J. Phys. Chem. 1994,98, 401-403
401
Picosecond Dynamics of Contact Ion Pairs and Solvent-Separated Ion Pairs in the Photosolvolysis of Diphenylmethyl Chloride Kevin S. Peters' and Bulang Li Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-021 5 Received: September 29, 1993; I n Final Form: November 12, 1993'
Picosecond absorption spectroscopy is used to examine the dynamics of the diphenylmethyl cation produced upon the 266-nm photolysis of diphenylmethyl chloride in acetonitrile. The experiments reveal that a contact ion pair is formed with a lifetime of 150 ps which decays by collapse of the ion pair to form diphenylmethyl chloride, kl = 3.81 X lo9 s-I, and ion pair separation to the solvent-separated ion pair, k2 = 2.87 X 109 s-1. The solvent-separated ion pair decays by return to the contact ion pair, k3 = 1.31 X lo8 s-I, and diffusional separation to the free ion, k4 = 7.84 X lo8 s-l
Introduction
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The theory for the S Nmechanism, ~ as originally formulated by Hughes and Ingold' and extended by Hammett,2 has been subject to continual development and refinement.3-5 A significant modification of the theory was offered by Winstein and coworkers6 postulating that heterolytic bond cleavage should not be envisioned as a continuous dissociation process leading to free molecular ions (FI) but instead that at least two chemically distinct ion pair species, the contact ion pair (CIP) and the solventseparated ion pair (SSIP), intervene in the dissociation p r o c e ~ s . ~ Numerous experimental and theoretical studies have probed the equilibrium properties of CIP and SSIP.8-9 In addition, a limited number of theoretical studies have examined the dynamical nature of ion pairs.l0-I4 In contrast, from the vantage of experiment, little is known about the kinetic behavior of ion pairs. For example, the parameters that control the dynamics of the collapse of the CIP to form a covalent bond or its separation to SSIP are virtually unexplored as heretofore no molecular system has been developed that allows for the direct probing of the dynamics associated with a CIP. Recently, we reported a series of experimental investigations into the dynamics of the contact radical ion pairs formed upon photochemically-induced electron transfer between trans-stilbene and f ~ m a r o n i t r i 1 e . I ~The ~ ~ solvent dependence of the kinetics for the partitioning between back electron transfer within the contact radical ion pair and its diffusionalseparation to the solvent separation radical ion pair were elucidated. In the present report, we present a picosecond kinetic investigation into the dynamics of the diphenylmethyl cationxhloride anion (DPMTl-) CIP in acetonitrile.'* The dynamics of the collapse of the CIP to form diphenylmethyl chloride, covalent bond formation, and the evolution of the CIP into the SSIP are resolved for the first time. Furthermore, a kinetic description of the collapse of the SSIP to form CIP or its separation to free ions (FI) is derived. Experimental Section The picosecond absorption spectrometer, based upon a Continuum (PY61C-10) Nd:YAG laser with a 19-ps pulse width, employed in obtaining transient absorption spectra and kinetics has previously been de~cribed.'~The energy of the excitation beam, 266 nm, was 200 pJ focused to an area of 7 "2. Over the energy range 100-500 pJ the kinetics were independent of laser power. The sample was passed through a flowing cuvette by means of a syringe pump. Diphenylchloromethane (Aldrich) was purified by vacuum distillation. Acetonitrile (Mallinckrodt) was refluxed over CaHz for 48 h and then distilled. Abstract published in Advance ACS Abstracts, January 1, 1994.
0022-3654/94/2098-0401$04.50/0
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Figure 1. Transient absorption spectra following the 266-nm excitation of 10 pM diphenylmethyl chloride in acetonitrile at 22 OC: top curve, 25 ps; bottom curve, 4 ns.
The method of deconvolution of the kinetic data has been presented.16 The observed transient signal A(t) results from the convolution of the instrument response function I ( t ) with the transient signal, F ( t ) .
A(t) =
s'
-(D
Z(7)
F(t-7) d r
(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 ( ? ) = (2?ra)4,s exp(-(t - to)2/2a2)
(2) whereais the widthand to thepositionofthepeakoftheGaussian.
