Reaction Rates in a Magnetic Field through Langevin Dynamics

Abstract

Theoretical studies of reaction rates in a magnetic field have gained renewed interest due to recent experimental observations of magnetic effects and the development of frameworks for chemical dynamics that include pseudomagnetic forces. In this thesis, I estimate the contribution from a magnetic field to the transmission factor for a reaction associated with a double-well potential constructed under the Empirical Valence Bond (EVB) model and analyze the low-friction phenomenon of rate increase in a magnetic field. By studying the dynamics around the transition state saddle point, a correction to the rate constant is obtained. The correction is given by the ratio of the positive roots of the characteristic polynomial with and without the magnetic field and may be considered the magnetic analogy to the Grote-Hynes transmission coefficient for friction. The work on this magnetic correction is concluded with a derivation of a closed-form expression for weaker fields. For this adiabatic reaction model problem, I find that above a threshold field, the field universally slows reactions. Below this threshold, I observe that for a symmetric potential, the field may appreciably increase the rate in the low friction regime. The mechanism of this rate increase is analyzed through a position autocorrelation function, and ultimately a promising connection is found between the field dependence of the orientational decorrelation and the field dependence of the rate. A compelling continuation of this work would be the extension of the presented analysis of rates in a magnetic field to nonadiabatic reactions, where magnetic field effects are strongest.