Labidi, N.S2023-05-312023-05-312022-01-01N.S. Labidi ,A DFT STUDY OF HYPER-RAYLEIGH SCATTERING (HRS) FIRST HYPERPOLARIZABILITY OF SUBSTITUTED POLYENE: PART (II) . Journal of Fundamental and sciences. vol.14, no 1. January 2022. Faculty of exact sciences. university of el oued. [visited in 01/01/2022]. available from [ labidi19722004@yahoo.fr]http://dspace.univ-eloued.dz/handle/123456789/25173articleSeveral DFT functionals have been carried out to study the first hyperpolarizabilities βHRS of push-pull polyene as a function the basis sets, of electron correlation, of the size, of the frequency dispersion and the geometry. These calculations confirm the huge effects of electron correlation, the Møller–Plesset (MP2) results reproduces the values of the first hyperpolarizability obtained with the reference CCSD(T) level. Among density functional theory exchange- correlation functionals, B3LYP, M062X, B3P86 and CAM-B3LYP are comparable to the MP2 for characterizing the dynamic first hyperpolarizability. The TDB3LYP/6-31+G* level show that, as increasing the the separation distance (dN···N /Å) and introducing a stronger donor the avereage BLA value decreases and the βHRS increase. In addition, a quantitative relationship was established between the first hyperpolarizability HRSand the separation distance (dN···N /Å) at MP2, B3LYP and M062X level of theory.enfirst hyperpolarizabilities; HRS; D/A Π-conjugated polyene; DFT; MP2Article