The quantum simulation of hydrogen in metals

Abstract

Realistic quantitative calculations on atomistic models for hydrogen in metals are difficult because quantum effects must be included. We show that quantum simulation based on Feynman's path-integral formulation of quantum mechanics gives a powerful way of making such calculations. After summarizing some essential facts about metal-hydrogen systems, we explain the principles of pathintegral simulation. We present the results of classical molecular-dynamics and quantum path-integral simulations of hydrogen in Pd and Nb based on simple empirical interaction models. Results are given for the probability density ρ(r) of hydrogen as a function of position r in the unit cell, and for a quantity proportional to the diffusion coefficient. We point out that diffraction measurements of ρ(r) would allow an important test of the interaction models. The simulated diffusion coefficient for H in Nb shows the experimentally observed break in Arrhenius slope at ∼250 K, which we argue represents a cross-over from quantum to classical behaviour; the low- and high-temperature activation energies are in reasonable agreement with experiment. We conclude with a general discussion of the significance of quantum simulation for metal-hydrogen studies.