Results and Discussion The time-resolved absorption spectra following the 266-nm irradiation of 10 pM diphenylmethyl chloride (DPMC) in acetonitrile are shown in Figure 1. Within 20 ps a spectrum appears with absorption maximum at 435 nm and a smaller peak at 520 nm. During the period of 4 ns, the amplitude of the peak at 435 nm decays while the amplitude of the peak at 520 nm remains constant, suggesting the presence of two species. From previous nanosecond studies of the DPMC by Steenken and McClelland,20 it has been shown that there are two transient species formed upon photolysis which are the product of heterolysis, the diphenylmethyl cation (DPM+), and homolysis, the diphenylmethyl radical (DPM'). The quantum yield, derived by Steenken and McClelland,20for the production of these two species in acetonitrile, measured at 20 ns following photolysis, is 0 1994 American Chemical Society
402 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 0.15
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Letters
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TIME (NS) Figure2. Dynamicsof the diphenylmethyl cation, monitoring at 440 nm, following the 266-nm irradiation of 10 pM diphenylmethyl chloride in
acetonitrile. Points: experimental data which are the average of four experiments, 10-ps time increments. Solid curve: calculated kinetics based upon Scheme 2 and the associated rate constants given in Table 1; to = 58 ps and u = 19.0 ps.
0.13 for the formation of diphenylmethyl cation and 0.23 for the formation of diphenylmethyl radical. The spectrum of diphenylmethyl cation has an absorption maximum at 430 nm while the spectrum of diphenylmethyl radical has a maximum in the visible at 523 nme21Thus, within the 20-ps time resolution of the present experiment both the ion and radical species appear. The mechanism for the photochemical dissociation process producing the two transient species is not revealed by the present study. The will be a subject of a future investigation. The dynamics for the decay of DPM+ were monitored at 440 nm for 2 ns in 10-ps increments (Figure 2) and for 4 ns in 20-ps increments (not shown). The kinetics are characterized by a decay in the DPM+ absorbance during the first 200-ps interval. The only viable process leading to the decrease in concentration of DPM+ is covalent bond formation with the chloride producing DPMC. Electron transfer from the chloride anion to DPM+ producing a radical pair is not energetically feasible as the ion pair in acetonitrile is enthalpically more stable than the radical pair by 54 kcal/mol.20 A minimal kinetic model that would account for the observed dynamics is one where the CIP is apportioned between covalent bond formation, kl, and ion pair diffusional separation to the SSIP, k2 (Scheme 1).
SCHEME 1
- k2
ki
DPMC
CIP
SSIP
In thedevelopmentofthekineticmodelforF(t),eq 1,it isassumed that DPM+ extinction coefficient in the CIP and SSIP is the same. The best fit of the model described by Scheme 1 to the kinetic data is shown in Figure 3 with kl = 2.20 X 109 s-l and k2 = 1.80 X lo9 s-l. The sum of the square of the residuals is 8.89 X lo" OD2, corresponding to an average error to the fit of each data point of 0.002 OD. The average of the estimated error in the kineticdata for each point in time is 0.0007OD. Comparing the kinetics derived from Scheme 1 with the experimental data, it is evident that there is a second decay process for DPM+ on the nanosecond time scale. Consequently, the model depicted in Scheme 1 cannot account for the observed kinetic behavior. To rationalize the observed kinetic behavior at 440 nm, it is necessary to postulate the existence of three kinetically distinct species each absorbing at 440 nm. In analogy with the theoretical framework provided by the Winstein model for the S Nmech~ anism? the three postulated ionic species are the CIP, SSIP, and
2.0
TIME (NS) Figure 3. Points: same experimental data as in Figure 2. Solid curve: calculated kinetics based upon Scheme 1 with kl = 2.20 X 109 s-1 and kz = 1.80 X 109 s-1; to = 58 ps and u = 19.0 ps.
TABLE 1: Rate Coefficients (9-1) for the Decay of the Diphenylmethyl Cation, Monitored at 440 nm, Produced upon the 266-nm Photolysis of Diphenylmethyl Chloride in Acetonitrile Based upon the Kinetic Model Presented in Scheme 2' kl (3.81 0.38) X lo9 kz (2.87 0.29) X 109 kj (1.31 0.60) X 108 k4 (7.84 3.90) X lo8 Error represents 1 standard deviation.
* *
*
FI. The following kinetic model was employed in the analysis of the data.
SCHEME 2
ki
DPMC
ki k3
k4
SSIP
CIP
FI
The process leading to the observed nanosecond decay of DPM+ is collapse of the SSIP, kg,to the CIP followed bycarbon4hlorine bond formation, k,. Separation of the SSIP to FI, k4, prevents further decay DPM+ on the IO-ns time scale. Steenken and McClelland found that DPM+ undergoes reaction with the solvent, acetonitrile, on the 400-11s time scale to form the nitrilium ion, with a rate constant of (2.5 f 0.2) X 106 s-l. Thus, this latter process will not be manifested in the kinetic data displayed in Figure 2. Employing Scheme 2 for the modeling of F(t), eq 1, and assuming that the extinction coefficient for DPM+ is independent of the nature of the ion pairing results in the kinetic parameters given in Table 1; the corresponding fit to the experimental data is shown in Figure 2. The sum of square of the residuals for the fit of the kinetic data to the model is 9.3 X le5OD2, which corresponds to an average error of fit to each data point of 0.OOO 68 OD, a value within the estimated error of the experiment. Within this model for temporal behavior of the CIP and the SSIP the respective lifetimes for the two species are 150 ps and 4.8 ns. Since the rate parameters k2 and ks determine the equilibrium constant for the CIP and SSIP, the free energy change at 22 OC for the conversion of the CIP into the SSIP in acetonitrile is AG = -1.8 f 0.4 kcal/mol. The model for the ion pair dynamics depicted in Scheme 2 assumes that there is a single species of CIP and SSIP leading to exponential form for the rate laws. Such an assumption leads to an excellent fit of the model to the kinetic data. However, there may be numerous molecular configurations for the CIP and SSIP so that the true dynamical behavior does not take the form of simple exponential kinetics. However, given the resolution of the present experiment, a more sophisticated theoretical framework for the data analysis is unwarranted.
