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 (${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$) 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 ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ includes self-consistent local-field effects, and is a simple function of the linear response of the system. We compute the static ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ 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 ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ for second-harmonic generation using TD-LDA. © 1996 The American Physical Society.