Integrating the Car-Parrinello equations. III. Techniques for ultrasoft pseudopotentials

Abstract

New methods for integrating the Car-Parrinello equations with ultrasoft pseudopotentials are introduced. In particular, the difficulties associated with the generalized orthonormality constraint condition 〈φ i|Ŝ({RI})|φj〉 = δij 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 usual N3 scaling associated 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 electronic 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. © 1995 American Institute of Physics.