Spin-Orbit Coupling in Biradicals. Ab Initio MCSCF Calculations on Trimethylene and the Methyl-Methyl Radical Pair

Spin-orbit coupling (SOC) constants are computed by ab initio MCSCF (multiconfiguration self-consistent field) theory for the trimethylene biradical, 'CH₂CH₂CH₂', and for a pair of interacting methyl radicals as functions of separation and relative orientation of radical centers. The effects of through-bond coupling are analyzed by comparing SOC values for the biradical with those for a radical pair with the same orientation of 'CH₂centers. Ab initio results for the radical pair are found to be well-described by the semiempirical formula, SOC = B|S| sin ϕ, where ϕ is the acute angle between radical p orbitals, S is the orbital overlap integral, and B = 15 cm^-1. Predicted values require correction by a factor of 3.0 or less in the event of strong steric interaction with a radical p orbital. The principal effect of through-bond coupling by a single CH₂moiety is to increase SOC by another factor of about 2.5. We discuss the implications of these computational results for the interpretation of recently measured rate constants for intersystem crossing in a 1,3- and a 1,4-biradical system. We conclude that the slower rate in the 1,3-biradical is due to the Boltzmann factor associated with the activation energy required to reach the singlet-triplet crossing.