Transition states of spin-forbidden reactions

Spin-orbit coupling plays an important role in determining the mechanisms and kinetics of spin-forbidden reactions and many reactions exhibiting two-state reactivity. Spin-orbit coupling can allow the system to change its spin state, especially when potential energy surfaces (PESs) of two spin states approach each other. Here, we introduce a convenient new approximation method for locating stationary points on the lowest mixed-spin potential energy surface along a reaction pathway by using density functional calculations. The mixing of different spin states is achieved by introducing the spin-orbit coupling into the electronic Hamiltonian using a pre-defined coupling constant. Two examples are given using the new methodology: (a) a CO association reaction with the coordinatively unsaturated Fe(CO)₄ complex and (b) an α-H elimination reaction of a model complex containing W. We computed a Gibbs free energy of activation of 2.8 kcal mol^-1 for the CO association reaction, which is reasonably consistent with the experimentally measured reaction rate. For the H elimination reaction, the spin change occurs at a relatively low energy, and the present treatment allows one conclude that kinetics of the reaction can be reasonably well described without spin-orbit coupling.