Simple Flux-Side Formulation of State-Resolved Thermal Reaction Rates for Ring-Polymer Surface Hopping

Abstract

Employing the recently developed isomorphic Hamiltonian framework for including nuclear quantum effects in mixed quantum-classical non-adiabatic dynamics, we present a flux-side formulation of state-resolved thermal reaction rates for ring-polymer surface hopping (iso-RPSH). An appealing aspect of the new approach is that calculation of multiple stateresolved non-adiabatic thermal reaction rates is enabled with only a single free-energy surface calculation, whereas previous non-adiabatic flux-side formulations for surface hopping involve multiple free-energy surface calculations. The method is shown to be robust and straightforwardly implemented, and numerical results reveal that RPSH in the isomorphic Hamiltonian framework leads to better dividing-surface independence than alternative RPSH methods, due to improved preservation of the pathintegral statistics.

Polariton-Mediated Electron Transfer via Cavity Quantum Electrodynamics

“…The same analyses we have done in this work can be easily generalized and incorporated into those alternative ET rate theories to describe PMET processes. Here, we only briefly mention some of these theories: (i) to incorporate nuclear quantum effects from high-frequency vibrational modes, one can explicitly include the quantized vibrational states by using the Jortner theory, [125][126][127] or using the linearized path-integral Fermi's golden rule (FGR) rate expressions, [128][129][130] the state-dependent imaginary-time path integral approaches, [131][132][133][134][135] or the state-dependent Instanton theory, [136][137][138] (ii) to obtain accurate rate from the weak to strong electronic coupling regimes, one can use the state-dependent Instanton theory, 136,138,139 or compute rate through the fluxside correlation function 140 using linearized pathintegral approach, 141,142 state-dependent ringpolymer rate approaches, 133,134 or mixed quantumclassical approaches, [143][144][145][146][147][148][149][150] (iii) to incorporate memory effects of the bath, one can use the Zusman theory 151 that provides accurate non-markovian and non-adiabatic ET rate, [151][152][153][154] or use the linearized path-integral FGR rate expressions, [128][129][130] (iv) to treat non-equilibrium initial condition, one can employ the recently developed non-equilibrium FGR rate theory…”

Nonadiabatic dynamics with quantum nuclei: simulating charge transfer with ring polymer surface hopping

“…By analyzing the rate constants for charge transfer between two ethylene-like molecules in a bath of Ne atoms we have shown that nuclear quantum effects are not of major importance at 300 K but become significant at lower temperatures. In future, we intend to compare the rate constants calculated with reactive flux formulation [71][72][73] with the rate constants computed here. Additionally, we aim at studying the temperature dependence of charge transport in more realistic systems, e.g.…”

An analysis of isomorphic RPMD in the golden rule limit

“…It does share the single most important feature of standard adiabatic RPMD, in that it obeys quantum detailed balance by construction (provided a MQC method with this property is used). 1,2 We also expect that iso-RPMD will be accurate for systems in which the non-adiabatic transition is effectively classical and nuclear quantum effects are important for crossing a barrier away from this transition. In fact, the accuracy of iso-RPMD has already been demonstrated in such a situation by Tao et al in their calculation of state-resolved reaction rates for a one-dimensional two-state model of the F + H 2 reaction.…”

“…In fact, the accuracy of iso-RPMD has already been demonstrated in such a situation by Tao et al in their calculation of state-resolved reaction rates for a one-dimensional two-state model of the F + H 2 reaction. 1,2 Application of the method to similar but more complex systems will no doubt provide physical insight in the future.…”

“…To set the scene for this investigation, let us begin by introducing the iso-RPMD formalism. 1,2 Although this formalism is in principle applicable to systems with many electronic states, it will be sufficient for our purposes to consider just a two level system, for which the Hamiltonian can be written in the diabatic representation aŝ…”