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

Abstract

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.

Spin‐flip approach within time‐dependent density functional tight‐binding method: Theory and applications

“…The SF‐TDDFTB and SF‐TDLCDFTB methods drastically reduced the computational cost with improved accuracy for MECI structures compared with SF‐TDDFT. Furthermore, as shown in our previous study obtained by SF‐TDDFT, the SF‐TDDFTB and SF‐TDLCDFTB calculations indicated the controlling factors, that is, K HL ≈ 0 at S 0 / S 1 MECIs.…”

“…Finally, we verified the controlling factors of S 0 / S 1 MECI discovered in our previous studies at the SF‐TDDFTB and SF‐TDLCDFTB levels. Figure shows the HOMO−LUMO exchange integral, K HL , of Equation in hartree for S 0 EQ and S 0 / S 1 MECI structures of 29 molecules.…”

“…Figure a,b show the results of the SF‐TDDFTB and SF‐TDLCDFTB calculations, respectively. As shown in our previous studies obtained by SF‐TDDFT, the SF‐TDDFTB and SF‐TDLCDFTB calculations indicated the controlling factors, that is, K HL ≈ 0 at S 0 / S 1 MECIs. The average values of K HL obtained from SF‐TDDFTB and SF‐TDLCDFTB calculations at S 0 / S 1 MECIs were 0.0004 and 0.0003 hartree, respectively.…”

“…However, this ambiguity might not affect the condition of K HL ≈ 0. In our previous study, the S 0 / S 1 MECI optimization method utilizing the condition of K HL ≈ 0 was able to obtain the S 0 / S 1 MECI structures more efficiently than the conventional optimization techniques. In both DFTB and LCDFTB calculations, the exchange integral of Equation , K HL , is defined with Mulliken approximation as By using Equation , an investigation similar to the DFT treatment might be carried out for the DFTB case.…”

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

“…Its accuracy is reportedly comparable to that of conventional ab initio electronic structure methods (including SF-TD-DFT), but its computational cost is several orders of magnitude lower. 20,27 The root of the second difficulty, that is, the high computational cost, is the high-order scaling of the computational time required for typical excited-state calculation methods with system size. Traditionally, this type of problems has been treated by molecular-mechanical (point-charge) description of the solvent molecules, or continuum solvation models, for example, the polarizable continuum model, the conductor-like screening model, and the generalized Born model.…”