Modeling Nonadiabatic Dynamics At Molecule-Metal Interfaces

The coupled electronic-nuclear dynamics at molecule-metal interfaces are fundamental processes that underlie many distinct areas of science: from electrochemistry, chemisorption, heterogeneous catalysis, quantum dots, all the way to molecular conduction. Simulating these coupled dynamics at molecule-metal interfaces is very challenging, due to the breakdown of the Born-Oppenheimer approximation and the inclusion of a manifold of electrons from the metal. Two methods are presented to investigate these nonadiabatic dynamics: a) In the outer sphere regime (weak electronic coupling between molecule and metal), a surface hopping approach is developed to treat nuclear motion classically with electronic motion captured by hopping between different potential energy surfaces; b) In the inner sphere regime (strong electronic coupling between molecule and metal), electronic dynamics are incorporated into a frictional force (i.e. electronic friction) together with a random force. In addition, a natural combination of these two methods called a broadened classical master equation (BCME) is developed. As benchmarked against numerical exact solutions, the BCME works well in both inner and outer sphere regimes. Finally, a universal form of electronic friction is derived. Such a formula unifies many different forms of electronic friction in the literature and allows the inclusion of electron-electron interactions, and can demonstrate interesting Kondo resonances at low temperature

Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: Non-equilibrium entropy production and higher order corrections

We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Phys. Rev. B 101, 184304 [2020]), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population. In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation

Electron transfer at molecule-metal interfaces under Floquet engineering: Rate constant and Floquet Marcus theory

Electron transfer (ET) at molecule-metal or molecule-semiconductor interfaces is a fundamental reaction that underlies all electro-chemical and molecular electronic processes as well as substrate-mediated surface photochemistry. In this study, we show that ET rates near a metal surface can be significantly manipulated by periodic modulations of an impurity level of the molecule near a metal surface. We employ the analytical Marcus theory and two numerical Floquet surface hopping algorithms that are developed previously, to calculate the ET rates near metal surface as a function of driving amplitudes and driving frequencies. We find that ET rates become faster with increasing the driving amplitude but no turnover effect, while have a turnover effect with increasing driving frequencies.Comment: 15 pages, 5 figure

Electronic Friction Near Metal Surface: Incorporating Nuclear Quantum Effect with Ring Polymer Molecular Dynamics

Molecular dynamics with electronic friction (MDEF) approach can describe nonadiabatic effects accurately at metal surfaces in the weak nonadiabatic limit. That being said, MDEF treats nuclear motion classically, such that the nuclear quantum effects are missing completely in the approach. To address this limitation, we combine electronic friction with Ring Polymer Molecular Dynamics (RPMD). In particular, we apply the averaged electronic friction from the metal surface to the centroid mode of the ring polymer. We benchmark our approach against quantum dynamics to show that electronic friction with RPMD (EF-RPMD) can capture zero-point energy as well as transition dynamics accurately. In addition, we show EF-RPMD can correctly predict the electronic transfer rate near metal surfaces in the tunneling limit as well as the barrier crossing limit. We expect our approach will be very useful to study nonadiabatic dynamics near metal surface when nuclear quantum effects become essential

Floquet driven frictional effects

When the coupled electron-nuclear dynamics are subjected to strong Floquet driving, there is a strong breakdown of the Born-Oppenheimer approximation. In this article, we derive a Fokker-Planck equation to describe non-adiabatic molecular dynamics with electronic friction for Floquet driven systems. We first provide a new derivation of the Floquet quantum-classical Liouville equation (QCLE) for driven electron-nuclear dynamics. We then transform the Floquet QCLE into a Fokker-Planck equation with explicit forms of frictional force and random force. We recast the electronic friction in terms of Floquet Green's functions such that we can evaluate the electronic friction explicitly. We show that the Floquet electronic friction tensor exhibits antisymmetric terms even at equilibrium for real-valued Hamiltonian, suggesting that there is a Lorentz-like force in Floquet driven non-Born Oppenheimer dynamics even without any spin-orbit couplings.Comment: Main: 5 pages, 3 figuers, Supplement: 5 pag