Non-Markovian Effects in Quantum Rate Calculations of Hydrogen Diffusion with Electronic Friction

We address the challenge of incorporating non-Markovian electronic friction effects in quantum-mechanical approximations of dynamical observables. A generalized Langevin equation (GLE) is formulated for ring-polymer molecular dynamics (RPMD) rate calculations, which combines electronic friction with a description of nuclear quantum effects (NQEs) for adsorbates on metal surfaces. An efficient propagation algorithm is introduced that captures both the spatial dependence of friction strength and non-Markovian frictional memory. This framework is applied to a model of hydrogen diffusing on Cu(111) derived from ab initio density functional theory (DFT) calculations, revealing significant alterations in rate constants and tunnelling crossover temperatures due to non-Markovian effects. Our findings explain why previous classical molecular dynamics simulations with Markovian friction showed unexpectedly good agreement with experiment, highlighting the critical role of non-Markovian effects in first-principles atomistic simulations.