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

The polarization (P) dependence of the exchange-correlation energy (Exc) of semiconductors results in an effective field (∂²{E}xc/∂{P}²)P≡{{γ}}₁$P in the Kohn-Sham equations [Gonze et al., Phys. Rev. Lett 74, 4035 (1995)]. This effective field is absent in local-density approximations such as LDA and GGA. We show that in the long-wavelength limit γ₁{}χLDA^-1-χₑₓₚₜ^-1 where {χ} is the linear susceptibility. We find that γ₁ scales roughly linearly with average bond length suggesting a simple, weakly material-dependent function Exc[P]. For medium-gap group IV and III-V semiconductors γ₁ is remarkably constant: γ₁=-0.25±{}0.05. Using the average LDA band gap mismatch {Δ} and the average quasiparticle gap Eg a simplified quasiparticle approach yields χLDA^-1-χQP^-1{}-{Δ}/(Eg{χ})=-0.27 *0.10 in good agreement with the value of γ₁. However, for materials containing first-row elements (B,C,N,O) γ₁ varies by a factor of 2 while {Δ}/(Eg{χ}) is roughly constant. That is, the simple quasiparticle estimate fails to reproduce the polarization dependence of Exc[P]. For nonlinear response functions, an analysis of Exc[P] leads to Miller-like expressions χₑₓₚₜ⁽ⁿ⁾{}[χₑₓₚₜ/χLDA{]}^{n+1{{0ex}{0ex}}}χLDA⁽ⁿ⁾, n= 2, 3, where the formula for χ⁽³⁾ is valid only when χ⁽²⁾=0. For χ⁽²⁾, this estimate works well for all the materials including those containing first-row elements. {} 1996 The American Physical Society.