Max L. Berkowitz

A smooth particle mesh Ewald method

The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1. Furthermore, efficient calculation of the virial tensor follows. Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less.

Ewald summation for systems with slab geometry

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities

Hardness and softness kernels η(r,r’) and s(r,r’) are defined for the ground state of an atomic or molecular electronic system, and the previously defined local hardness and softness η(r) and s(r) and global hardness and softness η and S are obtained from them. The physical meaning of s(r), as a charge capacitance, is discussed (following Huheey and Politzer), and two alternative ‘‘hardness’’ indices are identified and briefly discussed.

Many-body effects in molecular dynamics simulations of Na +(H2O)n and Cl-(H2O) n clusters

Many‐body effects were examined in a series of molecular dynamics computer simulations on the ionic aqueous clusters Na+(H2O)n (n=4,5,6,14) and Cl−(H2O)n (n=4,5,6,7,8,14). Two potential models were used in the simulations. In one model (TIP4P) the potential was pairwise additive, while in the second model (SPCE/POL) the many body effects were explicitly included through a self‐consistent polarization routine. The two models produce equilibrium structures which are significantly different in energy and geometry. The SPCE/POL model consistently predicts energetically more stable products. In addition, for the anion cluster systems the SPCE/POL model places the Cl− on the surface of the water cluster.

Structure of Dipalmitoylphosphatidylcholine/Cholesterol Bilayer at Low and High Cholesterol Concentrations: Molecular Dynamics Simulation

By using molecular dynamics simulation technique we studied the changes occurring in membranes constructed of dipalmitoylphosphatidylcholine (DPPC) and cholesterol at 8:1 and 1:1 ratios. We tested two different initial arrangements of cholesterol molecules for a 1:1 ratio. The main difference between two initial structures is the average number of nearest-neighbor DPPC molecules around the cholesterol molecule. Our simulations were performed at constant temperature (T = 50 degrees C) and pressure (P = 0 atm). Durations of the runs were 2 ns. The structure of the DPPC/cholesterol membrane was characterized by calculating the order parameter profiles for the hydrocarbon chains, atom distributions, average number of gauche defects, and membrane dipole potentials. We found that adding cholesterol to membranes results in a condensing effect: the average area of membrane becomes smaller, hydrocarbon chains of DPPC have higher order, and the probability of gauche defects in DPPC tails is lower. Our results are in agreement with the data available from experiments.

Molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer with NaCl.

Molecular dynamics simulations are performed on two hydrated dipalmitoylphosphatidylcholine bilayer systems: one with pure water and one with added NaCl. Due to the rugged nature of the membrane/electrolyte interface, ion binding to the membrane surface is characterized by the loss of ion hydration. Using this structural characterization, binding of Na(+) and Cl(-) ions to the membrane is observed, although the binding of Cl(-) is seen to be slightly weaker than that of Na(+). Dehydration is seen to occur to a different extent for each type of ion. In addition, the excess binding of Na(+) gives rise to a net positive surface charge density just outside the bilayer. The positive density produces a positive electrostatic potential in this region, whereas the system without salt shows an electrostatic potential of zero.

Molecular dynamics with stochastic boundary conditions

Abstract We present and illustrate a simple approach for carrying out molecular dynamics simulations subject to stochastic boundary conditions. Methods of this type are expected to be useful in the study of chemical reactions and other localized processes in dense media.

Structure and Dynamics of Water at the Pt(111) Interface: Molecular Dynamics Study

We prescribe an analytical form of the interaction potential between rigid water and a rigid platinum metal surface, which takes into account the surface symmetry and corrugation. Using this potential we perform a molecular dynamics computer simulation on water lamina restricted by two Pt(111) surfaces and investigate the structure and dynamics of water at the Pt interface. At 300 K the water layer adjacent to the metal surface displays solid‐like properties. Patches of ice‐like structure embedded in this layer are observed in the simulation. The next two layers of water display ordering similar to ice‐I. Beyond these three layers the structure and dynamics of water are bulk‐like.

Dielectric constant of water at high electric fields: Molecular dynamics study

Molecular dynamics computer simulations have been carried out for water enclosed between Pt(111) surfaces at high external electric fields. The dielectric constant of water as a function of electric fields has been calculated. Two-dimensional Ewald summation technique has been used for the calculation of long-range Coulombic forces. Simulations with a larger distance between walls, different surfaces, and bulk water have been done to confirm the macroscopic nature of the dielectric constant. Calculated dielectric constants have been compared with those obtained by a theoretical prediction and a recent simulation study.

A classical fluid-like approach to the density-functional formalism of many-electron systems

Within the framework of a new local thermodynamic transcription [Ghosh, Berkowitz, and Parr, Proc. Natl. Acad. Sci. U.S.A. 81, 8028 (1984)] of ground state density‐functional theory, the electron cloud is interpreted as an inhomogeneous fluid at an effective local temperature. The correlation functions are defined and integral equations are introduced for this electron fluid along the lines of the theory of inhomogeneous classical liquids. An equation of state and a local compressibility equation are also developed. Extension to a mixture of two fluid components is explored as a means for investigating spin‐polarized cases. The formalisms broaden the scope of the hydrodynamic analogy to quantum mechanics and provide an alternative integral equation method for calculation of the electron density of many‐electron systems.