Compensating Mass Matrix Potential for Constrained Molecular Dynamics

Abstract

Rigid internal constraints are used in molecular models to speed up molecular dynamics (MD) simulations. It is well recognized that statistical averages from such constrained MD simulations differ by a metric tensor-dependent term from similar averages computed using conventional unconstrained MD simulations. Fixman proposed augmenting the standard potential with a compensating term which depends on the metric tensor to nullify the effects of this bias term. However, in the absence of tractable algorithms to compute this compensating tensor potential and its gradient its use has been impractical. This paper derives a new algorithm for computing the compensating potential, as well as its gradient for tree topology molecular systems. The algorithm is quite straightforward and is an extension of the spatial operators basedO(N) algorithm that has been recently proposed for constrained dynamics. Indeed, the compensating potential is closely related and computed from the articulated body inertia quantities available from thisO(N) algorithm.