Detailed study of the direct numerical observation of the Kramers turnover in the LiNC⇌LiCN isomerization rate

Abstract

According to Kramers, rates of molecular process are expected to follow a rise and fall from low friction (at little to no interaction with the environment) to high friction (at typical liquid densities and above). This so-called Kramers turnover was recently observed and delineated in the case of the LiNC LiCN isomerization reaction in the presence of an argon bath [P. García-Müller, R. Hernandez, R. M. Benito, and F. Borondo, Phys. Rev. Lett. 101, 178302 (2008)]. The rates were obtained using direct molecular dynamics of an all-atom representation and the Langevin dynamics of a projected representation. We now provide further evidence that the forward and backward rates are indeed exhibiting the turnover. The rates are also seen to agree remarkably well with the Pollak-Grabert-Hänggi rate formulas in regimes satisfying the theory underlying assumptions. At higher temperatures, when the theory is expected to fail, the solvated LiCN isomerization continues to exhibit activated dynamics following the turnover.

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces

“…This reaction has been extensively studied by some of us in the past and very recently in connection to THz reactivity control [36]. Most relevant in the present context, it furnished the first observation [25,37] of the turnover predicted by Kramers in his 1940 seminal paper [24,26,38].…”

“…Extensive molecular dynamics (MD) simulations of this molecule in a bath of 512 argon atoms were reported in Refs [25,37]. It was found there that the isomerization rates for the transitions from the Li-NC to Li-CN configuration and back can be well described by a onedimensional model in which the molecule is assumed to move along the minimum energy path (MEP).…”

Spectral and Pseudospectral Methods of Solution of the Fokker-Planck and Schrödinger Equations

“…References 1-40 in the introduction section of the paper by Voigtlaender and Risken (1985) refers to a large number of applications of the Kramers equation. Numerical methods for the efficient solution of the Kramers equation are of considerable importance (Berezhkovskii et al 1996;Bicout et al 2001;Schindler et al 2005;Bi and Chakraborty 2009;Coffey et al 2009;Müller et al 2012).…”

Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators

“…Indeed, the local limit, that is, the Langevin equation, has given rise to the much celebrated treatment of one-dimensional chemical reactions that gave rise to the Grote-Hynes rate formula [27,28]. It forms the basis for the description of a large number of chemical reactions using a chosen reaction coordinate coupled to a statistical bath [29][30][31][32][33][34][35][36][37]. Moreover, the bath can be colored [38][39][40][41], spacedependent [42], or even nonstationary [19,43,44].…”