Uncertainty quantification for classical effective potentials: An extension to potfit

Abstract

Effective potentials are an essential ingredient of classical molecular dynamics (MD) simulations. Little is understood of the consequences of representing the complex energy landscape of an atomic configuration by an effective potential or force field containing considerably fewer parameters. The probabilistic potential ensemble method has been implemented in the potfit force matching code. This introduces uncertainty quantification into the interatomic potential generation process. Uncertainties in the effective potential are propagated through MD to obtain uncertainties in quantities of interest (QoI), which are a measure of the confidence in the model predictions. We demonstrate the technique using three potentials for nickel: two simple pair potentials, Lennard-Jones and Morse, and a local density dependent embedded atom method potential. A potential ensemble fit to density functional theory (DFT) reference data is constructed for each potential to calculate the uncertainties in lattice constants, elastic constants and thermal expansion. We quantitatively illustrate the cases of poor model selection and fit, highlighted by the uncertainties in the quantities calculated. This shows that our method can capture the effects of the error incurred in QoI resulting from the potential generation process without resorting to comparison with experiment or DFT, which is an essential part to assess the predictive power of MD simulations.