Some fundamental problems for an energy-conserving adaptive-resolution molecular dynamics scheme

Adaptive-resolution molecular dynamics (MD) schemes allow for changing the number of degrees of freedom on the fly and preserve the free exchange of particles between regions of different resolution. There are two main alternatives on how to design the algorithm to switch resolution using auxiliary “switching” functions: force based and potential energy based approaches. In this work we show that, in the framework of classical MD, the latter presents fundamental conceptual problems which make unlikely, if not impossible, the derivation of a robust algorithm based on the potential energy.

Figure 1

(Color online) Schematic picture of the partitioning of space in high resolution (atomistic) region $\mathbf{B}$, low resolution (coarse grained) region $\mathbf{A}$, and transition region $\Delta$. $w\left(x\right)$ is the switching function which allows a smooth transition from a coarse grained to an atomistic resolution and vice versa. Below the pictorial representation of a tetrahedron molecule that changes resolution according to the position in space is presented. This representation is taken from [7].