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Linear and nonlinear optical properties of the twelve styryl dyes are investigated using density functional theory (DFT). Range-separated hybrid CAMÀ B3LYP and global hybrid BHandHLYP estimate high second order hyperpolarizability. Mean polarizability (α 0 ), polarizability anisotropy (Δα), static first-order hyperpolarizability (β 0 ) and second hyperpolarizability (γ) were found to be overestimated in CAMÀ B3LYP than in BHandHLYP. As bond length alternation (BLA) increases first order hyperpolarizability increases. Multilinear regression analysis (MLR) shows the solvent basicity, polarizability and dipolarizabilty are responsible for absorption solvatochromism. The ratio of the dipole moments increases as donor strength and conjugation increases which support charge transfer. The figure of merit (FOM) and intrinsic hyperpolarizability found more in chromophores with dialkylamine donors. As the stability indicated by electrophilicity indices decreases the hyperpolarizability increases. Interrelationships between α 0 , β 0 and γ were evaluated and it shows good linear fit. Absorption is red shifted and hyperpolarizability increases with the amplitude of the sine-shaped potential along the conjugation chain. A high molecular electrostatic potential was observed in dyes containing 2-piperidinothiophene donor. Figure 1. 2-(1,1-dioxidobenzo[b]thiophen-3(2H)-ylidene)malononitrile2-(1,1dioxidobenzo[b]thiophen-3(2H) ylidene)malononitrile

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Analogs of 2-[(2Z)-2-[[4-(dihexylamino)-2-methylphenyl]methylidene]-1,1-dioxo-1-benzothiophen-3-ylidene]propanedinitrile (Foron blue SR, Disperse Blue 354) are studied in terms of photophysical, structural aspects and its nonlinear optical properties evaluated by using Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TD-DFT). The structures were optimized by using function B3LYP and basis set used was 6-31G(d). Polarizability (α), first and second order hyperpolarizability (β and γ) was determined by three density functionals B3LYP, CAM-B3LYP and BHandHLYP. B3LYP functional and the basis set 6-311+G(d,p) shows high values of α, β and γ. The B3LYP functional gives the highest first order hyperpolarizability value for (Z)-2-(2-(4-(dimethylamino)benzylidene)-1,1dioxidobenzo[b]thiophen-3(2H)-ylidene)malononitrile (3a) is 373.31 × 10 −30 e.s.u and 486.32 × 10 −30 e.s.u in ethylacetate and dimethylformamide respectively. Effect of bond length alteration (BLA) and bond order alteration (BOA) on first order hyperpolarizability was evaluated. Intrinsic hyperpolarizability shows the compound (Z)-2-(4-(dimethylamino)benzylidene)benzo[b]thiophen-3(2H)-one 1,1-dioxide (1a) intrinsically good. Perturbation potential is found to decrease as absorption energy deceases and hyperpolarizability increases.