Feasibility of Direct Use of Ab Initio Energies in Replica Exchange Monte Carlo Simulation of Ion Disorder in Solids

The Metropolis Monte Carlo (MMC) algorithm has seen much application in the simulation of order-disorder transitions and prediction of phase diagrams in systems such as alloys and disordered oxides. Usually, ab initio total energy methods are deemed too expensive to provide sufficient configuration sampling, and the usual approach is to use lightweight models derived via, e.g., cluster expansion fitting of ab initio energies. However, deriving quantitative models can be quite challenging for systems with complex long-range interactions such as multivalent ion oxides and heterointerfaces [1]. Here, we reexamine the feasibility of directly calculating ab initio energies at every MMC trial step. We also consider the replica exchange method [2] to speed up the equilibration and sampling. The feasibility of this idea, especially using modern-day supercomputers, is demonstrated on the calculation of temperature-dependent cation disorder in MgAl₂O₄ spinel. [1] Seko and Tanaka, J. Phys. Condens. Matter 26, 115403 (2014). [2] Hukushima and Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).