Linear optical response in silicon and germanium including self-energy effects

We calculate the optical response of silicon, ₁ (), below the optical-absorption threshold and the static dielectric constant of germanium. The time-dependent local-density approximation (LDA) is modified by the addition of a self-energy term taken to be a ``scissors operator, '' P₂₊₊. This form leads to a Ward identity replacement p (₍₊-H₊^LDA{) ^-1} (₍₊-H₊) p. For silicon, we obtain 11. 3 for ₁ (=0), compared to 11. 7 for experiment, 13. 1 in our LDA calculation, and 8. 4 in a naive self-energy corrected theory (i. e. , simply modifying the eigenvalues without modifying the momentum operator). For germanium, the corresonding values as 16. 5, 15. 8, 21. 3 and 10. 4