The effects of external electric field: creating non-zero first hyperpolarizability for centrosymmetric benzene and strongly enhancing first hyperpolarizability for non-centrosymmetric edge-modified graphene ribbon H2N-(3,3)ZGNR-NO2

How to generate a non-zero first hyperpolarizability for a centrosymmetric molecule is a challenging question. In this paper, an external (pump) electric field is used to make a centrosymmetric benzene molecule generate a non-zero value of the electric field induced first hyperpolarizability (beta (F) ). This comes from the centrosymmetry breaking of electron cloud. Two interesting rules are exhibited. (1) beta (F) is anisotropic for different directional fields (F (i), i = X, Y, Z). (2) The field dependence of beta (F) is a non-monotonic function, and an optimum external electric field causes the maximum value of beta (F) . The largest first hyperpolarizability beta (F) reaches the considerable level of 3.9 x 10(5) a.u. under F (Y) = 330 x 10(-4) a.u. for benzene. The external electric field effects on non-centrosymmetric edge-modified graphene ribbon H2N-(3,3)ZGNR-NO2 was also studied in this work. The first hyperpolarizability reaches as much as 2.1 x 10(7) a.u. under F (X) = 600 x 10(-4) a.u. for H2N-(3,3)ZGNR-NO2. We show that the external electric field can not only create a non-zero first hyperpolarizability for centrosymmetric molecule, but also remarkably enhance the first hyperpolarizability for a non-centrosymmetric molecule.