Theory of spin-orbit coupling. Application to singlet-triplet interaction in the trimethylene biradical

Efficient methods are developed for the computation of spin-orbit coupling constants in polyatomic molecules using complete active space multiconfiguration self-consistent field wave functions. All electron-nuclear and electron-electron spin-orbit interactions in the Breit-Pauli Hamiltonian are retained without storing or transforming spin-orbit integrals. This technique is applied to the calculation of spin-orbit coupling constants between singlet and triplet electronic states. Allowing nonorthogonality of the singlet and triplet molecular orbitals in the active space improves the quality of the wave functions and presents no serious computational difficulties. To test the method, spin-orbit coupling constants are computed for the diatomic molecules NH, OH⁺, PH, and O₂ and compared with similar calculations reported in the literature. Calculations are also carried out for the organic biradical trimethylene (ĊH₂CH₂ĊH₂). The coupling constant is found to vary from 0 to 2.5 cm^-1 depending upon geometry. It is very sensitive to rotation of the terminal methylenes but relatively insensitive to the CCC angle. These results contribute to our understanding of the role of the triplet state in biradical reactions.