Polarization-dependent density-functional theory and quasiparticle theory: Optical response beyond local-density approximations

The polarization (P) dependence of the exchange-correlation energy (E(xc)) of semiconductors results in an effective field (partial derivative E(xc)/partial derivative P-2) P=gamma(1)P in the Kohn-Sham equations [Gonze et al., Phys. Rev, Lett 74, 3835 (1995)]. This effective field is absent in local-density approximations such as LDA and GGA. We show that in the long-wavelength limit gamma(1) similar or equal to chi(LDA)(-1)-chi(expt)(-1) where chi is the linear susceptibility. We find that gamma(1) scales roughly linearly with average bond length suggesting a simpler weakly material-dependent function E(xc)[P]. For medium-gap group IV and m-V semiconductors gamma(1) is remarkably constant: gamma(1)=-0.25+/-0.05. Using the average LDA band gap mismatch Delta and the average quasiparticle gap E(g) simplified quasiparticle approach yields chi(LDA)(-1)-chi(QP)(-1)similar or equal to-Delta/(E(g) chi)=-0.27+/-0.10 in good agreement with the value of gamma(1). However, for materials containing first-row elements (B,C,N,O) gamma(1) varies by a factor of 2 while Delta/(E(g) chi) is roughly constant. That is, the simple quasiparticle estimate fails to reproduce the polarization dependence of E(xc)[P]. For nonlinear response functions, an analysis of E(xc)[P] leads to Miller-like expressions chi(expt)((n))similar or equal to[chi(expt)/chi(LDA)](n+1)chi(LDA)((n)), n = 2, 3, where the formula for chi((3)) is valid only when chi((2))=0. For chi((2)), this estimate works well for all the materials including those containing first-row elements.