Hans C. Andersen

Molecular dynamics simulations at constant pressure and/or temperature

In the molecular dynamics simulation method for fluids, the equations of motion for a collection of particles in a fixed volume are solved numerically. The energy, volume, and number of particles are constant for a particular simulation, and it is assumed that time averages of properties of the simulated fluid are equal to microcanonical ensemble averages of the same properties. In some situations, it is desirable to perform simulations of a fluid for particular values of temperature and/or pressure or under conditions in which the energy and volume of the fluid can fluctuate. This paper proposes and discusses three methods for performing molecular dynamics simulations under conditions of constant temperature and/or pressure, rather than constant energy and volume. For these three methods, it is shown that time averages of properties of the simulated fluid are equal to averages over the isoenthalpic–isobaric, canonical, and isothermal–isobaric ensembles. Each method is a way of describing the dynamics of ...

Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids

The different roles the attractive and repulsive forces play in forming the equilibrium structure of a Lennard‐Jones liquid are discussed. It is found that the effects of these forces are most easily separated by considering the structure factor (or equivalently, the Fourier transform of the pair‐correlation function) rather than the pair‐correlation function itself. At intermediate and large wave vectors, the repulsive forces dominate the quantitative behavior of the liquid structure factor. The attractions are manifested primarily in the small wave vector part of the structure factor; but this effect decreases as the density increases and is almost negligible at reduced densities higher than 0.65. These conclusions are established by considering the structure factor of a hypothetical reference system in which the intermolecular forces are entirely repulsive and identical to the repulsive forces in a Lennard‐Jones fluid. This reference system structure factor is calculated with the aid of a simple but accurate approximation described herein. The conclusions lead to a very simple prescription for calculating the radial distribution function of dense liquids which is more accurate than that obtained by any previously reported theory. The thermodynamic ramifications of the conclusions are presented in the form of calculations of the free energy, the internal energy (from the energy equation), and the pressure (from the virial equation). The implications of our conclusions to perturbation theories for liquids and to the interpretation of x‐ray scattering experiments are discussed.

A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters

An improved metal stamped and formed screw is disclosed. The subject screw is stamped and formed from continuous web of metal stock to form a plurality of screws joined by a carrier strip. The thus formed strip of screws can be machine applied to prebored holes and manually withdrawn therefrom and reapplied by conventional means.

Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations

An algorithm, called RATTLE, for integrating the equations of motion in molecular dynamics calculations for molecular models with internal constraints is presented. The algorithm is similar to SHAKE, which is one of the standard methods for performing such calculations. RATTLE calculates the positions and velocities at the next time from the positions and velocities at the present time step, without requiring information about the earlier history. Like SHAKE, it is based on the Verlet algorithm and retains the simplicity of using Cartesian coordinates for each of the atoms to describe the configuration of a molecule with internal constraints. RATTLE guarantees that the coordinates and velocities of the atoms in a molecule satisfy the internal constraints at each time step. RATTLE has two advantages over SHAKE. On computers of fixed precision, it is of higher precision than SHAKE. Since it deals directly with the velocities, it is easier to modify RATTLE for use with the recently developed constant temperature and constant pressure molecular dynamics methods and with the nonequilibrium molecular dynamics methods that make use of rescaling of the atomic velocities.

Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time

Van der waals picture of liquids, solids, and phase transformations.

tD(T)

Optimized Cluster Expansions for Classical Fluids. I. General Theory and Variational Formulation of the Mean Spherical Model and Hard Sphere Percus‐Yevick Equations

, where

Scaling behavior in the beta -relaxation regime of a supercooled Lennard-Jones mixture.

D(T)

Electronic excited state transport in solution

is the diffusion constant. The time range for which these curves follow the master curve is identified with the

The role of long ranged forces in determining the structure and properties of liquid water

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