How to calculate the rate constants for nonradiative transitions between the M_S components of spin multiplets?

Abstract

Predicting the rates of spin-dependent processes characterised by nonradiative transitions between electronic states with different spin multiplicities is important for understanding the mechanisms of many photochemical and catalytic reactions. To calculate these rates, it is necessary to define the spin state representation and the couplings between these states that drives the interstate transitions. In this work, we describe three different approaches to calculating the spin–orbit coupling (SOC), transition probabilities, and rate constants between the M_S components of the electronic states with different spin multiplicities. We implemented these approaches in our nonadiabatic statistical theory (NAST) software package, which predicts the transition probabilities and rate constants of spin-dependent processes using information obtained from electronic structure calculations. We discuss the advantage and drawbacks of each approach and, as an example, calculate the rate constants for transitions between the spin states in the active site model of the protein rubredoxin.

GRAPHICAL ABSTRACT

KEYWORDS:

• Spin–orbit coupling
• reaction rate constants
• nonadiabatic statistical theory
• spin-forbidden reactions
• rubredoxin

Acknowledgements

SAV would like to thank Peter Gill for valuable advice, continuing support, and inspiring the author to work on hard problems. The authors thank Ilya Dergachev for fruitful discussions and comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supporting Information

The Supporting Information (SI) contains the results for the quartet-sextet crossing in the rubredoxin active site model, and the input files for NAST calculations.

Code and data availability

The source code of the NAST package is available free of charge at https://github.com/svarganov/NAST.

Additional information

Funding

This material is based upon work partially supported by the National Science Foundation through a CAREER Award (CHE–1654547) and the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Established Program to Stimulate Competitive Research under Award Number DE-SC0022178.