3580
J. Phys. Chem. 1996, 100, 3580-3586
Picosecond Kinetic Study of the Dynamics for Photoinduced Homolysis and Heterolysis in Diphenylmethyl Chloride Matthew Lipson, Ashok A. Deniz, and Kevin S. Peters* Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0215 ReceiVed: September 12, 1995X
The kinetics of both the ions and radicals formed upon photolysis of diphenylmethyl chloride, (4methoxyphenyl)phenylmethyl chloride, and bis(4-methoxyphenyl)methyl chloride in acetonitrile and propionitrile are examined by picosecond pump-probe spectroscopy. Both radical pairs and ion pairs are formed directly from a common excited state. In addition, the geminate radical pair decays by electron transfer to form either the contact ion pair or a covalent bond, as well as undergoes diffusional separation to free radicals.
Introduction Photoexcitation of many aromatic alkyl halides in polar solvents yields products due to the formation of both ion pairs and radical pairs, Figure 1.1-3 A central question raised by these observations is, do both of these reaction pathways proceed directly from a common excited state? Since the ion pairs are energetically more stable than the radical pairs in polar solvents, does electron transfer occur within the geminate radical pair to form the contact ion pair? In this work, we report the results of picosecond pump-probe spectroscopy experiments that follow the kinetics of both the radicals and ions formed and thereby address these issues. We have previously reported picosecond pump-probe studies of the ion pairs formed upon photolysis of diphenylmethyl chloride (DPMC), Figure 2, in acetonitrile and propionitrile.4,5 The decay of the absorption of the diphenylmethyl cation, on the sub-nanosecond time scale, is modeled well by a four state model: the DPMC molecule, a contact ion pair (CIP), a solvent separated ion pair (SSIP), and free ions (FI), where the CIP is formed within the duration of the laser pulse.
Figure 1. Scheme of the photocreation of ion pairs and radical pairs from alkyl chlorides in polar solvents. In polar solvents, the ion pair is lower in energy than the radical pair.
SCHEME 1
With this model in place, we used an Arrhenius analysis to measure the activation barriers that separate these states and concluded that the conversion of CIP to DPMC occurs under conditions of solvent polarization caging, in which the rate of reaction is controlled by the rate of solvent reorganization.5 We herein extend our previous studies of ion pair dynamics to include two methoxy substituted derivatives of DPMC, Figure 2, as well as investigate the dynamics of the geminate radical pairs. Although we limit these studies to diarylmethyl chlorides, a number of photolabile systems have been studied which appear to yield both ion pairs and radical pairs.1-3,6 Much of the literature has concentrated on aryl and diarylmethyl systems, but substrates in which the chromophore is separated from the leaving group by one or more saturated carbons have also been studied. As leaving groups, bromides, acetates, phenoxides, hydroxides, and trimethylammonia salts show qualitatively equivalent photochemical behavior. We have chosen to concentrate our studies on DPMC and its substituted derivatives for two reasons. One, the UV-vis X
Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-3580$12.00/0
Figure 2. Diarylmethyl chlorides used in this study.
absorptions of both the cations and radicals formed have been fully characterized, simplifying our experiment.7 Second, product quantum yields for both the parent compound and a number of its derivatives have been reported in the literature.7 From our previous work, we found the photolysis of DPMC in acetonitrile yields ion pairs at a rate greater than the =20 ps response time of our instrument.4,5 Since in acetonitrile the radical pair formed is higher in energy (64 kcal/mol) than the ion pair (11 kcal/mol), it is possible that the radical pair is formed more rapidly than the ion pair and that the ion pair is then formed via electron transfer within the radical pair, Figure 1.7,8 Such a reaction pathway has been proposed by Pincock and co-workers for benzyl acetates and 1-naphthylmethyl esters.3,9,10 © 1996 American Chemical Society
Homolysis and Heterolysis in DMPC Steenken and co-workers used a combination of nanosecondmicrosecond laser flash photolysis and product studies to measure the quantum yields of ion and radical pair production for DPMC and a number of substituted derivatives.7 They report that photolysis of DPMC in acetonitrile leads to ion pairs and radical pairs in comparable yields, 13% ion and 23% radical. For MeO, those quantum yields are 0.32 and 0.26, and for DiMeO, 0.31 and 0.24. We will attempt to explain these ratios with this work, but, of equal importance, we wish to understand why these quantum yields do not add to 1. It is unlikely that such deactivation pathways as fluorescence or intersystem crossing to the molecule’s triplet manifold or internal conversion to ground state could compete efficiently with such rapid dissociation pathways; therefore, the most reasonable explanation for