J. Phys. Chem. 1988, 92, 3391-3394 very short molecular dynamics simulation, especially in the quasiperiodic regime. It is also now possible to generate a time-dependent spectrum which only samples short time intervals and can give new insight into energy flow in these large systems. In the realm of small molecules, McDonald and MarcusI6 first demonstrated the use of time-dependent spectra. It is also possible that the MUSIC method would be of some use in discerning intramolecular tran~iti0ns.l~The technique is especially useful for generating spectra of polymer systems since structural changes would blur a normal FFT spectra and the M D simulations are more time consuming. We have made use of this advantage in a calculation of spectral shifts in stressed polyethylene.'* Also, in subsequent work, we have found this method to be very useful in computing semiclassical spectral transitions in the chaotic (16) McDonald, J. D.; Marcus, R. A. J . Chem. Phys. 1976, 65, 2180. (17) Martens, C. C.; Davis, M. J.; Ezra, G. S. Chem. Phys. Lett. 1987, 142, 519. (18) Noid, D. W.; Pfeffer, G. A., submitted for publication in J . Polym. Phys.
3391
regime,19computing local frequencies to locate resonance zones,20 and to compute frequencies from trajectories generated from quantum chemistry methods.21 The computational requirements for MUSIC are somewhat more than the FFT method but are trivial compared with CPU times needed for the molecular dynamics calculation. Acknowledgment. This research was sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc. S.K.G. acknowledges partial support from the donors of the Petroleum Research Fund, administered by the American Chemical Society. We also acknowledge helpful discussions with Professor G. A. Pfeffer in the early stages of this work. (19) Noid, D. W.; Gray, S. K. Chem. Phys. Lett. 1988, 145, 9. (20) Wozny, C. E.; Gray, S. K.; Noid, D. W., manuscript in preparation. (21) Noid, D. W.; Bloor, J. E.; Spotswood, M.; Koszykowski, M. L., to be submitted for publication in Chem. Phys. Lett.
Molecular Aspects of Nonequillbrium Solvation: A Simulation of Dipole Relaxation Omar A. Karim, A. D. J. Haymet,*.+ Department of Chemistry, University of California, Berkeley, California 94720
Matthew J. Banet, and John D. Simon*?+ Department of Chemistry B-014 and the Institute for Nonlinear Science R-002, University of California, San Diego. La Jolla. California 92093 (Received: November 30, 1987)
The molecular dynamics method has been used to simulate solvent relaxation around a dissolved solute molecule after a sudden change in its permanent dipole moment. The solvation process was followed for two cases: (1) a 4-D (debye) moment that is suddenly rotated 180° without a change in magnitude and (2) a 4-D moment that is instantaneously changed to 12 D without a change in direction. The evolution to equilibrium is found to occur on a time scale different than that predicted by dielectric continuum models. In addition, we have examined the relaxation dynamics of various solvent shells. Our simulations show that molecular aspects of the solvent, which are not included in dielectric continuum models, are important in understanding the mechanism of solvations. These simulation data provide insight into recent experimental studies of solvation measured by monitoring the time-resolved Stokes shift of probe molecules in polar solvents.
The molecular structure and dynamics of solvation of ions and depending on the nature of the perturbation: for the case of a dipoles have been the subject of numerous recent theoretical and point charge, T~ is related to T D by T L = (c,/to) T D . In a polar experimental studies.I-l7 These studies have been encouraged, in part, by a desire to understand the dynamic role of the solvent (1) Marcus, Y. Ion Soluation; Wiley: New York, 1985. in chemical reactions. In the past decade, there have been sig(2) Impey, R. W.; Madden, P. A.; McDonald, I. R. J . Phys. Chem. 1983, 87, 5071. nificant advances in the theoretical modeling of the equilibrium (3) Robinson, G. W.; Thistlewaite, P. J.; Lee, J. J . Phys. Chem. 1986, 90, properties of polar solvents."J8-21 On the other hand, none4244. quilibrium systems, and relaxation of perturbed systems back to (4) Friedrich, V.; Kivelson, D. J . Chem. Phys. 1987, 86, 6425. equilibrium, have proven difficult to study. (5) van der Zwan, G.; Hynes, J. T. J . Phys. Chem. 1985, 89, 4181. Most nonequilibrium models employ a dielectric c o n t i n ~ u m ~ ~ , ~ ~(6) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 257. (7) Karim, 0. A.; McCammon, J. A. J. Am. Chem. SOC.1986,108, 1762. representation of the solvent. In these models, the time-dependent (8) Calef, D. F.; Wolynes, P. G. J . Chem. Phys. 1983, 78, 4145. properties of the medium are treated by the relaxation behavior (9) Loring, R. F.; Mukamel, S. M. J . Chem. Phys. 1987, 87, 1272. of the frequency-dependent dielectric constant, t(w), for which, (10) Wolynes, P. G. J . Chem. Phys. 1987, 86, 5133. (11) Rossky, P. J. Annu. Reu. Phys. Chem. 1985, 36, 321. in general, a Debye form is used. t(w)
=
t,
€0 +1+ ~ W T D
In this equation, E,,, e,, and T D are the static dielectric constant, the high-frequency dielectric constant, and the Debye relaxation time, respectively. In addition to T D , a second relaxation time, the longitudinal relaxation time 71, is used commonly to gauge solvation dynamics. The functional form for T L varies slightly National Science Foundation Presidential Young Investigators 1985-1990, Alfred P. Sloan Fellows.
0022-3654/88/2092-3391$01.50/0
(12) J., Ed.; (13) (14)
Hubbard, J. B.; Wolynes, P. G. In Physics oflonic Soluation; Ulstrup, Elsevier: Amsterdam, 1986. Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 6221. Castner, E. W., Jr.; Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 1090. (15) Nagaragan, V.; Brearley, A. M.; Kang, T.-J.; Barbara, P. F. J . Chem. Phys. 1987, 86, 3183. (16) Su,S.-G.; Simon, J. D. J . Phys. Chem. 1987, 91, 2693. (17) Maroncelli, M.; Castner, E. W., Jr.; Webb, S . P.; Fleming, G. R. In Ultrafast Phenomena V; Siegman, A. E., Fleming, G. R., Eds.; SpringerVerlag: New York, 1986; p 303. (18) Mezei, M.; Beveridge, L. J . Chem. Phys. 1981, 74, 622. (19) Chandler, D.; Andersen, H. C. J . Chem. Phys. 1973, 57, 1930. (20) Pettitt, B. M.; Rossky, P. J. J . Chem. Phys. 1982, 77, 1451.
0 1988 American Chemical Society
3392 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 solvent, such as water, eo >> em and T~ (0.18 ps)
