Weighted multibody expansions for computing stable structures of multiatom systems

The effect of structural relaxations in alloys is described using a multibody energy expansion formalism. N-body potentials in the multibody expansion are computed from energies of isolated clusters, which, in turn, are calculated from empirical potentials or self-consistent quantum mechanical calculations. Convergence characteristics of multibody expansions (MBEs) are improved by weighting energies obtained from various truncations of many-body expansions in a method called weighted MBE (WMBE). It is shown that multibody expansions of many-atom systems can be efficiently constructed using interpolation of isolated cluster energies from databases. In contrast to the method of cluster expansion, WMBE focuses on positional degrees of freedom and, hence, explicitly handles structural relaxations during computations of stable atom clusters and periodic or amorphous phase structures.