the low quantum yields that Steenken and co-workers measure in the photolysis of DPMC at nanosecond time scales is efficient cage recombination within the initially formed ion pair and within the initially formed radical pair on the picosecond time scale. The present study directly monitors the dynamics of cage recombination for ion pairs and radical pairs. Further, although extensive literature documents cage recombination reactions within carbon-centered radical pairs, the geminate reaction, in solution, between a carbon-centered radical and a halogen atom has yet to be studied at ambient temperatures.11,12 Experimental Section Diphenylmethyl chloride (DPMC) and all substituted derivatives were produced from the corresponding alcohols, (Aldrich) with thionyl chloride and purified by vacuum distillation or sublimation to >95% purity as measured by NMR, IR, and gas chromatography (HP5890, FID, DB17 column). Acetonitrile, (Burdick and Jackson, UV grade) was distilled from calcium hydride. Tetrahydrofuran (Aldrich) was distilled from sodium. Cyclohexane, (Fisher Scientific, ACS Grade) was used as received. Propionitrile (Aldrich, 97%) was refluxed over sodium methoxide prior to fractional distillation. This purity of solvent proved usable for our experiments on DPMC and MeO, but DiMeO proved thermally unstable in it. A detailed description of our picosecond pump-probe experiment has been reported elsewhere.13 The laser is a Continuum (PY61C-10) Nd:YAG (=30 ps fwhm). All samples were pumped at 266 nm (=200 µJ focused to 2 mm at the sample). Notch filters were used to select the probe light frequency out of a white light continuum generated by focusing either 532 nm (good down to =350 nm) or 355 nm (good down to =300 nm) laser pulses to a point in D2O/H2O. Probe intensity is measured by Oriel 71902 UV-enhanced photodiodes interfaced to a Stanford (SRS 250) boxcar integrator. Samples were prepared so as to exhibit ground state optical density of 1.5 at 266 nm and were stirred in a 1 cm quartz cuvette throughout the experiment; flowing the samples through the cuvette did not change the experimental results. Laser pump power was in the region where signal intensity increased linearly with laser power and kinetics showed no sensitivity to laser power. The experiment was not sensitive to the polarization of the pump beam relative to that of the probe. The cations formed by photolysis of DPMC and MeO were probed at 440 nm. The cation formed by photolysis of DiMeO was probed at 480 nm. All radicals were probed at 330 nm. For ions, typically 200 data points were collected per run. Each point is the average of 25 laser shots, and the decay between points is 5-15 ps. For radicals, 100 data points were collected per run. All reported decays are the average of 3-6 runs. Traces shown in this report are point grouped for display purposes. The method of deconvolution of the kinetic data has been presented.13 The observed transient signal A(t) results from the
J. Phys. Chem., Vol. 100, No. 9, 1996 3581
Figure 3. Transient absorption of the diarylmethyl radicals formed upon photolysis of the corresponding diarylmethyl chlorides in acetonitrile at 23 °C: laser excitation at 266 nm; radicals monitored at 330 nm; A ) DPMC, B ) MeO, and C ) DiMeO.
Figure 4. Transient absorption of the diarylmethyl radical formed upon photolysis of DiMeO in acetonitrile at 9.3 and 47.4 °C: laser excitation at 266 nm; radicals monitored at 330 nm.
convolution of the instrument response function I(t) with the transient signal, F(t).
A(t) ) ∫-∞I(τ) F(t-τ) dτ t
(1)
The instrument response function, I(t), results from the convolution of the pump and probe pulse and is assumed to have the analytical form of a Gaussian
I(t) ) (2πσ)-0.5 exp(-(t - t0)2/2σ2)
(2)
where σ is the width and t0 the position of the peak of the Gaussian. To measure the response time of our instrument, we use the instantaneous excited state absorption of pyrene at 440 and 480 nm and of naphthalene at 330 nm. For naphthalene, it is necessary to subtract fluorescence from the data before optical density is calculated. The response function of our instrument at both wavelengths of interest is 20 ( 3 ps, as measured by repeated experiments. Results The Radicals. Acetonitrile solutions of DPMC, MeO, and DiMeO at 23 °C were irradiated at 266 nm, and the dynamics of the resulting transient species were monitored at 330 nm. Figure 3 shows the normalized transient absorption decays we assign, in agreement with literature reports, to the diarylmethyl radicals formed upon photolysis of the corresponding diarylmethyl chlorides in acetonitrile.7 Figure 4 shows the decays of the radical of DiMeO in acetonitrile at two temperatures. In acetontrile, all radicals decay exponentially to a constant absorbance by 600 ps. The DPMC radical reaches this plateau more rapidly than do the methoxy substituted radicals. An increase in temperature leads to an increase in both the rate of decay and in the constant absorbance, Figure 4, but the effect is subtle. In contrast to the behavior of the radicals in
3582 J. Phys. Chem., Vol. 100, No. 9, 1996
Lipson et al.
