Calculation of the first static hyperpolarizability tensor of 3D periodic compounds with a local basis set. A comparison of LDA, PBE, PBE0, B3LYP and HF results

The computational scheme for the evaluation of the second-order electric susceptibility tensor in periodic systems, recently implemented in the CRYSTAL code within the coupled perturbed Hartree–Fock HF scheme, has been extended to local-density, gradient-corrected, and hybrid density functionals coupled-perturbed Kohn–Sham and applied to a set of cubic and hexagonal semiconductors. The method is based on the use of local basis sets and analytical calculation of derivatives. The high-frequency dielectric tensor and second-harmonic generation susceptibility have been calculated with hybrid functionals PBE0 and B3LYP and the HF approximation. Results are compared with the values of and d obtained from previous plane-wave local density approximation or generalized gradient approximation calculations and from experiment. The agreement is in general good, although comparison with experiment is affected by a certain degree of uncertainty implicit in the experimental techniques.