Unified approach to the quantum-Kramers reaction rate

Abstract

The quantum analog of Kramers rate theory is derived from a unique many-body rate approach (Miller formula), being valid at all temperatures. In contrast to the imaginary free energy method (‘‘bounce’’ method) for a dissipative system we do not have to invoke a different prescription of the rate formula for temperatures below the crossover temperature T0 to tunneling dominated escape. Miller’s many-body quantum transition state theory is shown to produce the results of the imaginary free energy technique; in particular it also describes correctly the subtle regime near crossover T∼T0.

Periodic Orbit Approach to the Quantum‐Kramers‐Rate

“…It also should be noticed that this procedure yields a closed expression for the multidimensional quantum TST-rate that holds true for all temperature [23]. Further, with the density of states for a harmonic oscillator, i.e.…”

“…Following the reasoning of Miller [27] which he put forward to obtain the improved quantum condition for the eigenvalues of an ergodic system, we now construct an improved, and rather appealing expression for k ( E ) , i.e. following Hgnggi and Hontscha [23] we use the tunneling energy in (10) and set C9,231…”

“…In doing so, we cover the whole temperature regime from T = 0 up to room temperature on a unified basis. In a previous item [23], see also Refs. [8b,9], we have already reported the results of the continuum limit of this multidimensional WKB quantum rate approach.…”

Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions

“…Indeed, for nuclear configurations in which the diabatic potentials are degenerate (i.e., V 0 (R) = V 1 (R)), the combined thermal weight of all ring-polymer configurations with k kink-pairs is proportional to (βK) 2k . [50][51][52] This connection between imaginary-time path-integral statistics and the diabatic coupling K lies at the heart of semiclassical instanton (SCI) theory, [53][54][55][56][57][58] and it underpins the accuracy of the RPMD method for the description of thermal reaction rates in the deep-tunneling regime. [59][60][61] For these reasons, the formation of kink-pairs during nonadiabatic transitions is an important feature to preserve in any extension of the RPMD method to multi-level systems.…”

Semiclassical evaluation of kinetic isotope effects in 13-atomic system

“…On the other hand, in cases when PES is not known, or when a direct path integral approach requires a considerable computational effort, a simplified way of rate constant estimation looks attractive. 20,32 One of such methods is based on the semiclassical instanton theory, 21,[33][34][35][36][37][38][39][40][41][42][43][44][45][46] and is capable of accounting for nuclear quantum effects such as zero-point energy and tunneling. Another merit of the instanton approach is that it provides more conceptual insight on the role of nuclear quantum effects, and tunneling in particular, in the mechanism of a chemical reaction.…”