ALBERT

Notes: Molecular dynamics simulations are used to determine the time-dependent friction for pair diffusion in an isotropic Lennard-Jones fluid as a function of the separation between two diffusing particles. A numerical method proposed by Straub, Borkovec and Berne is used. It is found that both the initial value and the detailed time-dependence of the friction are dependent on the interparticle separation. The dependence of the pair diffusion coefficient on separation is determined. Comparisons are made with various hydrodynamic and collision theories. The rate constant for diffusion controlled reactions is discussed.

Notes: A method is presented that uses integral equation theory to determine analytic temperature derivatives of the radial distribution functions. It is illustrated by studying the solvation thermodynamics of monatomic solutes in aqueous solution. The results agree well with the density derivative method developed previously [Yu and Karplus, J. Chem. Phys. 89, 2366 (1988)]. An expression for the solvation enthalpy is derived which allows direct comparison with experimental and isobaric–isothermal (NPT) ensemble simulation data. Satisfactory agreement with experiment is found for pure water and for the aqueous solvation of monovalent ions. Simple equations that exploit the site–site HNC closures are given for the decomposition of the potential of mean force into its enthalpic (or energetic) and entropic components. Since the extended RISM (HNC-RISM) theory yields an incorrect (trivial) value of the dielectric constant, two different ways to correct for the asymptotic behavior of the solute–solute potential of mean force are compared. They lead to similar results but the method in which the solvent dielectric constant is modified from the outset can be applied more generally.The interactions between nonpolar and between polar solutes in water are decomposed into enthalpic and entropic contributions. This is difficult to do by computer simulations because of the lack of precision in such calculations. The association of nonpolar solutes in water is found to have comparable enthalpic and entropic contributions; this result disagrees with the usual description of an entropy-dominated hydrophobic interaction. For ions, the somewhat surprising result is that the association of like-charged species is enthalpy driven while for oppositely charged ions entropic effects are dominant. The process of bringing two like-charged ions together leads to higher local charge density; the more favorable solvation enthalpy arising from this increase in charge density (q2 dependence) more than compensates for the Coulombic repulsion. For oppositely charged ions, association leads to a partial charge neutralization in which the favorable Coulombic attraction is overwhelmed by the loss of stabilizing solvation enthalpy. The entropic increase is due to the greater freedom of the surrounding water molecules resulting from the partial charge neutralization.

Notes: The average solvent distribution near complex solid substrates of arbitrary geometry is calculated by solving the hypernetted chain (HNC) integral equation on a three-dimensional discrete cubic grid. A numerical fast Fourier transform in three dimensions is used to calculate the spatial convolutions appearing in the HNC equation. The approach is illustrated by calculating the average solvent density in the neighborhood of small clusters of Lennard-Jones particles and inside a periodic array of cavities representing a simplified model of a porous material such as a zeolite. Molecular dynamics simulations are performed to test the results obtained from the integral equation. It is generally observed that the average solvent density is described accurately by the integral equation. The results are compared with those obtained from a superposition approximation in terms of radial pair correlation functions, and the reference interaction site model (RISM) integral equations. The superposition approximation significantly overestimates the amplitude of the density peaks in particular cases. Nevertheless, the number of the nearest neighbors around the clusters is well reproduced by all approaches. The present calculations demonstrate the feasibility of a numerical solution of HNC-type integral equations for arbitrarily complex geometries using a three-dimensional discrete grid. © 1995 American Institute of Physics.

Notes: An approach is developed to obtain statistical properties similar to those of an infinite bulk system from computer simulations of a finite cluster. A rigorous theoretical formulation is given for the solvent boundary potential which takes the influence of the surrounding bulk into account. The solvent boundary potential is the configuration-dependent solvation free energy of an effective cluster composed of an arbitrary solute and a finite number of explicit solvent molecules embedded inside a hard sphere of variable radius; the hard sphere does not act directly on the solute or the explicit solvent molecules, and its radius varies according to the instantaneous configurations. The formulation follows from an exact separation of the multidimensional configurational Boltzmann integral in terms of the solvent molecules nearest to the solute and the remaining bulk solvent molecules. An approximation to the solvent boundary potential is constructed for simulations of bulk water at constant pressure, including the influence of van der Waals and electrostatic interactions. The approximation is illustrated with calculations of the solvation free energy of a water molecule and of sodium and potassium ions. The influence of bulk solvent on the conformational equilibrium of molecular solutes is illustrated by performing umbrella sampling calculations of n-butane and alanine dipeptide in water. The boundary potential is tested to examine the dependence of the results on the number of water molecules included explicitly in the simulations. It is observed that bulk-like results are obtained, even when only the waters in the first hydration shell are included explicitly.

Notes: A statistical mechanical integral equation theory is developed to describe the average structure of a polar liquid around a complex molecular solute of irregular shape. The integral equation is formulated in three-dimensional Cartesian coordinates from the hypernetted chain (HNC) equation for a solute at infinite dilution. The direct correlation function of the pure solvent used in the theory is taken from the analytical solution of the mean spherical approximation (MSA) equation for a liquid constituted of nonpolarizable hard spheres with an embedded dipole at their center. It is demonstrated explicitly that, in the limit where the size of the solvent particles becomes very small, the present theory reduces to the well-known equations for macroscopic electrostatics in which the solvent is represented in terms of a dielectric continuum. A linearized version of the integral equation corresponds to a three-dimensional extension of the familiar MSA equation. This 3D-MSA integral equation is illustrated with numerical applications to the case of an ion, a water molecule, and N-methylacetamide. The numerical solution, obtained on a discrete three-dimensional cubic grid in Cartesian coordinates, yields the average solvent density and polarization density at all the points x,y,z around the solute. All spatial convolutions appearing in the theory are calculated using three-dimensional numerical fast Fourier transforms (FFT). © 1996 American Institute of Physics.

Notes: The intramolecular proton transfer in the enol form of acetylacetone is investigated at various temperatures both classically and quantum-mechanically using computer simulations. The potential energy surface is modeled using the empirical valence bond (EVB) approach of Warshel and fitted to the results of ab initio calculations. Quantum-statistical results are obtained via discretized Feynman path integral simulations. The classical and centroid potential of mean force for the reaction coordinate is obtained using umbrella sampling. The proton transfer rate is calculated based on classical and on Feynman path integral quantum transition state theory. For the classical system, the transmission coefficient is obtained from activated dynamics. Two different reaction coordinates are compared, the first one involving explicitly the transferring proton and the second one involving only heavy atoms in the molecules. The influence of isotopic substitutions is investigated by considering a fully deuterated version of acetylacetone. It is observed that there are significant differences between classical and quantum-mechanical calculations caused mainly by the lack of tunneling effects in the former. The quantum fluctuations of heavy atoms are found to have a considerable influence on the magnitude of the proton transfer rate. © 1997 American Institute of Physics.