Ab initiocalculation ofε2(ω)including the electron-hole interaction: Application to GaN andCaF2

We present a computationally efficient first-principles scheme to calculate ${\epsilon }_2\left(\omega \right)$ for crystalline insulators, including the electron-hole interaction. The effective Hamiltonian for electron-hole pairs contains both the exchange and direct parts of this interaction. An iterative scheme is used in which the $\omega$ moments of ${\epsilon }_2\left(\omega \right)$ are computed by repeated action of the Hamiltonian on electron-hole pair states. The scheme is applied to two insulators where there are significant experimental uncertainties in their ultraviolet optical properties: GaN and ${\mathrm{CaF}}_2.$