We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill’s formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.

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Molecular dynamics (MD) simulations of the model SN2 reaction Cl−+CH3Cl→ClCH3+Cl− in water, and variants thereof, are presented. The resulting transmission coefficients κ, that measure the deviations of the rates from the transition state theory (TST) rate predictions due to solvent-induced recrossings, are used to assess the validity of the generalized Langevin equation (GLE)-based Grote–Hynes (GH) theory. The GH predictions are found to agree with the MD results to within the error bars of the calculations for each of the 12 cases examined. This agreement extends from the nonadiabatic regime, where solvent molecule motions are unimportant and κ is determined by static solvent configurations at the transition state, into the polarization caging regime, where solvent motion is critical in determining κ. In contrast, the Kramers theory predictions for κ fall well below the simulation results. The friction kernel in the GLE used to evaluate the GH κ values is determined, from MD simulation, by a fixed-particle time correlation function of the force at the transition state. When this is expressed as a (Fourier) friction spectrum in frequency, marked similarities to the pure solvent spectrum are observed, and are used to identify the water solvent motions that determine the transmission coefficient κ. The deviations of κ from unity, the TST value, are dominated by solvent motions (translational and reorientational) which on the time scale of the recrossings are essentially static configurations. The deviations from the frozen solvent, nonadiabatic limit values κNA are dominated by the hinderd rotations (librations). Finally, the underlying assumptions of the GLE and the GH theory are discussed within the context of the simulation results.

Using ultrafast, time-resolved, 1.54 angstrom x-ray diffraction, thermal and ultrafast nonthermal melting of germanium, involving passage through nonequilibrium extreme states of matter, was observed. Such ultrafast, optical-pump, x-ray diffraction probe measurements provide a way to study many other transient processes in physics, chemistry, and biology, including direct observation of the atomic motion by which many solid-state processes and chemical and biochemical reactions take place.

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