Comparison of the polarizability of periodic systems computed by using the length and velocity operators

The theorem relating the length (L) and velocity (V) operators, that permits to compute in two alternative ways the polarizabilities of finite systems, is generalized to periodic infinite cases. The two alternative strategies have been implemented in the CRYSTAL code, that uses Gaussian type basis sets, within the CPHF and CPKS formalisms. The dielectric constant of diamond, SiC, silicon and MgO has been obtained with four different hamiltonians (HF, LDA, PBE, B3LYP). The effect of basis set and other computational parameters are discussed. It turns out that when a relatively extended basis set is used, LDA and PBE results obtained with the L and V operators nearly coincide, whereas HF and B3LYP schemes provide different results, as expected on the basis of the non-commutability of the HF-exchange and length operators.