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 (β ^F ). This comes from the centrosymmetry breaking of electron cloud. Two interesting rules are exhibited. (1) β ^F is anisotropic for different directional fields (F _i, i?=?X, Y, Z). (2) The field dependence of β ^F is a non-monotonic function, and an optimum external electric field causes the maximum value of β ^F . The largest first hyperpolarizability β ^F reaches the considerable level of 3.9?×?10⁵ a.u. under F _Y?=?330?×?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?×?10⁷ a.u. under F _X?=?600?×?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.