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The authors formulate a non-Markovian generalized Langevin dynamics framework that retains coordinate-dependent electronic friction and quantum colored noise to simulate nonequilibrium vibronic dynamics at molecule-metal interfaces. By representing force-derived memory kernels through exponential decompositions, the framework avoids the breakdown of conventional Markovian approximations via an efficient Markovian embedding scheme. Validated against numerically exact hierarchical equations of motion (HEOM) on molecular junctions, the approach accurately stabilizes nonequilibrium vibrational regimes where traditional electronic friction catastrophically fails.
Standard electronic friction approximations catastrophically break down under nonequilibrium conditions, but capturing memory kernels via Markovian embedding stabilizes molecular dynamics to match exact quantum benchmarks.
We present a general framework for simulating the nonequilibrium vibronic dynamics of molecules interacting with metal surfaces, which utilizes non-Markovian electronic friction and the corresponding generalized Langevin equation. The method employs a Markovian embedding scheme to sample coordinate-dependent quantum colored noise, with the underlying memory kernels represented systematically by exponential decompositions obtained directly from the electronic forces. In doing so, the approach extends the widely used electronic friction and Langevin dynamics formalism beyond the conventional Markovian approximation while retaining the coordinate dependence of the electronic back-action. We demonstrate the method for nonequilibrium charge transport through a vibrationally coupled molecular junction, where comparisons with numerically exact hierarchical equations of motion simulations show that the non-Markovian formulation is both more accurate and more robust than its Markovian counterpart. In particular, we find that non-Markovian electronic forces play a decisive role in the nonequilibrium vibrational dynamics, stabilizing regimes in which the conventional Markovian approximation fails.