Figure 5. Transient absorption of the diarylmethyl radical formed upon photolysis of DiMeO in acetonitrile at 23 °C, fit to the model shown in Scheme 2: laser excitation at 266 nm; radical monitored at 330 nm; rate constants listed in Table 1; σ ) 24 ps; t0 ) 153 ps.
acetonitrile, no decay is observed for the radicals formed upon photolysis of DPMC in either cyclohexane or tetrahydrofuran (data not shown). The radical decays are fit to the model depicted in Scheme 2, SCHEME 2
where RP denotes a geminate radical pair; RP is formed instantaneously. This model predicts a single exponential decay (with a rate constant kRP equal to the sum of kd and kesc) to a constant absorbance given by
[RP]∞ )
kesc [RP]0 kesc + kd
(3)
On the time scale of our experiment, radicals that escape their cage to become free radicals do not return. Figure 5 shows the fit of the Scheme 2 model to the data for DiMeO in acetonitrile at 23 °C. Although the residuals to the fits are, in general, rather good, the values we obtain for the rate constants are not very precise, (20% (estimated). One parameter employed in fitting the data is the response function of our instrument whose value 20 ( 3 ps is measured by fitting the instantaneous rise of the transeint absorption of naphthalene at 330 nm. The uncertainty in this response function leads to uncertainty in deconvoluting the intensity of the signal at early times and therefore leads to uncertainty in fitting the two rate constants kd and kesc. We further note that the data for DPMC, MeO, and DiMeO are only fit acceptably if we set the instrument response function at the somewhat low value of 15, 13.8, and 24.0 ps, respectively. Figure 6 shows the fits we obtain to the radical kinetics of DPMC when we fix the response function at 20 and 15 ps. A possible explanation for the failure of the model depicted in Scheme 2 to fit the experimental data with σ ) 20 ps is that the rate constants associated with processes kd and kesc are time dependent and not time independent, as assumed.14-16 Presently we do not have the time resolution that would allow for a detailed analysis of the time dependence of the rate constant and therefore assume for the present study that kd and kesc are time independent and their value reflects an “average” value of the time dependent processes. The data reported in Table 1 are that derived from the fitting procedure which gives the best residuals which necessitates a variation in σ. As shown in Table 2, the value of the rate constants kesc and kd are not very sensitive to the value of σ.
Figure 6. Transient absorption of the diphenylmethyl radical formed upon photolysis of DPMC in acetonitrile at 23 °C, fit to the model shown in Scheme 2: laser excitation at 266 nm; radicals montitor at 330 nm; A, fit with σ ) 20 ps, kd ) 2.0 × 1010 s-1, kesc ) 1.7 × 1010 s-1, t0 ) 123 ps; B, fit with σ ) 15 ps; rate constants listed in Table 1; t0 ) 118 ps.
TABLE 1
compound
solventa
DPMC
Acn
MeO
Prop Acn
DiMeO
Prop Acn
ion kineticsb (×109/s)
radical kineticsb (×109/s)
temp (C)
k1
k2
Rc
kd
kesc
10 23 55 23 10 23 55 23 10 23 48
3.1 4.1 4.5 11.6 2.4 3.5 4.5 4.1 0.8 1.7 2.4
2.8 3.6 4.0 8.5 2.1 3.6 3.3 3.5 0.7 2.0 3.0
0.0 0.0 0.0 0.4 0.3 0.3 0.3 0.4 0.4 0.4 0.4
7.1 8.2 6.8 5.6 6.2 7.0 6.2 7.3 4.3 5.1 6.4
11.0 13.0 13.0 16.0 3.9 5.0 5.9 7.5 3.2 4.0 5.2
a Acn ) acetonitrile; Prop ) propionitrile. b Uncertainties in the fits are (20%; the values for k3 and k4, Scheme 3, are not given. c R ) [RP]0/([RP]0 + [CIP]0); where [RP]0 is the concentration of radical pairs that feed into the CIP.
TABLE 2: Dependence of the Rate Constants from Scheme 2 on the Instrument Response Function, σ, at 23 °C compound DPMC MeO
σ
kesc (s-1)
kd (s-1)
20.0 15.1 20.0 13.8
1.7 × 1010 1.3 × 1010 5.6 × 109 5.0 × 109
2 × 1010 8 × 109 9.2 × 109 7.0 × 109
Ions. Acetonitrile solutions of DPMC, MeO, and DiMeO at 23 °C were irradiated at 266 nm, and the dynamics of the resulting transient species were monitored at 440 nm for DPMC and MeO and at 480 nm for DiMeO. Figure 7 shows the normalized transient absorption decays we assign, in agreement with literature reports, to the diarylmethyl cations formed upon
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J. Phys. Chem., Vol. 100, No. 9, 1996 3583
Figure 7. Transient absorption of the diarylmethyl cations formed upon photolysis of the corresponding diarylmethyl chlorides in acetonitrile at 23 °C: laser excitation at 266 nm; A (DPMC) and B (MeO) monitored at 440 nm; C (DiMeO) monitored at 480 nm.
