Molecular dynamics study onβ-phase vanadium monohydride with machine learning potential

Abstract

The formalism to construct the machine learning potentials (MLPs) is presented. We introduce the spilling factor for the simultaneous error estimation and the recursive bisection method for the reduction of the computational cost. The formalism is applied for the $\ensuremath{\beta}$-phase vanadium monohydride. The first-principles calculations based on density functional theory (DFT) are used to prepare the sample data set from which the MLP for the vanadium monohydride (VH) system is constructed. In the molecular dynamics simulation with the MLP, the time-averaged structure of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{VH}$ is predicted correctly to be the body-centered tetragonal structure with the octahedral $(O)$ site occupation of H. The average lattice constants are in good agreement with the experimental data which are not able to be reproduced by the static DFT calculation. The $O$-site occupation of H observed in the average structure is, however, a saddle point on the potential-energy surface, and the actual hydrogen occupation is found to be the $4T$ configuration.