The Au and thiol substituted 1,4-divinylcyclohexene molecule has been studied for the zero field and various levels of applied external electric fields (EFs) using Density functional theory (DFT). The variation in bond length, variation in atomic charges calculated from MPA and NPA methods, reduction of HOMO-LUMO gap (HLG) and the increase of electric dipole moment with the increase of external EFs (from zero to 0.21 VÅ-1) of the molecule have been analyzed. From the isosurface representation of molecular orbitals, it is clear that all the atoms of 1,4-divinylcyclohexene molecule between the two terminal thiol atoms are not delocalized. Hence, in this molecular system, even though small HLG exists for higher applied field, the possibility of conduction through the molecule is found to be very less, therefore, almost it acts as an insulator.