Truncated methods applied to the direct calculation of exciton binding energies.

Optical processes in insulators and semiconductors, including excitonic effects, can be described in principle exactly using time-dependent density-functional theory (TDDFT). Within this formalism, a family of exchange-correlation kernels known as long-range-corrected (LRC) kernels (fxc=-α/q²) have shown to accurately reproduce optical spectra for several insulators and semiconductors. More recently, Ullrich and co-workers adapted the Casida equation formalism suitable for determining molecular excitations to periodic solids, this way the exciton binding energy may be calculated in a direct way without having to compute explicitly the response function. However, it appears that no LRC-type kernel is capable of simultaneously produce good optical spectra and quantitatively accurate exciton binding energies. In the present work we have adapted Casida's formalism following a different approach. The long range nature of the kernel, i.e. the q→0 singularity, is regularized employing a super-cell wigner-seitz truncation that clearly alters the previously calculated alpha values of the kernel. We will justify our calculation method and provide the alpha values for several insulating/semi-conducting materials.