Density-functional theory of the nonlinear optical susceptibility: Application to cubic semiconductors

We present a general scheme for the computation of the time-dependent (TD) quadratic susceptibility (chi((2))) of an extended insulator obtained by applying the `'2n + 1'' theorem to the action functional as defined in TD density-functional theory. The resulting expression for chi((2)) includes self-consistent local-field effects, and is a simple function of the linear response of the system. We compute the static chi((2)) of nine III-V and five II-VI semiconductors using the local density approximation (LDA), obtaining good agreement with experiment. For GaP we also evaluate the TD chi((2)) for second-harmonic generation using TD-LDA.