Boundary based on exchange symmetry theory for multilevel simulations. I. Basic theory.

In this paper, we lay the foundations for a new method that allows multilevel simulations of a diffusive system, i.e., a system where a flux of particles through the boundaries might disrupt the primary region. The method is based on the use of flexible restraints that maintain the separation between inner and outer particles. It is shown that, by introducing a bias potential that accounts for the exchange symmetry of the system, the correct statistical distribution is preserved. Using a toy model consisting of non-interacting particles in an asymmetric potential well, we prove that the method is formally exact, and that it could be simplified by considering only up to a couple of particle exchanges without a loss of accuracy. A real-world test is then made by considering a hybrid MM(∗)/MM calculation of cesium ion in water. In this case, the single exchange approximation is sound enough that the results superimpose to the exact solutions. Potential applications of this method to many different hybrid QM/MM systems are discussed, as well as its limitations and strengths in comparison to existing approaches.