The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies.

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.