary solvation process. Yet, the evolution in S,of ADMA is simultaneously an ET process and solvation process. The ET character of the evolution of the probability distribution is em-
+
(22) For example, see: Wax, N. Selected Papers on Noise and Stochastic Process; Dover Publications: New York, 1954. (23) Okuyama, S.; Oxtoby, D. W. J . Chem. Phys. 1986, 84, 5824.
1
wavelength/ nm
6
Figure 16. Simulated time-resolved fluorescence spectra for ADMA in N,N-dimethylformamide obtained from the probability distribution function shown in Figure 14. The free energy parameters are as follows: k, = 13.0 kcal mol-’, P = 10.5 kcal mol-’, and HLE,CT = 0.8 kcal mol-’. A two-exponential function of A(t) (eq 6-7) with A , = 0.55, A2 = 0.45, T , =. 0.75 ps, and T * = 2.5 ps was used to represent the solvation dynamics.
phasized by considering the dependence of CL#) on the solvent coordinate z, as shown in Figure 15. Note that the LE ‘character” and of SIvaries as z varies because of the strong mixing (HLE,CT) the avoided crossing of the C T and LE states. The SI ET reaction is strongly adiabatic so that the small energy bamer that would be present at z = -0.3 in the “weakly” adiabatic picture is virtually eliminated by the strong mixing between LE and CT. We discuss the ET process in the separate paper, where we introduce a general definition of k,,(t). We now turn to the simulation of the fluorescence dynamics. Figure 16 shows a simulation of fluorescence using the probability distribution functions of Figure 14. For times t > 0.3 ps, the simulation is qualitatively very similar to the experimental spectra in Figure 6, although the band maximum, viax, at t = 0.3 ps is at 469 nm, a shorter wavelength than that in the observed spectrum (498 nm). Evaluating C(t) for the simulated fluorescence spectra using eq 4-1 yields a value of 1.53 ps for the average relaxation time ( T ) ~ This ~ . is very close to the experimentally observed time ( T),,, = 1.7 ps. Thus, the experiment and simulation are in semiquantitative agreement, further supporting the validity of the Kang et al. approach. The similarity of the evolution in Figure 14 and a simple solvation process has been noted above, and in section 4. For a simple solvation process, the potential would be exactly harmonic according to linear response theory. Furthermore, the average solvation time would be exactly Jzdt c(t),i.e., ( T ~ ) .In the present
10484 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
Figure 17. Simulated time-resolved fluorescence spectra for A D M A in N,N-dimethylformamidewith the presence of the added hypothetical fast solvation component. The free energy parameters are as follows: k, = 13.0 kcal mol-’, fl = 10.5 kcal mol-’,and HLErr= 0.8 kcal mol-’. A three-exponentialfunction of A(1) (eq 6-7) with A, = 0.20, A2 = 0.44, A3 = 0.36, = 0.05 ps, T~ = 0.75, and T~ = 2.5 ps was used to represent the solvation dynamics.
case, ( T ~ is) an input to our simulation from solvation dynamics measurements and ( T ~ )= 1.5 ps. and ( T ) further ~ ~establishes ~ The similarity of (7,)to ( the close similarity of the SI evolution of ADMA to a solvation process. It is interesting to compare this behavior to Kang et al.9 simulations of the adiabatic dynamics in SI BA. For this latter compound, this potential energy surface had a shallow minimum near z = 0 due to high L E character. A small barrier (AF*= 0.5 kcal mol-‘) separates this minimum from a much deeper C T minimum; for BA the time-dependent probability distribution has LE and C T peaks at early times as a consequence of the barrier. The time-dependent spectra from SIhave, very roughly speaking, a region of “LE” emission and “CT” emission. The LE emission region can be used to simply measure the time dependent coefficient of LE and ke,. The situation in SI ADMA is very different. The potential of SI ADMA lacks a LE minimum because the c~ reaction is near the barrierless regime, and the H L ~ , mixing removes the cusp in the surface. Another interesting issue in the simulations is the possible inaccuracy of the C ( t ) data derived from the coumarin transient Stokes shift measurements, due to limited time resolution in this type of experiment. Molecular dynamics simulations on transient solvation suggest that there are ultrafast ( 6 0 fs) components of solvation that may be too fast to resolve in state-of-the-art transient fluorescence mea~urements.l~,~~ It is difficult to estimate how important this effect may be in real liquids. We have estimated that unresolvably rapid components with amplitudes in the range of 0-25% would be consistent with the magnitude of the transient Stokes shift we observe in organic aprotic solvent^?^ We have explored the potential impact of these potentially unresolved fast components of solvation dynamics on the SI ADMA problem by doing a simulation for D M F with a C(t) of the form C ( t ) = 0.20 exp(-t/0.05 ps) 0.44 exp(-t/0.75 ps) 0.36 exp(-t/2.5 ps) (6-9)
+
+
The first component is the added hypothetical fast component. The ADMA SI fluorescence simulations using this C(t) are shown in Figure 17. These simulations are even in closer agreement with experiment in the t > 0.3 ps time scale where the spectral reconstruction data are valid. For example, at t = 0.3 ps, the simulated value of v”,,, is 489 nm. This may be new evidence for the existence of unresolved fast components in the emission dynamics. (24) Maroncelli, M. J . Chem. Phys. 1991,94,2084. Fonseca, T.; Ladanyi,
