Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Abstract

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.

arXiv commentSubmitted to the Journal of Chemical Physics. 16 pages with 5 figures

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Cited by in corpus (16)

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• Electron transfer across a thermal gradient
• Ring-polymer instanton theory of electron transfer in the nonadiabatic limit
• Analytic continuation of Wolynes theory into the Marcus inverted regime
• Effects of tunnelling and asymmetry for system-bath models of electron transfer
• Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State Systems
• Should Thermostatted Ring Polymer Molecular Dynamics be used to calculate thermal reaction rates?
• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
• How to obtain thermostatted ring polymer molecular dynamics from exact quantum dynamics and when to use it
• Semiclassical analysis of the quantum instanton approximation
• Nonadiabatic instanton rate theory beyond the golden-rule limit
• Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems
• Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations
• Revisiting nuclear tunnelling in the aqueous ferrous-ferric electron transfer
• An improved path-integral method for golden-rule rates
• Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime