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 H 3 as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S 0 /S 1 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. K E Y W O R D S conical intersection, degenerate phenomena, long-range correction, spin-flip, time-dependent density functional tight-binding method

Minimum-energy conical intersection (MECI) geometries play an important role in photophysics, photochemistry, and photobiology. In a previous study [Nakai et al., J. Phys. Chem. A 122, 8905 (2018)], frozen orbital analysis at the MECI geometries between the ground and first electronic excited states (S0/S1 MECI), which considers the main configurations contributing to the excitation, inductively clarified two controlling factors. First, the exchange integral between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) approximately becomes zero. Second, the HOMO–LUMO gap becomes close to the HOMO–LUMO Coulomb integral. This study applies the controlling factors to the penalty function method, which is the standard MECI optimization technique, and minimizes the energy average of the two states with the constraint that the energy gap between the states vanishes. Numerical assessments clarified that the present method could obtain the S0/S1 MECI geometries more efficiently than the conventional one.

The minimum energy conical intersection (MECI) geometries play an important role in photophysics and photochemistry. Although a number of MECI geometries can be identified using quantum chemical methods, their chemical interpretation remains unclear. In this study, a systematic analysis was performed on the MECIs between the singlet (S0) and lowest singlet excited (S1) states of organic molecules. The frozen orbital analysis (FZOA), which approximates the excited states with minimal main configurations, was adopted to analyze the excitation energy components at the S0/S1 MECI geometries as well as the S0 and S1 equilibrium geometries. At the S0/S1 MECI geometries, the HOMO–LUMO gaps decreased as expected but did not disappear. The remaining gaps were balanced with the HOMO–LUMO Coulomb integrals. Furthermore, we discovered that the HOMO–LUMO exchange integrals became approximately zero. On the basis of this fact, a systematic interpretation of the S0/S1 MECI geometries has been described.

The crossing of potential energy surfaces plays an important role in photo-decay processes and photochemical reactions. The energies and geometries of the crossing points have been reported for various molecules using quantum chemical calculations. In this research, excitation energy components of uracil are investigated to understand the characteristics of the crossing points. We revealed that the HOMO − LUMO exchange integral becomes approximately zero at the minimum energy conical intersection between S0 and S1 states. Furthermore, it was found that the HOMO − LUMO gap is close to the HOMO − LUMO Coulomb integral at the crossing structures.