Orthogonalized linear combinations of atomic orbitals. II. Calculation of optical properties of polymorphs of silicon

By using the method of orthogonalized linear combinations of atomic orbitals developed recently, it is possible to obtain ab initio electronic wave functions of complex crystals like the two polymorphs of Si [$\mathrm{Si} \mathrm{III} (BC-8)$ and $\mathrm{Ge} \mathrm{III} (ST-12)$ structures] with basis-function sets of only moderate size. From these wave functions the dielectric functions (imaginary part) for these two Si polymorphs are obtained by computing the momentum matrix elements over the Brillouin zone. The present first-principles results are compared with previous works based on empirical methods. Possible implications on the optical-absorption properties of amorphous Si are discussed.