The present article deals with a comparative quantum chemical calculations on fluorinated liquid crystals namely; p-phenylene-4-methoxybenzoate-4-trifluoromethylbenzoate (Nematic), and 4-propyloxyphenyl-4-(4-trifluoromethyl benzoyloxy) benzoate (Smectic) by using the Density functional theory (DFT) and Hartree-Fock (HF) methods supplemented with basis set 6-31++G(d.p). The molecules show excellent chemical and thermal stability because of the strong, and unique physical properties of C-F bond, which contributes to the display, and photonic applications. The observed vibrational spectra has resolved and assigned in detail for comparision with the molecules. Further, the frontier molecular orbital analysis for both the molecules has been carried out. It has been observed that the DFT and HF values are slightly different as HF calculation does not include electron-electron interaction term. Furthermore, an increment in the alkyl chain length, thermal vibration increases which indicates low packing efficiency of the molecule with high electrical conductivity.