Unveiling controlling factors of the S₀/S₁ minimum energy conical intersection (2): Application to penalty function 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.