Figure 8. Transient absorption of the diarylmethyl cation formed upon photolysis of DiMeO in acetonitrile at 9.8 and 47.7 °C: laser excitation at 266 nm; cation monitored at 480 nm.
Figure 10. Transient absorption of the diarylmethyl cation formed upon photolysis of DiMeO in acetonitrile at room temperature: A fit to the model shown in Scheme 1, k1 ) 6.5 × 108 s-1, k2 ) 4.6 × 108 s-1, σ ) 24 ps, t0 ) 72 ps; B fit to the model shown in Scheme 3, rate constants listed in Table 1, σ ) 24 ps, t0 ) 162 ps; laser excitation at 266 nm; cation monitored at 480 nm.
SCHEME 3
Figure 9. Transient absorption of the diphenylmethyl cation formed upon photolysis of DPMC in acetonitrile at 23 °C, fit to the model shown in Scheme 1: laser excitation at 266 nm; cation monitored at 440 nm; rate constants listed in Table 1; σ ) 24 ps; t0 ) 72 ps.
photolysis of the corresponding diarylmethyl chlorides in acetonitrile7 Figure 8 shows the decay of the cation of DiMeO in acetonitrile at 9.8 and 47.7 °C. Of note, the absorption of DPMC appears to decay more rapidly than that of MeO which decays more rapidly than that of DiMeO. Further, the actual decay appears to begin more slowly for DiMeO than for MeO, which is slower than for DPMC. This “delay” in the decay is seen strikingly for DiMeO at low temperatures and less so at higher tmperatures, Figure 8. All transient absorptions decay to a constant absorbance that is sensitive to temperature. We previously reported4,5 that the kinetics of the ion pair formed upon photolysis of DPMC in acetonitrile and propionitrile can be modeled well, Figure 9, by Scheme 1. In this model, CIP, SSIP, and FI have a common extinction coefficient and all ion pairs are formed instantaneously as CIPs. However, this model fails to reproduce the kinetics of the ion pairs formed from MeO and DiMeO, Figure 10A. In light of the studies of
Pincock and co-workers3,10 who proposed that CIP can be formed from the geminate radical pair through electron transfer, we expand the model to Scheme 3, where the RP (geminate radical pair) has no transient absorption at the absorption wavelength of the cation, the initial concentration of transients is split between the CIP and the RP, and the RP feeds into the CIP irreversibly at a rate kRP[RP]. kRP is fixed to the value kRP ) kesc + kd derived from the corresponding kinetics for the radicals monitored at 330 nm. We vary the ratio
R)
[RP]0 [RP]0 + [CIP]0
to find the best fit for the data, Figure 10B. Note that [RP]0 here is not the total number of radical pairs formed. Instead it is the total number of radical pairs that decay into the CIP, and [CIP]0 is the initial amount of CIP formed directly from the excited singlet state. Table 1 lists the kinetic parameters which yield the best fits to the data. For the case of DPMC at 23 °C, changing the initial concentration of RP relative to CIP has only a small effect on the quality of the fits. Changing R from 0 to 0.9 increases the residuals in the fit by 9%. That same change in R, however, changes k1 from 4.1 × 109 to 3.7 × 1010 s-1. For DPMC, we find the lowest residuals when we set R ) 0. The quality of the fits for DiMeO and MeO is a good deal more sensitive to R. For the case of DiMeO at 23 °C, an increase in R from 0 to 0.4 decreases the residuals in the fit by
3584 J. Phys. Chem., Vol. 100, No. 9, 1996 a factor greater than 3. A further increase in R from 0.4 to 0.9 increases the residuals by 8%. For DiMeO and MeO, we find the best fit to the data at R = 0.4 and 0.3, respectively. Also listed in Table 1 are the kinetic parameters we measure for the behavior of DPMC and MeO in propionitrile. Discussion Geminate Radical Pair Dynamics. The model in Scheme 2 we propose to rationalize the kinetic behavior of the radicals formed upon photoinduced homolysis of diarylmethyl chlorides in acetonitrile would appear to be oversimplified: photolysis generates a solvent caged singlet radical pair which may either escape from the cage or collapse in a time independent fashion. A typical rate for radical pair diffusional escape from a solvent cage is of the order of 5 × 109 s-1, in reasonable agreement with the values of kesc we report in Table 1.17 The escape process we observe, however, is not likely to be a simple diffusional separation of two independent particles. If it were, one would predict that the rate of this process would be controlled by the rate of diffusion of the smaller radical, in our case the chlorine atom, and thus should be the same for the three molecules. It is clear, though, in Table 1, that kesc is dependent upon substituents on the phenyl rings of the aryl radical as kesc increases from 4 × 109 s-1 for DiMeO to 1.3 × 1010 s-1 DMPC. Further, if this escape process were purely diffusional, it should slow as solvent viscosity is increased. As shown in Table 1, kesc (for DPMC and MeO) increases from acetonitrile to propionitrile even though viscosity increases as well.18 It would appear the barrier to geminate radical separation depends not only on forces associated with solvent caging but also upon the electronic interaction between the two radicals, as evidenced by the effect of substituents upon the rate of this process. Another aspect of this model for a caged radical pair is perplexing. Although singlet radical pairs normally couple readily,11 such does not appear to be the case for carbonchlorine radical pairs. We observe no decay in the absorbance of diarylmethyl radicals in cyclohexane or tetrahydrofuran. The obvious property difference between these two solvents and acetonitrile is that cyclohexane and tetrahydrofuran have markedly lower dielectric constants. However, the rates of radical coupling reactions