Partial derivatives of molecular dynamics calculations

摘要

The molecular dynamics technique can be viewed as a deterministic mathematical mapping between, on one hand, the force field parameters that describe the potential energy interactions and input macroscopic conditions, and, on the other, the calculated corresponding macroscopic properties of the bulk molecular system. The differentiability of such a mapping in conventional molecular dynamics calculations is affected by the discontinuities introduced through the use of the minimum image convention and other simplifications commonly employed in the calculation of interparticle potential and forces. A modified force function which is almost everywhere continuous and differentiable, and exhibits a natural periodicity has recently been proposed by Stefanovic and Pantelides (1999). These characteristics make it possible to apply standard methods for the computation of the partial derivatives of the molecular dynamics mapping based on the integration of either the adjoint equations, or the sensitivity equations of the classical Newtonian equations of motion. We present procedures for these computations in the standard microcanonical (N, V, E) ensemble, and compare the computational efficiency of the two approaches. As an illustration, we apply these techniques to a system of flexible ethane molecules, computing the partial derivatives of temperature and pressure with respect to density, energy and all potential function parameters.