The present article deals with computational study of molecular geometries, electronic properties, and vibrational characteristics using the density functional theory (DFT) and Hartree-Fock methods supplemented with basis set 6-31++G(d.p) at Gaussion-09 program. The Raman and infrared spectra of two liquid crystalline disubstituted biphenylcyclohexanes (BCH RX) of general formula R-C6H10-C6H4-C6H4-X with R: C3H7; X = H (BCH30) and R: C5H11; X = CN (BCH5CN) have been analyzed and vibrations corresponding to particular frequency are assigned in detail. Most of the modes have wavenumbers/frequencies in the expected range, and the error obtained was minimum. Aromatic ring with terminal cyano group confers a positive dielectric anisotropy, and high optical anisotropy. Cyanobiphenyls possess high dielectric anisotropy and good electro-optical characteristics are used to decrease the switching time of liquid crystalline materials. It has been observed that the DFT based calculations consider the different types of interactions between electrons, thus it gives more accuracy as compared to HF method. Further, the electronic properties of the mesogenic compounds have been reported to understand the molecular reactivity, charge transfer, electro-optical, and other molecular properties.