Density functional theory (DFT) and time-dependent DFT computations were employed to examine linear and nonlinear optical (NLO) characteristics of (E)-4-((1,1-dioxido-3-oxobenzo[b]thiophen-2(3H)-ylidene) ethyl)-1-phenyl-1H-pyrazol-5(4H)-one derived styryl dyes. NLO properties were computed using the two different global hybrid functionals B3LYP, BHandHLYP and three range separated hybrid functionals CAM B3LYP, wB97, wB97X and wB97XD with the basis sets 6–311++G(d,p), cc-pVDZ and cc-pVTZ. The compounds shows higher values of dipole moment around 8–9 Debye than the other compounds. They show higher values of α
0, ß
0 and γ
0 values. The values of γ
0 are around 204–544 × 10−36 e.s.u. with the method, B3LYP/6–311++G(d, p). We have calculated the mean absolute error (MAE) for dipole moment, α
0, ß
0 and γ
0 values. It is observed that MAE is less (0.89) for wB97/6–311++G(d,p) which indicates that wB97 is the most suited functional for all three compounds. Chemical stability and reactivity of these dyes were studied using electrophilicity index and chemical hardness and hyperhardness.