The quantum simulation of hydrogen in metals

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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.