The FT-IR solid phase (4000-450 $cm^{-1}$) and FT-Raman spectra (3500-100 $cm^{-1}$) of 3,5-Dimethylbenzophenone (3,5-DMBP) was recorded at room temperature. Density functional theory calculations with B3LYP/ 6-31+$G(d, p)$ basis sets was used to determine ground state molecular geometries (bond lengths and bond angles), harmonic vibrational frequencies, infrared intensities, Raman activities and bonding features of this compound. The assignments of the vibrational spectra have been carried out with the help of normal co-ordinate analysis (NCA) following the Scaled Quantum Mechanical Force Field methodology (SQMFF). The first order hyperpolarizability $(β_0)$ of this novel molecular system and related properties $(β, α_0$ and $\Delta α$) of DMBP are calculated using HF/6-31+$G(d,p)$ method on the finite-field approach. Stability of the molecule have been analyzed using NBO analysis. The calculated first hyperpolarizability shows that the molecule is an attractive molecule for future applications in non-linear optics. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. Mulliken population analysis on atomic charges is also calculated. On the basis of vibrational analyses, the thermodynamic properties of the title compounds at different temperatures have been calculated. Finally the calculations results were applied to simulate infrared and Raman spectra of the title compound which show good agreement with observed spectra.