The semiclassical calculation of nonadiabatic tunneling rates

Abstract

Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systemsIn this paper semiclassical low-temperature rate theory is extended to treat nonadiabatic transitions which are typically important in electron transfer reactions. This theory is appropriate for arbitrary coupling strength between electronic states. As in adiabatic semiclassical tunneling theory, it is found that the leading order contribution to the tunneling rate is due to periodic orbits which exist in the barrier region of configuration space between reactant and product. In the current case, these orbits move on effective potentials generated from upside-down ͑nuclear͒ potentials of the coupled electronic states. A stable method of finding these mixed quantum/classical ''trajectories'' is developed using a Newton-Raphson method. Examples employing model systems demonstrate that the current nonadiabatic theory well-reproduces the known adiabatic and Golden Rule limits and that the theory can indeed be applied to systems with more than one degree of freedom.

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

“…Since any multidimensional potential barrier of a chemical system has exactly one unstable mode, the one that corresponds to the reaction coordinate, so the partition function of a multidimensional barrier, which in the separable limit is a product of partition functions of each mode is pure imaginary. 26 A multidimensional potential well, instead, has only stable modes and thus its partition function is pure real. General potential energy surfaces of chemical systems have both stable (minimums) and unstable (barriers) extremums, therefore their partition functions always have real as well as imaginary parts.…”

“…41 The search of instanton trajectories by looking for their initial conditions is therefore an extremely ill-posed numerical problem. 42 There exist several methods in literature for the search of instanton trajectories. 10,[15][16][17] In this section we propose another algorithm which turned out to be sufficiently stable, intuitive, and simple.…”

Semiclassical evaluation of kinetic isotope effects in 13-atomic system

“…51, although alternative algorithms are also available. 40,45,48 An¯β-periodic trajectory can be represented in terms of Fourier series with coordinates {Q 3N− 6 } in the form…”

“…These trajectories are sufficiently easy to find using methodology described in the present paper or other methods. 40,45,48 While for known PES, the semiclassical instanton approach can provide a simple and rather accurate estimate of quantum reaction rate constants, for molecular systems with unknown PES the determination of instanton trajectories can be efficiently combined with on the fly ab initio calculations of PES, which has been already successfully implemented in Refs. 47,49, and 50.…”

Stochastic simulations of electrochemical electron transfer reactions

“…For the case of homogeneous reactions various approximate schemes have been proposed (see e.g. [6,7] and references therein). For electrochemical reactions Mohr and Schmickler [8] have derived an exact expression for the transition rate, which is valid for all interaction strengths, as long as solvent dynamics is not rate determining.…”