Framework solid electrolytes: Effective potentials and conditional probabilities for correlated motion

For framework systems, Brownian dynamics is usually valid for determining response properties, because of effective timescale separation between mobile-ion and lattice motions. The mobile ion motions, however, are strongly correlated, and, in the presence of nonuniform potential of the framework, the ionic many-body problem is quite complex. As a possible alternative to dynamic simulations, we propose a static decoupling which is based upon rewriting the three-particle conditional density as a static, zero-temperature equilibrium expression. This procedure yields two-particle conditional densities which appear to treat both the long-range and nonuniform potentials reasonably. Effects of screening and pinning for both incommensurate systems are properly described.