Evaluating the efficiency of power‐series expansions as model potentials for finite‐temperature atomistic calculations. Issue 11 (2nd February 2023) - Bichelmaier, Sebastian; Carrete, Jesús; Madsen, Georg K. H.
Abstract: Given the cost of ab‐initio calculations, predictive studies of temperature‐dependent phenomena in strongly anharmonic systems pose a serious challenge. Using a relatively inexpensive surrogate model for the potential energy surface to build temperature‐dependent effective harmonic potentials is a possible solution. Automatic differentiation makes high‐order Taylor potentials as surrogate models a relatively accessible possibility. Here Lennard‐Jones clusters and solids are used as a test bench on which to perform a detailed analysis of such a procedure. It is found that results might only be valid in a narrow temperature regime, outside of which the local nature of Taylor expansions leads to drastic artifacts in the free energies and derived quantities such as the thermal expansion. Those shortcomings are traced to the limited flexibility of polynomials as approximants and are therefore fundamental. The observed behavior is confirmed using density functional theory on a five‐atom silver cluster. A global interpolation strategy, in the form of a neural‐network force field, is suggested as a better path to cost‐effective surrogate models. Abstract : In high‐dimensional Gaussian distributions, most of the probability mass is concentrated in a hyperspherical shell away from the origin. This means that even high‐order Taylor approximations of the potential energy surface inevitably incur large errors for realistic displacements. Here, the effect is illustrated for the radial displacement in a three‐atom Lennard‐Jones cluster.