Molecular dynamics as a mathematical mapping. II. Partial derivatives in the microcanonical ensemble

Performing molecular dynamics in a fully continuous and differentiable fram ework can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy intera ctions and input macroscopic conditions, and, on the other, the calculated corresponding macroscopic properties of the bulk molecular system. Within this framework, it is possible to apply standard methods of variatio nal calculus for the computation of the partial derivatives of the molecula r dynamics mapping based on the integration of either the adjoint equations or the sensitivity equations of the classical Newtonian equations of motio n. We present procedures for these computations in the standard microcanoni cal (N, V, E) ensemble, and compare the computational efficiency of the two approaches. The general formulations developed are applied to the specific example of bulk ethane fluid. With these procedures in place, it is now possible to compute the partial d erivatives of any property determined by molecular dynamics with respect to any input property and any potential parameter. Moreover, these derivative s are computed to essentially the same level of numerical accuracy as the o utput properties themselves.