Molecular dynamics as a mathematical mapping. I. Differentiable force functions

The molecular dynamics technique can be viewed as a deterministic mathemati cal mapping between, on one side, the force field parameters that describe the potential energy interactions and the input macroscopic conditions, and , on the other, the calculated macroscopic properties of the bulk molecular system. The differentiability of such a mapping in the conventional molecular dynam ics calculations is affected by the discontinuities in particle positions i ntroduced by the periodic boundary conditions and the discontinuities intro duced by the minimum image convention and other methods commonly employed t o approximate the calculation of interparticle potential and force. This paper proposes an alternative molecular dynamics framework based on mo dified force functions which are almost everywhere continuous and different iable, and exhibit a natural periodicity. These characteristics obviate the need for both the periodic boundary conditions and the minimum image conve ntion, as well as for any corrections for long-range interactions. They als o make it possible to apply standard methods of variational calculus for th e computation of partial derivatives of the molecular dynamics mapping. The modified framework is first introduced for the case of simple monoatomi c fluids where the nature of the forces exerted between any pair of two par ticles is identical. A more general model describing the interactions of fl exible molecules is then developed. We describe the application of this app roach to mixtures of alkane molecules interacting via the NERD force field.