Modeling of Spin‐Forbidden Reactions

Abstract

Chapter 2 is a tutorial on computing spin-forbidden reactions. Most chemists solving problems with quantum chemical tools typically work on a single potential energy surface but there are many chemical transformations where two or more potential energy surfaces need to be included to describe properly the event that is taking place. How one goes about treating changes in spin multiplicity in this situation is a daunting task. Described for the novice is the importance of the minimum energy crossing point (MEXP) and a rationalization of how spin–orbit coupling provides a mechanism for spin-forbidden reactions. An explanation of crossing probabilities, the Fermi golden rule and the Landau–Zener semiclassical approximation are given. Methodologies for obtaining spin–orbit matrix elements are presented including, among others, the Klein–Gordon equation, the Dirac equation, the Foldy–Wouthuysen transformation and the Breit–Pauli Hamiltonian. With this background the novice is taken through a tutorial that explains how to locate the MEXP. Programs available for modeling spin-forbidden reactions are provided and examples of such calculations on diatomic and polyatomic molecules are given. The chapter covers: Overview of Reactions Requiring Two States Spin-Forbidden Reaction, Intersystem Crossing Spin–Orbit Coupling as a Mechanism for Spin-Forbidden Reactions General Considerations Atomic Spin–Orbit Coupling Molecular Spin–Orbit Coupling Crossing Probability Fermi Golden Rule Landau–Zener Semiclassical Approximation Methodology for Obtaining Spin–Orbit Matrix Elements Electron Spin in Non-Relativistic Quantum Mechanics Klein–Gordon Equation Dirac Equation Foldy–Wouthuysen Transformation Breit–Pauli Hamiltonian Zeff Method Effective Core Potential-Based Method Model Core Potential-Based Method Douglas–Kroll Transformation Potential Energy Surfaces Minimum Energy Crossing Point Location Available Programs for Modeling Spin-Forbidden Reactions Applications to Spin-Forbidden Reactions Diatomic Molecules Polyatomic Molecules Molecular Properties Dynamical Aspects Other Reactions Biological Chemistry