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Owing to its successful application to complex molecular systems, computational density functional theory (DFT) has been used to study the effect of an electric field on the molecular polarizability and HOMO–LUMO gap of 1-phenyl-4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}benzene (1) and its fluoro-, chloro-, and cyano-derivatives, namely,1-fluoro-4-(4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}phenyl)benzene (2), 1-chloro-4-(4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}phenyl)benzene (3), and 4-(4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}phenyl)benzonitrile (4). These molecules belong to the family of nematic liquid crystals with three rings: two benzene and one cyclohexane. Furthermore, two DFT approaches, namely, B3LYP and M062X, have been used to examine the results obtained. This study reveals a remarkable feature: the polarizability of these molecules follows nearly a step function when varied with respect to the electric field. The 4-(4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}phenyl)benzonitrile (4) polarizes more than all other derivatives, whereas 1-fluoro-4-(4-{2-[(1s,4r)-4-pentylcyclohexyl]ethyl}phenyl) benzene (2) has the widest stability region of them all. With the increase in the electric field, polarizability increases in a smooth manner until a point called here the shoot-up point at which polarizability switches to a higher value and remains nearly constant as the field increases further. However, beyond a certain value of the electric field, polarizability undergoes a steep fall. It is also found that the effective length (long molecular axis) of the molecule has a direct effect on its polarizability.