Semiclassical transition state theory based on fourth order vibrational perturbation theory: Model system studies beyond symmetric Eckart barrier.

Abstract

The following one-dimensional model potential barriers are studied to compute the tunneling probabilities using semiclassical transition state theory (SCTST) based on fourth order vibrational perturbation theory (VPT4): (i) Morse barrier, (ii) asymmetric Eckart barrier, (iii) adjacent well barrier, and (iv) first order approximation to the symmetric Eckart barrier. The current investigation extends a previous study performed for the symmetric Eckart barrier. The performance of VPT4-SCTST is investigated for a broad range of energies, including the very deep tunneling regime (approximately 1% of the barrier height), and the results are compared to the exact quantum mechanical treatment, as well as to the popular second order vibrational perturbation theory (VPT2)-SCTST approach. While the VPT4-SCTST results are in excellent agreement with their quantum mechanical counterparts for a wide range of energies above and below the barrier, it is found for systems (ii) and (iv) that higher order terms (in ) in energy expansion are important for similarly excellent agreement in the deep tunneling regime. For the asymmetric Eckart barrier, the convergence properties of SCTST are analyzed in terms of its analytically known Siegert eigenvalues. A simple empirical modification of VPT2-SCTST advocated in the aforementioned previous work for the symmetric Eckart barrier is also tested here for the new model systems, and it is shown not to provide a uniformly systematic improvement.