General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks
We report an implementation of the spin-flip (SF) variant of time-dependent density functional theory (TD-DFT) within the Tamm-Dancoff approximation (TDA) and non-collinear (NC) formalism for local, generalized gradient approximation, hybrid, and range-separated functionals. The performance of different functionals is evaluated by extensive benchmark calculations of energy gaps in a variety of diradicals and open-shell atoms. The benchmark set consists of 41 energy gaps. A consistently good performance is observed for the PBE family, in particular PBE0 and PBE50, which yield mean average deviations (MAD) of 0.126 and 0.090 eV, respectively. In most cases, the performance of original (collinear) SF-TDDFT with 5050 functional is also satisfactory (as compared to non-collinear variants), except for the same-center diradicals where both collinear and non-collinear SF variants that use LYP or B97 exhibit large errors. The accuracy of NC-SF-TDDFT and collinear SF-TDDFT with 5050 and BHHLYP is very similar. Using PBE50 within collinear formalism does not improve the accuracy.