Glenn Martyna

Modularly invariant equations of motion are derived that generate the isothermal–isobaric ensemble as their phase space averages. Isotropic volume fluctuations and fully flexible simulation cells as well as a hybrid scheme that naturally combines the two motions are considered. The resulting methods are tested on two problems, a particle in a one-dimensional periodic potential and a spherical model of C60 in the solid/fluid phase.

Nosé has derived a set of dynamical equations that can be shown to give canonically distributed positions and momenta provided the phase space average can be taken into the trajectory average, i.e., the system is ergodic [S. Nosé, J. Chem. Phys. 81, 511 (1984), W. G. Hoover, Phys. Rev. A 31, 1695 (1985)]. Unfortunately, the Nosé–Hoover dynamics is not ergodic for small or stiff systems. Here a modification of the dynamics is proposed which includes not a single thermostat variable but a chain of variables, Nosé–Hoover chains. The ‘‘new’’ dynamics gives the canonical distribution where the simple formalism fails. In addition, the new method is easier to use than an extension [D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. 204, 155 (1990)] which also gives the canonical distribution for stiff cases.

The Trotter factorization of the Liouville propagator is used to generate new reversible molecular dynamics integrators. This strategy is applied to derive reversible reference system propagator algorithms (RESPA) that greatly accelerate simulations of systems with a separation of time scales or with long range forces. The new algorithms have all of the advantages of previous RESPA integrators but are reversible, and more stable than those methods. These methods are applied to a set of paradigmatic systems and are shown to be superior to earlier methods. It is shown how the new RESPA methods are related to predictor–corrector integrators. Finally, we show how these methods can be used to accelerate the integration of the equations of motion of systems with Nosé thermostats.

Explicit reversible integrators, suitable for use in large-scale computer simulations, are derived for extended systems generating the canonical and isothermal-isobaric ensembles. The new methods are compared with the standard implicit (iterative) integrators on some illustrative example problems. In addition, modification of the proposed algorithms for multiple time step integration is outlined.

A new reciprocal space based formalism for treating long range forces in clusters is presented. It will be shown how the new formalism can be incorporated into plane-wave based density function theory calculations, standard Ewald summation calculations, and smooth particle-mesh Ewald calculations to yield accurate and numerically efficient descriptions of long range interactions in cluster systems.