Understanding the kinetics of spin-forbidden chemical reactions

Many chemical reactions involve a change in spin-state and are formally forbidden. This article summarises a number of previously published applications showing that a form of Transition State Theory (TST) can account for the kinetics of these reactions. New calculations for the emblematic spin-forbidden reaction HC + N₂ are also reported. The observed reactivity is determined by two factors. The first is the critical energy required for reaction to occur, which in spin-forbidden reactions is often defined by the relative energy of the Minimum Energy Crossing Point (MECP) between potential energy surfaces corresponding to the different spin states. The second factor is the probability of hopping from one surface to the other in the vicinity of the crossing region, which is largely defined by the spin–orbit coupling matrix element between the two electronic wavefunctions. The spin-forbidden transition state theory takes both factors into account and gives good results. The shortcomings of the theory, which are largely analogous to those of standard TST, are discussed. Finally, it is shown that in cases where the surface-hopping probability is low, the kinetics of spin-forbidden reactions will be characterised by unusually unfavourable entropies of activation. As a consequence, reactions involving a spin-state change can be expected to compete poorly with spin-allowed reactions at high temperatures (or energies).