Predicting kinetics of spin-dependent reactions in an external magnetic field with nonadiabatic statistical theory

We introduce a theoretical framework to study the kinetics of the chemical reactions involving transitions between electronic states with different spin quantum numbers in an external magnetic field. The new equations for calculating transition probabilities and rate constants are used to generalize the nonadiabatic statistical theory, which now accounts for both the spin-orbit and Zeeman couplings between electronic states. Focusing on the singlet-triplet transitions, we define two dimensionless parameters to characterize (1) the magnetic field strength relative to the strength of spin-orbit coupling and (2) the relative magnitudes of the spin-orbit coupling matrix elements that couple the singlet state to different components of the triplet state. Based on the values of these dimensionless parameters, we define distinct coupling regimes and propose specific approaches to calculating the transition probabilities and rate constants in these regimes. We apply the introduced theoretical framework to study the effect of an external magnetic field on the kinetics of spin-forbidden isomerization of the Ni(dpp)Cl2 [dpp = 1,3-bis(diphenylphosphino)propane] complex in the strong and weak field regimes. Our calculations predict that in a magnetic field of 50 T, the isomerization rate constant increases by about 10%. We hope this work will facilitate renewed efforts in controlling spin-dependent chemical reactions with an external magnetic field.