Spin-state energies of heme-related models from spin-flip TDDFT calculations

Spin-state energies of heme-related models are of vital importance in biochemistry. To compute the energies of different spin states, the traditional ΔSCF method based on the density functional theory (DFT) is usually employed. In this work, the spin-flip TDDFT (SF-TDDFT) approach is investigated to compute the spin-state energies, with six different exchange-correlation (XC) functionals. With the present protocol, the spin contamination is fully avoided by choosing appropriate reference states. Additionally, multiple excited states can be obtained with SF-TDDFT. Compared with the CCSD(T) results, it is shown that the SF-TDDFT calculations with the BHandHLYP functional provide better accuracy than ΔSCF for D-Q (doublet-quartet) and Q-S (quartet-sextet) gaps and agree well with the experimental results. A possible solution for the precise calculation of spin-state energies is proposed to improve the performance of SF-TDDFT, on account of that the excitation energies show highly linear dependence on the amount of Hartree-Fock (HF) exchange in the XC functionals.