Hyper-Rayleigh scattering (HRS) or the second harmonic Rayleigh scattering(SHLS) is a phenomenon in which light is scattered at harmonic frequencies of the incident light. It is an incoherent nonlinear optical process. It is important to take into account the effects of frequency dispersion correction in theoretical calculations because the hyperpolarizability obtained experimentally is under dynamic settings. To make our results useful for the experimentalists and theoreticians alike, frequency dependent NLO response in terms of the βHRS β (-2ω,ω,ω) is calculated. The βHRS is an alternative to electric-field-induced second harmonic generation (EFISHG) for directly measuring the β value of all molecules, regardless of their symmetry or charge. The efficiency of SHG for a molecule is primarily determined by the molecular second-order nonlinear polarizability, or first hyperpolarizability, β. Castet et al. devised a method to assess the HRS response βHRS (-2ω; ω; ω) effectively. The dynamic values used in this study were derived using an incident infrared wavelength (λ) of 1064 nm, which is typical of Nd: YAG laser. Second-harmonic hyperpolarizability β(-2ω,ω,ω) can be measured in solution using hyper-Rayleigh scattering where ω is the frequency of the light field. The βHRS hyperpolrizabilities of the molecules is calculated in Acetonitrile. The second-order NLO susceptibility Xlmn is a third-rank tensor and the presence of inversion symmetry of the molecule will make Xlmn= 0. In this context, molecules with inversion symmetry are not SHG active. The β (-2ω, ω, ω) can be described by the equation 10. The computed dynamic βHRS (au) values at the ω*B97XD/6-31g* level using 1064 nm incident wavelength in Acetonitrile are reported in Table .