Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism. III. Temperature-dependent magnetic circular dichroism induced by spin-orbit coupling

A methodology for calculating the temperature-dependent magnetic circular dichroism (MCD) of open-shell molecules with time-dependent density functional theory (TDDFT) is described. The equations for the MCD of an open-shell molecule including spin-orbit coupling in the low- and high-temperature limits are reviewed. Two effects lead to the temperature-dependent MCD: the breaking of degeneracies and the perturbation of transition dipoles by spin-orbit coupling. The equations necessary to evaluate the required terms using TDDFT-derived quantities are presented. The performance of the formalism is demonstrated through application to the MCD of several molecules. The spectra of these molecules have differing properties with respect to bandwidth, temperature dependence of the MCD, and relative magnitude of the temperature-dependent and temperature-independent components of the MCD. The important features of the experimental spectra are reproduced by the calculations.