are normally not strongly sensitive to solvent polarity.11 We therefore propose that direct adibatic coupling of chlorine atoms with diarylmethyl radicals does not occur. At this stage one can only speculate as to the nature of the electronic process or processes associated with kd. As will be discussed, direct coupling of the two radicals to form the carbon-chlorine bond must be considered a nonadibatic process as the potential energy surface associated with ground state dissociation correlates with the ion pair state in polar solvents and it is the excited state surface that correlates with the radical pair. An alternative pathway for the decay of the radical pair is through an electron transfer process, as has been proposed by Pincock and co-workers.3,10 If a charge transfer process is involved in the decay of the radical pair, the rate of this process should depend upon the polarity of the solvent, as is observed. Ion Pair Dynamics. The kinetic behavior of the ions formed upon photolysis of DPMC in acetonitrile can be an acceptably fit by the model shown in Scheme 1 in which all of the CIP are formed instantaneously. The CIP can either collapse to starting material or diffusionally separate into the SSIP. The SSIP can either return to the CIP or escape to FI. This model, though, fails to reproduce the dynamical behavior of the ions formed upon photolysis of MeO or DiMeO. Their behavior is only well-reproduced if the laser pulse initially creates two species, the CIP and the RP, and the RP feeds into
Lipson et al. the CIP irreversibly at a rate kRP[RP]. kRP is measured from the corresponding radical decays. The kinetics predicted by Scheme 1 are biexponential. By expanding Scheme 1, we are adding a new adjustable parameter, namely, the initial ratio of [RP]0/([RP]0 + [CIP]0) which we have labeled R. However, since Winstein and co-workers first proposed19 the basic model of an equilibrium between a CIP and an SSIP in 1954, numerous experimental and theoretical studies have supported it for both ion pairs and radical-ion pairs.4,13,18,20,21 We therefore feel it reasonable that the basic model of Scheme 1 should apply here as well as for the analysis of the MeO and DiMeO data. For both MeO, the best fit to the data is when R is set to =0.3, while, for DPMC, the best fit is when R ) 0. The value of R ) 0.3 for MeO would suggest that partitioning between the reaction pathways leading to the formation of the CIP corresponds to 70% coming directly from the excited singlet state and 30% coming from the radical pair via an electron transfer process. It is surprising that the best fit of Scheme 3 to DPMC kinetics occurs for R ) 0, suggesting that all of the CIP comes directly from the excited singlet state. If all the RP that decays through the process kd were to form CIP, the value of R would be 0.20 for DPMC. However, given the very small variation in the residuals with the change in R, electron transfer within the DPMC radical pair to produce the CIP may indeed occur and our experiment is not able to resolve this process, although the experiment should be sensitive to R values of 0.20.3. One reason the process is observed in MeO and DiMeO is that the geminate radical pair lifetimes (1/kRP) are 83 and 110 ps, and it is during this interval that electron transfer occurs to produce 30% of the CIP. The DPMC geminate radical pair, however, has a lifetime of only 47 ps, which may be too short to allow observation of the electron transfer in the formation of the DPMC CIP, particularly if the amount of the CIP derived from the geminate pair is small, R < 0.1. As a brief summary, we find that both radical pairs and ion pairs are created directly from a common excited state. Radical pairs are not simply solvent caged, as the rate of cage escape, kesc, depends upon the electronic structure of the radical species. Furthermore, radical pairs do not adiabatically couple to form the carbon-chlorine bond but, for MeO and DiMeO, decay by electron transfer to form CIP. Quantum Yields for Initial Production of CIP and Geminate Radical Pairs. The quantum yields for the production of radicals and ions, measured at 70 ns, for DPMC, MeO, and DiMeO in acetonitrile have been measured.7 For the series DPMC, MeO, and DiMeO the radical quantum yields are 0.23, 0.26, and 0.24, while the ion quantum yields are 0.13, 0.32, and 0.31. Assuming these transient species do not decay on the 1-70 ns time scale, it is then possible to derived the initial amounts of radicals and ions formed upon photolysis given the kinetic data in Table 1. For the radicals derived from DPMC, MeO, and DiMeO, the initial amount of geminate radical pair is 0.37, 0.62, and 0.54, respectively. The determination of the initial amount of CIP, derived from both the excited singlet state and from the radical pair, is somewhat more complicated as the ions do decay on the nanosecond time scale as a result of the processes associated with k3 and k4, Scheme 3. However, the amplitude for decay on this time scale is very small relative to the decay of the ions on the picosecond time scale, k1 and k2, and thus can be neglected. With this assumption, the initial amount of CIP is 0.28, 0.62, and 0.57 for the three ion species. To determine the initial amount of CIP that is produced directly from the excited singlet state, the contribution derived from the radical
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J. Phys. Chem., Vol. 100, No. 9, 1996 3585
Figure 11. Potential of mean force for the solvent equilibrated surfaces for diphenylmethyl chloride in acetonitrile. RP may either escape or cross to the ionic surface, from where it may either return to starting material or form CIP.
