The effects of exact exchange of density functionals on the evaluation of second hyperpolarizabilities of streptocyanines using sum-over-states method

Abstract

TDDFT calculations are used to discuss the effects of the exact exchange (Ex) on the evaluation of second hyperpolarizabilities (γyyyy) of streptocyanines (3–9 carbons). The results confirm that TDDFT calculations are reliable on the reproduction of the first excitation energies (E01) compared with experiments (within 0.3eV deviations). The sum-over-states (SOS) calculations based on TDDFT suggest that the percentages of Ex determines the γyyyy. The nonlinear optical (NLO) active region of streptocyanines is the π-bridge conjugation where the bond length is between 2 and 3au. Within this area, the higher the percentage of Ex is, the lower the γyyyy is (γyyyy is normally negative for streptocyanines). The γyyyy can be decomposed into T and N contributions according to the three-level SOS method. The decomposition shows that the T term significantly decreases with the increasing percentages of Ex, while N term gradually increases. Therefore, hybrid generalized gradient approximation (hGGA), hybrid meta-generalized gradient approximation (hybrid meta-GGA) and long-range corrected (LRC) functionals tend to overestimate γyyyy. The functional tuning process can improve the results due to the decreasing of ω. This means the deviation of γyyyy do NOT corresponds to the delocalization error (DE). Consequently, the pure GGA, pure meta-GGA, and LRC with small ω can give qualitative correct results.