Orbital-unrelaxed Lagrangian density matrices for periodic systems at the local MP2 level

In the present paper a method based on the Hylleraas functional is proposed in order to obtain correlated ground state density matrices for periodic systems at the level of local MP2. The general properties of these density matrices, namely size-extensivity, translational invariance, exponential decay of the off-diagonal elements, etc are discussed. As test examples we investigate the influence of the electron correlation on the density in diamond and strontium titanate (in the latter case via the Mulliken charges). The calculations reveal that in diamond the concentration of the electrons in the bond region decreases when the correlation is taken into account, but the change in the density relative to Hartree-Fock is small. In the case of SrTiO3, this change is more significant and causes a lowering of the ionicity of this crystal.