Thermodynamic integration by statistically sampling ensembles of dynamically unstable solids without molecular dynamics

The anharmonic free energy of dynamically unstable systems can be accurately calculated by thermodynamic integration, if the configurational ensemble obeying the true potential is obtained. This usually requires computationally costly $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ molecular dynamics (AIMD). The authors present here a way to accomplish this by direct statistical sampling of ensembles using interatomic force constants and without MD. Phase transition temperatures of binary shape-memory alloys are predicted to within 25% error at a speed-up of about three orders of magnitude over AIMD.