Spin−Orbit Coupling in Biradicals. 2. Ab Initio Methodology and Application to 1,1-Biradicals:  Carbene and Silylene

A general procedure is described for the computation of spin−orbit coupling of triplet states of organic biradicals with their singlet states and of the zero-field splitting parameters of the triplets, including the full one- and two-electron terms of the Breit−Pauli Hamiltonian and using a new ab initio computer program suite. Spin−orbit coupling matrix elements are obtained for each triplet sublevel separately and are analyzed in an intuitively appealing fashion in terms of vectorial contributions from individual atoms and individual natural hybrid orbital pairs. CASSCF(6,6) results for S 0 −T 1 spin−orbit coupling in CH 2 converge rapidly with increasing basis set size, and a polarized double-ζ basis set appears adequate. However, convergence with respect to the extent of electron correlation has not yet been reached at the CASSCF(6,6) level, whose results appear to be only semiquantitative. The experimental D ‘ and E ‘ values for CH 2 are reproduced within 5% at the CISD/aug-cc-pVTZ level, but the results obtained with less adequate electron correlation procedures and/or with smaller basis sets are only qualitatively correct. Results for spin−orbit coupling in CH 2 and SiH 2 as a function of the valence angle agree with expectations based on the algebraic 2-electrons-in-2-orbitals model of part 1. The T 1 parameters D ‘ and E ‘ in CH 2 and E ‘ in SiH 2 are dominated by spin−spin dipolar coupling, whereas D ‘ in SiH 2 is predicted to be dominated by spin−orbit coupling.