Fokker-Planck-Langevin and extended diffusion models of internal rotation in molecules. II. Quantum mechanical analogues

Abstract

Quantum mechanical analogues of the classical Fokker-Planck-Langevin (FPL) and extended diffusion (EDJ) models of stochastic dynamics have been developed by constructing quantum mechanical collision operators that resemble the classical ones. The analogues have been used to calculate NMR reorientational correlation times and angular momentum correlation factors associated with the rotation of a one-dimensional rotor attached to a molecule and subject to various barriers to internal rotation. Quantum mechanical effects have been explored by varying a parameter, Λ (=ħ/ IK B T), which is a measure of the expected importance of those effects. The FPL analogue and one of the EDJ analogues approach the classical results in the diffusion and dense gas regimes, when Λ is small. The other EDJ analogue, which superficially appears to be closest to the classical model, does not agree with the classical results for rotors with non-zero barriers. The discrepancy arises because the quantum and classical collision operators mix the rotor states in quite different ways, despite their formal similarity. In the dilute gas regime, the quantum mechanical and classical results do not agree because of fundamental differences in the respective free rotor correlationfunctions. The theories can be applied to non-Markovian processes and dynamics other than rotational relaxation.