Calculation of the Quantum-Mechanical Tunneling in Bound Potentials

Abstract

The quantum-mechanical tunneling is often important in low-energy reactions, which involve motion of light nuclei, occurring in condensed phase. The potential energy profile for such processes is typically represented as a double-well potential along the reaction coordinate. In a potential of this type defining reaction probabilities, rigorously formulated only for unbound potentials in terms of the scattering states with incoming/outgoing scattering boundary conditions, becomes ambiguous. Based on the analysis of a rectangular double-well potential, a modified expression for the reaction probabilities and rate constants suitable for arbitrary double-(or multiple-) well potentials is developed with the goal of quantifying tunneling. The proposed definition involves energy eigenstates of the bound potential and exact quantum-mechanical transmission probability through the barrier region of the corresponding scattering potential. Applications are given for several model systems, including proton transfer in a HO-H-CH 3 model, and the differences between the quantum-mechanical and quasiclassical tunneling probabilities are examined.

Evidence of Simultaneous Spectral Hole Burning Involving Two Tiers of the Protein Energy Landscape in Cytochrome b6f

“…One could note that the tunneling model used in this and earlier NPHB works employed free-particle wave functions. In reality, the wave functions in each well of the TLS must be closer to those of the harmonic oscillator , and the well populations would oscillate out of phase. Additionally, as demonstrated in ref , cooling of the sample in the beginning of the experiment (from RT to 5 K in 2 h) may result in the ensemble being not in thermodynamic equilibrium prior to burning.…”

Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation

“…The semi-classical description of tunnelling through a potential barrier is a very well-known subject in quantum mechanics and is routinely used in many applications of chemistry and quantum physics [31,43,44]. In order to describe the tunnelling between the two opposite persistent current states of the rf-SQUID qubit, we are going to use the formalism developed in [45], which applies to a generic, potentially asymmetric double-well potential.…”

Identification of residues potentially involved in optical shifts in the water-soluble chlorophyll-a binding protein through molecular dynamics simulations

“…Further improvement in terms of comparing MD and spectroscopic data could be achieved by introducing more rigorous quantum-mechanical modeling of tunneling between the wells of the landscape, including realistic energy levels, stationary-state wavefunctions, attempt frequencies and tunneling probabilities. 65 Although simple models employed for simulating spectroscopy data feature temperature-independent barriers (only transition rates are temperature-dependent), 5,6 it is possible that barrier heights do depend on temperature. The magnitudes of the spectral shifts, another parameter that could be compared between simulations and experiments, would depend on the distance between the rotating side-group and the pigment molecule and their mutual orientation.…”