Rate constants calculation with a simple mixed quantum/classical implementation of the flux-flux correlation function method

Abstract

A simple mixed quantum/classical (mixed-Q/C) implementation of the flux-flux correlation function method has been applied to evaluate rate constants for a two-dimensional model system. The model consists of an Eckart barrier resembling the collinear H + H(2) reaction, linearly coupled to a harmonic oscillator. Results are presented for a broad range of parameters for temperatures between 140 and 300 K. It is found that the mixed-Q/C method gives fairly accurate results as long as the reaction does not involve too many recrossings. This suggests that the methodology could be extended to treat direct polyatomic reactions in gas phase.

Direct mixed‐quantum/classical computations of k(T). An analysis of the use of different coordinate systems

“…Miller et al23 demonstrated that the rate constants for a gas‐phase reaction can be accurately calculated from where Q r ( T ) is the reactants partition function per unit volume and C ff ( t ) is the flux–flux correlation function, Here F̂ = [ Ĥ , h ] is the flux operator, h is the Heaviside step function, β = ( kT ) −1 , and F̂ (β) is the Boltzmannized flux operator By introducing the spectral decomposition of F̂ (β) into Eq. (2), a numerically convenient expression is obtained to evaluate C ff ( t )20, In this expression, f j and | u j 〉 are the eigenvalues and eigenfunctions of F̂ (β), respectively, N f is the number of such eigenfunctions with non‐negligible eigenvalues, and the | u j ( t )〉 is the time‐evolved eigenfunction of F̂ (β), To perform the mixed‐Q/C computations, the Hamiltonian is written as1, 20 In this equation, Ĥ s is the quantum Hamiltonian of the “system,” which only groups a selected set of coordinates, s , and their conjugated momenta. Ideally, s includes all the modes directly involved in the reactive event.…”

“…In a recent article1 we applied a mixed‐quantum/classical (Q/C) version of the flux–flux correlation function method to directly calculate thermal rate constants for a model system. The model, previously introduced by McRae et al2 consisted of an Eckart barrier resembling the collinear H + H 2 → H 2 + H reaction, bilinearly coupled to a harmonic oscillator.…”