Free Energy Simulations a

Monte Carlo or molecular dynamics simulations involve the numerical determinations of the statistical thermodynamics and related structural, energetic and (in the case of molecular dynamics) dynamic properties of an atomic or molecular assembly on a high-speed digital computer. Applications to molecular systems range from the study of the motions of atoms or groups of atoms of a molecule or macromolecule under the influence of intramolecular energy functions to the exploration of the structure and energetics of condensed fluid phases such as liquid water and aqueous solutions based on intermolecular potentials. The quantities determined in a typical Monte Carlo or molecular dynamics simulation include the average or mean configurational energy (thermodynamic excess internal energy), various spatial distribution functions for equilibrium systems, and time-correlation functions for dynamical systems, along with detailed structural and energetic analyses thereof. Diverse problems in structural and reaction chemistry of molecules in solution, such as solvation potentials, solvent effects on conformational stability and the effect of solvent on chemical reaction kinetics and mechanism via activated complex theory also require a particular knowledge of the configurational free energy, which in principle follows directly from the statistical thermodynamic partition function for the system. Considerations on free energy in molecular simulations take a distinctly different form for intramolecular and intermolecular degrees of freedom. For the intramolecular case, the problem involves vibrational and librational modes of motion on the intramolecular energy surface. We will discuss briefly a t the end of this paper the harmonic and quasiharmonic approximation used to compute vibrational contributions to the free energy, but we will restrict the focus herein to the intermolecular case, where the particles of the system undergo diffusional motion and a harmonic or quasiharmonic treatment breaks down. These considerations apply also in the case of a flexible molecule, where conformational transitions are effectively an intramolecular “diffusional mode.” Conventional Monte Carlo and molecular dynamics procedures for diffusional modes, although firmly grounded in Boltzmann statistical mechanics and dynamics, do not proceed via the direct determination of a partition function because of well-known

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