Anharmonic free energy of lattice vibrations in fcc crystals from a mean-field bond

It has recently been shown that the ab initio anharmonic free energy of fcc crystals can be approximated to meV/atom accuracy by a lattice of anharmonic nearest-neighbor bonds, where the bonding potential can be efficiently parametrized from the target system. We develop a mean-field approach for the free energy of a general bond lattice, analytically accounting for strong bond-bond correlations while enforcing material compatibility and thermodynamic self-consistency. Applying our fundamentally anharmonic model to fcc crystals yields free energies within meV/atom of brute force thermodynamic integration for core seconds of computational effort. Potential applications of this approach in computational materials science are discussed.