B. M. J . Phys. Chem. 1991, 95, 21 16.
Tominaga et al.
Figure 18. Best fit (solid line) and simulated (broken line) emission decay dynamics at 433 nm for A D M A in N,N-dimethylformamide. A two-exponential function, I ( t ) = 0.61 exp(-t/O.ll p) + 0.39 exp(-r/0.57 ps) fit the transient data best. Note that the vertical axis is In scale.
In our previous work”’ with the picosecond time-correlated single-photon-counting technique, we pointed out that ADMA could serve as a solvation probe molecule, although this compound undergoes E T reaction in the excited state. At the time this seemed surprising. However, we now see that the strong adiabatic coupling of the ET in the inverted regime makes the SI surface be like a harmonic potential, and thus, considering the large Stokes shift of this compound in the polar solvent, ADMA is similar to the more ideal solvation probes.Ib The early time ( t < 0.3 ps) fluorescence dynamics of S, ADMA is interesting from the standpoint of potentially observing the S2 emission before it decays as a result of the rapid Sz SI ET process. As noted above, the best data for analyzing the early time dynamics are the emission transients taken at 433 nm; see Table I and Figure 9. The simulations of the model used for Figure 16, which assumes that k , , ( S p S , ) is unresolvably rapid (instantaneous on the time scale of the simulation), lead to the values shown in Table I for DMF, propylene carbonate, and benzonitrile. The average relaxation time values are very close to the observed values. Figure 18 compares the simulated dynamics at 433 nm to the experimental decay, which was obtained by a best fit convolution and fit algorithm. Obviously, the model agrees with the experiment reasonably well. Note that there are no dynamical adjustable parameters in this model. Some papers have analyzed the dependence of the decay dynamics at the fluorescence blue edge in terms of the viscosity of the solvent in light of the TICT model.’Ith However, in the present work, the variation of the blue edge (433 nm) dynamics as a function of the solvent is primary due to the difference of microscopic solvation times, rather than the viscosity of the solvent. The agreement between experiment and simulation is strong supporting evidence for the two assumptions: First, k,,(Sz+Sl) must be more rapid than fs-’ because 433 nm is in the region where we should have observed any long-lived S2emission. Second, after the rapid internal conversion, the ET reaction is solvent controlled. It is also interesting to note that the average lifetime at 433 nm is much shorter than ( T ~even ) though the dynamics in S, are controlled by solvation diffusion with an average solvation time of 1.5 ps. This is a result of how the spectrum shifts as z evolves, rather than some special fast component to the ET and solvation dynamics. Consequently, the dynamics at 433 nm (or any single wavelength for that matter) should not be interpreted as if the dynamical parameters simply reflect ke,! In order to allow for more general discussion on the ET -rate constant” (ket(f)),a new theoretical definition of k,,(t) and experimental observable for ke,(t) should be introduced. A more rigorous procedure for measuring k,, is discussed ii the separate paper.18 The analysis in this work has shown that a simple relationship, [LE] a I(&,b,,t), is not general for the measurement of E T rate constant, where Z(Aob,t) is a transient emission decay at a particular wavelength. Therefore, it is necessary to construct a more
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10485
J. Phys. Chem. 1991,95, 10485-10492 general definition of the E T rate constant and experimental observable for the measurement of the ET rate as discussed elsewhere.I8
7. Summary The photodynamics of ADMA has been investigated by ultrafast fluorescence measurements in order to explore the role of the solvation dynamics in charge separation processes of an excited state of the organic electron donor and acceptor molecules with a strong driving force (AF‘).All manifestations of the ET process, including static absorption, static emission, and time-resolved emission spectra, can be rationalized in terms of an extension of the strongly adiabatic model of Kang et al.9 The solvent reorganizational effects, rather than the intramolecular vibrational motion, predominantly cause the variation of static absorption
and emission spectra as a function of solvent polarity. The simulation of the static spectra shows that the excited-state ET in polar solvents is in the Marcus inverted regime. The ET kinetics is composed of the two parts: a diabatic process from S2 to SI which corresponds to the faster kinetics (
