The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models

TLDR

The authors derive and apply stable‑states‑picture time‑correlation‑function formulas for rate constants to diverse gas‑phase and solution‑phase reaction models, including saddle‑point‑focused expressions, non‑Markovian Langevin dynamics, and diffusion‑limited processes, thereby improving computational efficiency and capturing short‑range dynamics. The SSP rate‑constant formulas reproduce standard trajectory results for gas‑phase bimolecular reactions, correct weak‑coupling unimolecular rates by up to 50 %, and reveal that solution‑phase barrier‑crossing rates deviate markedly from Kramers predictions, highlighting limitations of transition‑state theory.

Abstract

The time correlation function (tcf) formulas for rate constants κ derived via the stable states picture (SSP) of chemical reactions are applied to a wide variety (a–d) of gas and solution phase reaction models. (a) For gas phase bimolecular reactions, we show that the flux tcf governing κ corresponds to standard numerical trajectory calculation methods. Alternate formulas for κ are derived which focus on saddle point surfaces, thus increasing computational efficiency. Advantages of the SSP formulas for κ are discussed. (b) For gas phase unimolecular reactions, simple results for κ are found in both the strong and weak coupling collision limits; the often ignored role of product stabilization is exposed for reversible isomerizations. The SSP results correct some standard weak coupling rate constant results by as much as 50%. (c) For barrier crossing reactions in solution, we evaluate κ for a generalized (non-Markovian) Langevin description of the dynamics. For several realistic models of time dependent friction, κ differs dramatically from the popular Kramers constant friction predictions; this has important implications for the validity of transition state theory. (d) For solution reactions heavily influenced by spatial diffusion, we show that the SSP isolates short range reaction dynamics of interest and includes important barrier region effects in structural isomerizations often missed in standard descriptions.