A spin-flip time-dependent density functional tight-binding (SF-TDDFTB) method is developed that describes target states as spin-flipping excitation from a high-spin reference state obtained by the spin-restricted open shell treatment. Furthermore, the SF-TDDFTB formulation is extended to long-range correction (LC), denoted as SF-TDLCDFTB. The LC technique corrects the overdelocalization of electron density in systems such as charge-transfer systems, which is typically found in conventional DFTB calculations as well as density functional theory calculations using pure functionals. The numerical assessment of the SF-TDDFTB method shows smooth potential curves for the bond dissociation of hydrogen fluoride and the double-bond rotation of ethylene and the double-cone shape of H3 as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S0/S1 minimum energy conical intersection (MECI) structures are performed. The SF-TDDFTB and SF-TDLCDFTB methods drastically reduce the computational cost with accuracy for MECI structures compared with SF-TDDFT.
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