“Direct” Calculation of Thermal Rate Constants for the F + H₂ → HF + F Reaction

Abstract

We present "direct" calculations of the thermal rate constant for the F + H 2 reaction. The rate is obtained from the time integral of the flux-flux autocorrelation function, which is efficiently evaluated by taking advantage of the low rank of the half-Boltzmannized flux operator. Total rate constants are obtained from exact total angular momentum J * 0 calculations and compared with approximate approaches for including nonzero J. The rate constants obtained for the F + H 2 reaction on the new, highly accurate Stark-Werner potential energy surface are in good agreement with previous experimental results.

Some Trends in Quantum Thermodynamics

“…Once this path is established, the time dependences of all the non-equilibrium thermodynamic properties (e.g., composition, chemical potentials, chemical affinities, reaction coordinates, reaction rates), including, of course, the entropy, are known. In fact, the reaction rate in the literature is typically reported at a given temperature in terms of the so-called reaction rate constant (i.e., the forward reaction rate constant), which is determined both experimentally as well as numerically via a phletora of classical (e.g., [91]), quasi-classical (e.g., [92][93][94][95][96][97][98]), and time-independent (e.g., [99,100]) and time-dependent quantum methods (e.g., [100,101]). The SEA-QT results presented here and the more extensive ones in [71,72] are reported in terms of this parameter.…”

Quantum mechanical transition state theory and tunneling corrections

“…[13][14][15] In a multidimensional case the low rank is preserved by the Boltzmann factor which limits the contribution from the degrees of freedom parallel to the dividing surface to states of lower energy. ͑Naturally the number of these states increases with temperature.͒ Thus, if the dividing surface is placed at the transition state, the number of nonzero eigenvalues of F (␤) is approximately twice the number of thermally accessible states of the activated complex at temperature T. This fact has previously been exploited by Miller and co-workers 12,[16][17][18] and Manthe and co-workers 19,20 in the calculation of exact thermal rate constants for gas-phase chemical reactions ͑including recombination processes 18,21 ͒. Significant progress in this area has also been made by Light and co-workers.…”

“…16,20 The critical quantities required for the transition state theory are C f f (0) and C f f (0). Note that all the odd derivatives are zero since C f f (t) is an even function of time.…”

“…27,28 This basis of eigenstates can then be used to evaluate the trace required to obtain C f f (t). 16,20 Then the flux-flux autocorrelation function at zero time is…”

“…͑2.7͒ and ͑2.8͒ require no time propagation, but only a single Hamiltonian multiplication on each eigenvector. Exact calculations have been carried out for several reactions involving three and four atoms, 12,[16][17][18][19][20] indicating that the transition state theory should be applicable to quite large systems.…”