Quantum‐classical path integral evaluation of reaction rates with a near‐equilibrium flux formulation

Abstract

Quantum-classical formulations of reactive flux correlation functions require the partial Weyl-Wigner transform of the thermalized flux operator, whose numerical evaluation is unstable because of phase cancelation. In a recent paper, we introduced a non-equilibrium formulation which eliminates the need for construction of this distribution and which gives the reaction rate along with the time evolution of the reactant population. In this work, we describe a near-equilibrium formulation of the reactive flux, which accounts for important thermal correlations between the quantum system and its environment while avoiding the numerical instabilities of the full Weyl-Wigner transform. By minimizing early-time transients, the near-equilibrium formulation leads to an earlier onset of the plateau regime, allowing determination of the reaction rate from short-time dynamics. In combination with the quantumclassical path integral methodology, the near-equilibrium formulation offers an accurate and efficient approach for determining reaction rate constants in condensed phase environments. The near-equilibrium formulation may also be combined with a variety of approximate quantum-classical propagation methods.

A tensor network representation of path integrals: Implementation and analysis

“…For reactions with long time-scales, rate theory can often be used to gain valuable insights. Quantum mechanical rates are typically related to equilibrium correlation functions involving the flux operator, F = i Ĥ0 , ĥ where ĥ = |1 1| is the projector on the donor state, |1 [59][60][61][62][63]. Since the equilibrium of a system coupled to a solvent can often be challenging to compute, it has also been shown that the same information can be obtained from the non-equilibrium flux function [64], which also happens to be related to the instantaneous timederivative of the donor population.…”

Impact of solvent on state-to-state population transport in multistate systems using coherences

“…This Channel-Dependent Population Transfer (CDPT) method takes as a starting point the nonequilibrium rate 17 generalization of the flux-based rate theory. [18][19][20] Because the non-equilibrium rate theory captures the initial condition dependent transients, CDPT is capable of providing a time-dependent picture of how the transport happens across the various channels or pathways.…”