William G. Hoover

Bio: William G. Hoover is an academic researcher from University of California, Davis. The author has contributed to research in topics: Non-equilibrium thermodynamics & Equations of motion. The author has an hindex of 52, co-authored 244 publications receiving 27658 citations. Previous affiliations of William G. Hoover include University of Vienna & Applied Science Private University.

Canonical dynamics: Equilibrium phase-space distributions

Abstract: Nos\'e has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with ${V}^{1/D}$ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta ${p}_{s}$ and ${p}_{v}$. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, ${p}_{x}$, V, \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{}, and \ensuremath{\zeta}, where the x are reduced distances and the two variables \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{} and \ensuremath{\zeta} act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.

Melting Transition and Communal Entropy for Hard Spheres

Abstract: In order to confirm the existence of a first‐order melting transition for a classical many‐body system of hard spheres and to discover the densities of the coexisting phases, we have made a Monte Carlo determination of the pressure and absolute entropy of the hard‐sphere solid. We use these solid‐phase thermodynamic properties, coupled with known fluid‐phase data, to show that the hard‐sphere solid, at a density of 0.74 relative to close packing, and the hard‐sphere fluid, at a density of 0.67 relative to close packing, satisfy the thermodynamic equilibrium conditions of equal pressure and chemical potential at constant temperature. To get the solid‐phase entropy, we integrated the Monte Carlo pressure–volume equation of state for a “single‐occupancy” system in which the center of each hard sphere was constrained to occupy its own private cell. Such a system is no different from the ordinary solid at high density, but at low density its entropy and pressure are both lower. The difference in entropy between an unconstrained system of particles and a constrained one, with one particle per cell, is the so‐called “communal entropy,” the determination of which has been a fundamental problem in the theory of liquids. Our Monte Carlo measurements show that communal entropy is nearly a linear function of density.

Constant-pressure equations of motion

Abstract: Some of the differences among several alternative formulations of constant-pressure molecular dynamics are described. The formulations all agree in the large-system limit, but differ for small systems.

Computational statistical mechanics

Abstract: Hardbound. Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nos-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and analysis of nonequilibrium mass, momentum, and energy flows. Such a unified approach makes possible consistent mechanical definitions of temperature, stress, and heat flux which lead to a microscopic demonstration of the Second Law of Thermodynamics directly from mechanics. The intimate connection linking Lyapunov-unstable microscopic motions to macroscopic

Fifth and Sixth Virial Coefficients for Hard Spheres and Hard Disks

Abstract: New expressions for the fourth, fifth, and sixth virial coefficients are obtained as sums of modified star integrals. The modified stars contain both Mayer f functions and f functions (f≡f+1). It is shown that the number of topologically distinguishable graphs occurring in the new expressions is about half the number required in previous expressions. This reduction in the number of integrals makes numerical calculation of virial coefficients simpler and more nearly accurate. For particles interacting with a hard‐core potential, values of the modified star integrals are shown to depend strongly on dimension; for example, several modified star integrals are identically zero for hard disks (two dimensions), but give nonzero values for hard spheres (three dimensions). Of all the modified star integrals contributing to the fourth, fifth, and sixth virial coefficients, the complete star integrals are shown to be the largest. Mayer's expressions for these coefficients made the complete star integrals the small...

Molecular dynamics with coupling to an external bath.

Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

Scalable molecular dynamics with NAMD

Abstract: NAMD is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. Features for steering the simulation across barriers and for calculating both alchemical and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomolecular system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the molecular graphics/sequence analysis software VMD and the grid computing/collaboratory software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.

Polymorphic transitions in single crystals: A new molecular dynamics method

Abstract: A new Lagrangian formulation is introduced. It can be used to make molecular dynamics (MD) calculations on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamical equations given by this Lagrangian. This new MD technique is well suited to the study of structural transformations in solids under external stress and at finite temperature. As an example of the use of this technique we show how a single crystal of Ni behaves under uniform uniaxial compressive and tensile loads. This work confirms some of the results of static (i.e., zero temperature) calculations reported in the literature. We also show that some results regarding the stress‐strain relation obtained by static calculations are invalid at finite temperature. We find that, under compressive loading, our model of Ni shows a bifurcation in its stress‐strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. It is suggested that such a transformation could perhaps be observed experimentally under extreme conditions of shock.

A unified formulation of the constant temperature molecular dynamics methods

Abstract: Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.