Science Abstract

Abstract

I

In this paper and in a companion paper the problem of integrating the equations of motion in Car-Parrinello simulations is addressed. In this paper, new techniques for treating the constraint problem based on the velocity Verlet integrator and the Gaussian dynamics are presented. Questions of adiabaticity and temperature control are discussed, and it is shown how to combine the new techniques with the recently developed Nose-Hoover chain thermostat method. All new techniques are described using the formalism of operator factorizations applied to the classical Liouville propagator. In the companion paper, the formalism and application of multiple time scale methodology in Car- Parrinello simulations are discussed.

II

In this paper, new techniques for integrating the Car- Parrinello equations based on multiple time scale methodology are presented. The formalism of multiple time scale methodology based on operator factorizations of the classical Liouville propagator is reviewed. It is shown how the techniques are applied to Car-Parrinello for use with the velocity Verlet and Gaussian dynamics schemes presented in the preceding paper 101, 1302 (1994)>, and a detailed discussion is presented of how a reference system for Car-Paninello simulations may be chosen. It is shown that the use of such techniques can save up to a factor of 5-10 in cpu time over the standard methods.

III

New methods for integrating the Car-Parrinello equations with ultrasoft pseudopotentials are introduced. In particular, the difficulties associated with the generalized orthonormality constraint condition <ø_i|S({R_I})|ø_j>= ð_ij are addressed. It is shown that the equations of motion can be integrated using the velocity Verlet/RATTLE scheme, and a new method, the constrained nonorthogonal orbital method, that eliminates the need to enforce this constraint explicitly is introduced. In this new scheme, the generalized orthonormality constraint is satisfied implicitly, thus allowing the freedom to choose simpler constraint conditions. We show that the usual N³ scaling asssociated with the calculation of the Lagrange multipliers in the constraint force can be reduced to an N² calculation by the use of a simple set of norm or length constraints on the electonic orbitals without sacrificing accuracy. The constrained nonorthogonal orbital method is shown to be considerably simpler to implement and more efficient than the standard approach to the ultrasoft pseudopotential problem.