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When information about structure in equilibrium state is once obtained at well defined temperature, there can generally be multiple candidates of potential energy surface (PES) to reproduce the measured structure within given accuracy. Typically, in order to predict the PES, one should perform trial-and-error statistical thermodynamic simulation with assumed multibody interactions, where it is unclear whether the predicted PES is unique to provide the measured structure. Here we show that map from a set of selected structure in crystalline solids to that of corresponding PES is almost bijective within finite-dimensional configuration space under given class of spatial constraint on constituents of the system, where the PES can be inversely determined from the measured structure in equilibrium disordered states by simply acting special operator depending only on temperature and the spatial constraint. We provide quantitative measure of which structure can be applied to the map to reasonablly obtain the corresponding PES. We also propose practical modification of the special operator for the measured structure, where temperature and/or measured spatial region is unclear.

Accurate Prediction of Potential Energy Surface via Thermodynamically Equilibrium Structure