pair is subtracted. Thus, the initial amount of CIP formed from the excited singlet state is 0.28 for DPMC, 0.43 for MeO, and 0.34 for DiMeO. Combining these results for the initial yields of radical pairs and ion pairs derived from the excited singlet state, we find that the total quantum yield for the production of transient species is 0.65 for DPMC, 1.05 for MeO, and 0.88 for DiMeO. It is noteworthy that while almost all of the decay of the excited singlet states for MeO and DiMeO give rise to either radical pairs or ion pairs, this does not hold for DPMC. Solvent Dependence of the Potential Energy Surfaces for Radical Pairs and Ion Pairs. To understand in greater detail the possible reaction pathways for photoinduced bond homolysis and heterolysis in the condensed phase, it is informative to examine the solvent dependence of the free energy surfaces for these processes. Regrettably little is known, either experimentally or theoretically, about solvent dependence of the electronic structures associated with radical and ion processes of diphenylmethyl chloride. Some insights into the nature of these reactions may be gleaned from the theoretical studies of the homolysis and heterolysis of tert-butyl chloride by Hynes and co-workers.22-24 Their theoretical approach entails the coupling of two gas phase diabatic surfaces, one purely covalent and one purely ionic, to generate adiabatic surfaces through a nonlinear Schrodinger equation that accounts for the mutual influence of the solute electronic structure and solvent polarization under both equilibrium and nonequilibrium conditions. The two reaction coordinates are the carbon-chloride bond extension, r, and a solvent coordinate, s, which reflects the change in the solvation upon the production of ionic species. The potential of mean force for equilibrium solvation pathway (ESP) is obtained by invoking that with each incremental extension of the carbon-chlorine bond the solvent equilibrates, thus satisfying the condition
δG(r,s)/δs ) 0
(4)
The projection of this reaction pathway onto the r coordinate for the ground state (S0) for adiabatic bond heterolysis should lead to a ground state potential surface for heterolytic dissociation.23 On the basis of the tert-butyl chloride study, the diphenylmethyl chloride potential energy surface for heterolysis should appear as shown in Figure 11. The energy of the CIP is estimated to be 11 kcal/mol.7 The barrier to collapse of the CIP to form the carbon-chlorine bond is 3.0 kcal/mol, a value obtained in our prior picosecond study of DPMC in acetonitrile.5 The free energy profile for the first excited singlet state, S1, was not derived by Hynes in these first studies. However, a qualitative description for S1 may be deduced from the free energy for bond homolysis, 64 kcal/mol, and the optical transition of 110 kcal/mol for S0 f S1. The magnitude of the electronic coupling, β, between the two diabatic surfaces at the
transition state for bond cleavage of DPMC is not known. If β is of the order of 25 kcal/mol this would lead to a local minimum on the excited singlet state surface below the corresponding to homolytic dissociation limit.23 If β is substantially greater, such a minimum on the S1 surface should not occur. It is necessary to point out that the free energy diagram for the excited singlet state is only qualitative. In particular, it is not known whether the initial portion of the curve to which light induced excitation takes place corresponds to a repulsive potential; the surface could certainly be more complex, perhaps possessing a small electronic barrier along the dissociation curves whose magnitude is solvent dependent. It is further important to emphasize that these free energy surfaces correspond to the solvent equilibrated reaction pathways.23 However, for reaction processes that occur on the time scale of the solvent reorganization, these surfaces will be greatly modified. The question of nonequilibrium solvation of the ground state surface has been explicitly addressed by Hynes.22 In the Hynes solvation model, the solute electronic structure instantaneously feels the solvent electronic polarization, Pel, but the solvent orientational polarization, Por, may be out of equilibrium with the solute electronic structure. In the tertbutyl chloride study, if the solvent is not allowed to structurally reorganize about the developing ion pair upon heterolytic dissociation, the ion pair energy is destablized by 55 kcal/mol.22 For diphenylmethyl chloride, this would correspond to having the CIP higher in energy that the radical pair. Thus, it is only the reorganization of the solvent structure that allows for the ion pairs to become more stable that the radical pairs. Given the above picture of the solvent dependence of the potential energy surfaces associated with diphenylmethyl chloride homolysis and heterolysis, we can speculate as to the mechanism