Comparative study of nonlinear optical properties of red fluorescent coumarins was carried out with density functional theory based ab initio method using the popular global hybrid (GH) and range separated hybrid (RSH) functionals and correlated with the spectroscopic values. The GHs - M06 L, PBE1PBE, M06, BHHLYP, M062X and M06HF and RSHs - HISSbPBE, wB97, wB97X, HSEH1PBE, CAM-B3LYP and wB97XD in combination with the double zeta basis function 6-311 + G(d,p) were used. The computed polarizability (α), hyperpolarizability of the first order (β) and second order (γ) computed by the RSHs are closer to the spectroscopic values compared to GHs. Polarizabilities computed with the functionals BHHLYP and M06-2X are closer with the spectroscopic values. Incorporation of additional cyano group enhances the NLO response. An increase in electrophilic nature contributed from the reduced orbital band gap culminating an increase in α, β, and γ in all the cases. The NLO response was found to be highly solvent dependent that is the polarity of the micro environment created by the solvents. To understand the agreement and accuracy among the NLO parameters obtained from the selected DFT functionals and the spectroscopic values, the mean absolute error (MAE) and vibrational contribution parameters are presented. Two photon absorption (TPA) cross section depends upon the molecular structure where π-framework is an important factor rather than number of acceptors.
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