Algorithms and novel applications based on the isokinetic ensemble. II. Ab initio molecular dynamics

Abstract

In this paper (Paper II), the isokinetic dynamics scheme described in Paper I is combined with the plane-wave based Car–Parrinello (CP) ab initio molecular dynamics (MD) method [R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)] to enable the efficient study of chemical reactions and metallic systems. The Car–Parrinello approach employs “on the fly” electronic structure calculations as a means of generating accurate internuclear forces for use in a molecular dynamics simulation. This is accomplished by the introduction of an extended Lagrangian that contains the electronic orbitals as fictitious dynamical variables (often expressed directly in terms of the expansion coefficients of the orbitals in a particular basis set). Thus, rather than quench the expansion coefficients to obtain the ground state energy and nuclear forces at every time step, the orbitals are “propagated” under conditions that allow them to fluctuate rapidly around their global minimum and, hence, generate an accurate approximation to the nuclear forces as the simulation proceeds. Indeed, the CP technique requires the dynamics of the orbitals to be both fast compared to the nuclear degrees of freedom while keeping the fictitious kinetic energy that allows them to be propagated dynamically as small as possible. While these conditions can be easy to achieve in many types of systems, in metals and highly exothermic chemical reactions difficulties arise. (Note, the CP dynamics of metals is incorrect because the nuclear motion does not occur on the ground state electronic surface but it can, nonetheless, provide useful information.) In order to alleviate these difficulties the isokinetic methods of Paper I are applied to derive isokinetic CP equations of motion. The efficacy of the new isokinetic CPMD method is demonstrated on model and realistic systems. The latter include, metallic systems, liquid aluminum, a small silicon sample, the 2×1 reconstruction of the silicon 100 surface, and the Diels–Alder addition of 1,3-butadiene to the reconstructed silicon 100 surface.