for the production of radical pairs and ion pairs following photolysis. Prior to irradiation there will be an equilibrium solvent structure about DPMC which will be maintained upon photoexcitation of DPMC to S1. Presumably this initial solvent structure would not support the development of the CIP but would allow for the formation of the radical pair whose energetics should show only a minor solvent dependence. This assertion is based upon the observation that radical pairs are formed within less than 20 ps in both cyclohexane and THF. Following excitation to S1, the solvent structure may then begin to structurally evolve resulting in a lowering of the ionic surface. The time scale for solvent reorganization could be as fast as the longitudinal relaxation time of the solvent, 0.2 ps for acetonitrile.14 Concomitant with the lowering of the ionic surface is either the development of a conical intersection between the radical and ion surfaces or the development of an avoiding crossing leading to a strong electronic coupling between the two surfaces facilitating a nonadiabatic transition.25 It is during the development of the conical intersection or the strongly electronically coupled avoided crossing that the excited state population passes onto the ionic surface, which, upon further evolution in the solvent structure, allows for the creation of the CIP. One puzzling aspect of this model, as it is presented, is the entire S1 population either dissociates to radical pairs or ion pairs. Such appears to be the case for MeO and DiMeO. However, for DPMC, 35% of the initial population of S1 does not appear as either geminate radical pairs or CIP. One possible explanation is that the fluctuation in the solvent to a solvent orientation that allows for the surface crossing is not the structure that supports of development of the CIP; it is only upon further evolution in the solvent structure that the CIP is formed. However, it is feasible that once the system is on the ground state surface, the solvent structure may reorient in such a manner
3586 J. Phys. Chem., Vol. 100, No. 9, 1996 as to allow for the development of the carbon chlorine bond, returning the molecule to its original state. That this latter pathway does not appear to operate to any great extent in MeO and DiMeO, given the quantum yields for radical and ion pair formation, is the result of the difference in the electronic structures which undoubtedly will effect the position along the reaction coordinates, in either the r or s coordinates, of either the conical intersection or the avoiding crossing. An interesting question relates to the possible existence of a local minimum on the potential energy surface associated with the radical pair. As depicted in Figure 9, there is an energy minimum which results from the electronic coupling between the two diabatic states. However, this picture was developed from the Hynes model within the context of the solvent fully equilibrated to the ionic surface. If the reacting species are on the homolytic surface, the solvent structure equilibrated with the radical species will be different than that associated with the ionic species, and thus, it is not clear whether such a minimum should exist. A local minimum could result if there is an ionic component to the radical interaction. A proposal for ionic interactions in radical systems can be found in Walling’s studies of the thermal decomposition of a large number of diacyl peroxides where the process yields both radical derived and ion derived products in a ratio sensitive to solvent polarity.26 Walling proposed a single transition state for the decomposition that cannot be described as either radical or ionic in nature but as some resonance hybrid of the two electronic structures which then evolves into ion pairs or into radical pairs upon further separation, a process strongly dependent upon the nature of the solvent. If such interactions occur within the present system on the excited state surface, the magnitude of the interaction will be dependent both upon the electronic structure of the interacting species and upon the polarity of the solvent. Evidence for such a minimum should be manifested in substituent effects upon the rate of separation of the radical pairs, kesc. Indeed the rate of radical separation decreases as methoxy groups are added to the phenyl rings; the rate of escape, kesc, decreases from 1.3 × 1010 s-1 for DPMC to 4.0 × 109 s- for DiMeO. Also this separation process should be sensitive to both the viscosity and the dielectric of the solvent. Based upon viscosity considerations alone, the parameter kesc should decrease with an increase in viscosity. However, one finds that kesc actually increases on changing the solvent from acetonitrile to the more viscous solvent propionitrile,18 and thus, kesc appears to be sensitive to the dielectric of the solvent. Therefore, the increase in