Universality of electronic friction: Equivalence of von Oppen's nonequilibrium Green's function approach and the Head-Gordon–Tully model at equilibrium

Abstract

For a molecule moving near a single metal surface at equilibrium, following von Oppen et al (Beilstein J. Nanotechnol, 3, 144 (2012)) and using a non-equilibrium Green's function (NEGF) approach, we derive a very general form of electronic friction that includes non-Condon effects. We then demonstrate that the resulting NEGF friction tensor agrees exactly with the Head-Gordon/Tully (HGT) model, provided that finite temperature effects are incorporated correctly. The present results are in agreement with our recent claim that there is only one, universal electronic friction tensor arising from the Born-Oppenheimer approximation (Phys. Rev. Lett. 119, 046001 (2017)

Universality of electronic friction. II. Equivalence of the quantum-classical Liouville equation approach with von Oppen's nonequilibrium Green's function methods out of equilibrium

“…Furthermore, we have shown that non-Condon effects can be easily included into a nonequilibrium electronic friction. Thus, given our previous work proving that, at equilibrium, the QCLE friction agrees with the Head-Gordon-Tully model as well as many other forms of electronic friction, 46,50,51,55,65 we believe there is now very strong proof that, in the limit of Markovian dynamics, there is only one, universal electronic friction associated with the Born-Oppenheimer approximation in the adiabatic limit. Future work must address how to incorporate non-Markovian effects efficiently; is there an optimal approach or many different approaches depending on the Hamiltonian?…”

Universal approach to quantum thermodynamics of strongly coupled systems under nonequilibrium conditions and external driving

“…At equilibrium, due to time reversal symmetry, the friction tensor is symmetric (along with respect to α and ν) and positive definite 63,68,70 , such that there is always a dissipated work associated with driving, i.e. Ẇ (2) > 0.…”

A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping

“…Furthermore, according to the QCLE (and many other approaches 35,39,40,47,48 ), the correct electronic friction term is not given by Eq. (7), but rather also involves the spectral function (such that broadening is again included)…”