Optical Activity of Spin-Forbidden Electronic Transitions in Metal Complexes from Time-Dependent Density Functional Theory with Spin-Orbit Coupling

The calculation of magnetic transition dipole moments and rotatory strengths was implemented at the zeroth-order regular approximation (ZORA) two-component relativistic time-dependent density functional theory (TDDFT) level. The circular dichroism of the spin-forbidden ligand-field transitions of tris(ethylenediamine)cobalt(III) computed in this way agrees very well with available measurements. Phosphorescence dissymmetry factors (Formula presented.) and the corresponding lifetimes are evaluated for three N-heterocyclic-carbene-based iridium complexes, two of which contain helicene moieties, and for two platinahelicenes. The agreement with experimental data is satisfactory. The calculations reproduce the signs and order of magnitude of (Formula presented.), and the large variations of phosphorescence lifetimes among the systems. The electron spin contribution to the magnetic transition dipole moment is shown to be important in all of the computations.