kesc must be the result of a decrease in the electronic interaction within the radical pair with the decrease in polarity, leading to a lower barrier for radical separation. Unfortunately, it is not possible to separate the effect that the solvent has upon the electronic barrier for radical separation from the effect that the solvent viscosity has upon barrier for diffusional separation. There is evidence, however, that the two radicals are electronically coupled, producing a stabilization of the radical pair, and that this stabilization is sensitive to the electronic structure of the radicals and to the polarity of the solvent. Finally, there is the question as to why, upon electron transfer, the geminate radical pairs for MeO and DiMeO predominately form CIP while the geminate radical pairs for DPMC appear to predominately return to the ground state. If the geminate radical pairs exist in a local minimum on the excited state surface, the distance of this interparticle separation would place the radical pair above the transition state for heterolytic dissociation on the ground state surface. Thus, the transition to the ground state surface via electron transfer would place the system in the region of the transition state. The product distribution then would be
Lipson et al. determined by changes in both r and s coordinates. Apparently the electron transfer within the DPMC geminate radical pair places the system in such a region on the ground state surface that the predominate decay channel is toward formation of the covalent bond, while electron transfer within the MeO and DiMeO geminate radical pairs places the system in a region on the ground state surface that the predominate decay channel is toward CIP. That transitions occur to different regions on the ground state surface must reflect the different positions in the excited state local minimum due to differing electronic structures of the three geminate radical pairs. Conclusion We have established that photolysis of DPMC in acetonitrile leads directly to the formation of both radical pairs and contact ion pairs. Radical pairs do not directly recombine adiabatically, but cross onto the ground state ionic surface leading to the formation of either the contact ion pair or to the formation of a covalent bond. Future work will concentrate on radical pair and ion pair formation and decay pathways employing femtosecond laser absorptions spectroscopy. Acknowledgment. This work is supported by a grant from the National Science Foundation, CHE 9408354. We thank Lisha Barre for the synthesis of the compounds employed in this study. References and Notes (1) Cristol, S. J.; Bindel, T. H. In PhotosolVolysis and Attendant Photoreactions InVolVing Carbocations; Cristol, S. J., Bindel, T. H., Eds.; Dekker: New York, 1983; Vol. 6, pp 327-415. (2) Das, P. K. Chem. ReV. 1993, 93, 119-144. (3) Hilborn, J. W.; MacKnight, E.; Pincock, J. A.; Wedge, P. J. J. Am. Chem. Soc. 1994, 116, 3337-3346. (4) Peters, K. S.; Li, B. J. Phys. Chem. 1994, 98, 401-403. (5) Deniz, A. A.; Li, B.; Peters, K. S. J. Phys. Chem. 1995, 99, 1220912213. (6) Post, A. J.; Nash, J. J.; Love, D. E.; Jordon, K. D.; Morrison, H. J. Am. Chem. Soc. 1995, 117, 4930-4935. (7) Bartl, J.; Steenken, S.; Mayr, H.; McClelland, R. A. J. Am. Chem. Soc. 1990, 112, 6918-6928. (8) Wayner, D. D. M.; McPhee, D. J.; Griller, D. J. Am. Chem. Soc. 1988, 110, 132-137. (9) Arnold, B.; Donald, L.; Jurgens, A.; Pincock, J. A. Can. J. Chem. 1985, 63, 3140-3146. (10) Pincock, J. A.; Wedge, P. J. J. Org. Chem. 1994, 59, 5587-5595. (11) Walling, C. Free Radicals in Solution; Wiley: New York, 1957. (12) Step, E. N.; Buchachenko, A. L.; Turro, N. J. J. Org. Chem. 1992, 57, 7018-7024. (13) Peters, K. S.; Lee, J. J. Phys. Chem. 1992, 96, 8941-8945. (14) Simon, J. D. Acc. Chem. Res. 1988, 21, 128-134. (15) Kahlow, M. A.; Jarzeba, W.; Kang, T. J.; Barbara, P. F. J. Chem. Phys. 1989, 90, 151-158. (16) Castner, E. W. J.; Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1987, 86, 1090-1097. (17) Noyes, R. M. J. Am. Chem. Soc. 1956, 78, 5486-5490. (18) Li, B.; Peters, K. S. J. Phys. Chem. 1993, 97, 7648-7651. (19) Winstein, S.; Clippinger, E.; Fainberg, A. H.; Robinson, G. C. J. Am. Chem. Soc. 1954, 76, 2597. (20) Peters, K. S.; Li, B. J. Phys. Chem. 1992, 98, 401-403. (21) Arnold, B. R.; Noukakis, D.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Am. Chem. Soc. 1995, 117, 4399-4400. (22) Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc. 1992, 114, 1052810537. (23) Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc. 1992, 114, 1050810528. (24) Mathis, J. R.; Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc. 1993, 115, 8248-8262. (25) Klessinger, M. Angew. Chem., Int. Ed. Engl. 1995, 34, 549-551. (26) Walling, C.; Waits, H. P.; Milovanovic, J.; Pappiaonnou, C. G. J. Am. Chem. Soc. 1970, 92, 4927-4932.
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