Calculation of the dielectric function in a local representation

A formula for the dielectric tensor in real-space coordinates is derived. Expanding this formula in a plane-wave basis yields the well-known Adler-Wiser formula [S.L. Adler, Phys. Rev. 126, 413 (1962); N. Wiser, Phys. Rev. 129, 62 (1963)], which is appropriate for bulk systems. For systems with broken symmetry like the semi-infinite crystal this approach is not possible and an alternative can be found in localized functions. Therefore, we investigate the expansion of the dielectric function in a linear combination of atomiclike orbitals basis set and compare the results with the usual plane-wave approach. We found very good agreement for the microscopic dielectric function of diamond and GaAs but deviations in the description of local-field effects.