Letters In summary, DPMC is the first molecular system that reveals simultaneously the dynamics of the CIP for carbon-chloride covalent bond formation and ion pair diffusional separation. In addition,the kinetics in acetonitrileare such that dynamicsof ion pair interconversion can be monitored. This molecular system is ideally suited for an in-depth analysis of how the electronic structure of the ion pair and solvent control the dynamics of carbon4lorine bond formation; these issues have recently been addressed by Hynesand co-workers in their theoretical analysis of the S N reaction ~ m e c h a n i ~ m .Such ~ ~ a research program is in progress.
Ackaorsledgom~t.This work is supported by a grant from the National Science Foundation, CHE 9 120355. References md Notes (1) Hughes, E. D.; Ingold, C. K. J. Chem. Soc. 1935,254. (2) Steigman, J.; Hammett, L. P. J. Am. Chem. Soc. 1937, 59, 2536. (3) Kim, H. J.; Hynca, J. T. J . Am. Chem. Soc. 1992,114, 10508. (4) Kim, H. J.; Hynca, J. T. J. Am. Chem. Soc. 1992,114, 10528. (5) Mathis, J. R.; Kim, H. J.; Hynes, J. T. J. Am. Chem.Soc. 1993,115, 8248. (6) Winstein,S.; Clippinger, E.; Fainberg, A . H.; Robinson, G.C. J . Am. Chem. Soc. 1954,76,2597. (7) For review ace: Raber. D. J.: Harris. J. M.:Schlever. P. v. R. Ions andIon Pairs in Organic Reactions;Swarz, M:, Ed.; Wiley: New York, 1974; Vol. 2, pp 248-374.
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 403 (8) Ions a d Ion Pairs in Organic Reactions; Swarz, M.,Ed.; Wiley: New York, 1974; Vol. 1 . (9) Dcvlin, J. P.; Ritzheupt, C.; Fisher, M.; Woolridge, R. Faraday Discuss. Chem. Soc. 1988,85, 255. (10) Blech, A.; Merkowitz, M.; McCammon, J. A. J. Am. Chcm. Soc. 1986, 108, 1755. (1 1) Jorgeneen, W. J.; Buckner, J. K.; Houston, S. E.; Rossky, P. J. J. Am. Chcm. Soc. 1987,109, 1981. (12) Karim,O.A.; McCammon, J . A . J. Am. Chem.Soc. 1986,108,1762. (13) Ciccotti, G.; Farrario, M.; Hynes, J. T.; Kapral, R. Chem. Phys. 1989, 129, 241. (14) Ciccotti, G.; Farrario, M.; Hynes, J. T.; Kapral, R. J. Chem. Phys. 1990,93, 7137. (15) Peters, K. S.; Lcc, J. J. Phys. Chem. 1992, 96, 8941. (16) Peters, K. S.; Lee, J. J . Am. Chem. Soc. 1993, 115, 3643. (17) Li, B.; Peters, K. S . J. Phys. Chem. 1993, 97,7648. (18) Professor E. F. Hilinski has informed us that they have recently completed a similar study which is to be reported in the near future. (19) Peters, K. S.; Lee, J, J. Phys. Chem. 1993, 97, 3761. (20) Bartl, J.; Steenken, S.;Mayr, H.; McClelland J. Am. Chem. Soc. 1990, 112,6918. (21) The extinction coefficient for DPM+ at 430 nm is e = 4.36 X lW M-I cm-I, ref 20. The extinction coefficientfor DPM' at 523 nm has been reported to bet 370 M-I cm-l. See: Brombert, A.; Meisel, D. J. Phys. Chem. 1985, 89,2507. However, assuming thequantum for the formation of DPM'is0.23 and for the formation of DPM+ is 0.13 at 20 ns, ref 20, then the extinction coefficient for DPM' derived from the spectrum in Figure 1 is c = 2.46 X 10, M-1 cm-1. The source of this discrepancy is unclear.
