Test of long-range exchange-correlation kernels of time-dependent density functional theory at surfaces: Application to Si(111)2X1

We present an application of time-dependent density-functional theory (TDDFT) to the study of the optical properties of the Si(111)2X1 surface from the infrared to the ultraviolet. We have carried out ab initio calculations using different methods, from DFT to Bethe-Salpeter equation (BSE) and, within TDDFT, we have tested the ability of different kernels to describe the optical features in a wide range of energies. We find good agreement between TDDFT and BSE results, by using in TDDFT a long-range frequency-dependent exchange-correlation kernel derived from the many-body formalism (the MB kernel). The agreement between theory and experiment is very good in the whole frequency range studied. Excitonic effects, important in the infrared part of the spectrum, are less pronounced in the visible and UV ranges.