Matrice densità corretta per il rilassamento orbitalico a livello MP2 in approccio locale: aspetti formali ed implementazione.

In this work of Thesis we have formally developed and partly implemented a new algorithm for the evaluation of orbital-relaxed density matrix in crystalline periodic systems, at the local MP2 (LMP2) level. The formal development has been carried out through Lagrangian techniques, including the Brillouin condition as constraint. These results, well known in molecular field, have been extended for periodic systems through local approach. The implementation work has been carried out within the CRYSCOR code. Althought the part of the code has been structured for periodic systems, we started with the simplest case, that is the molecular one. A first contribution to the orbital relaxed density matrix has been implemented. This code has been tested on simple molecular systems, LiH and urea, showing that the so-obtained LMP2 correction to the density matrix has the correct behavior and symmetry properties. The entity of the relaxed MP2 correction is nearly ten times larger then the unrelaxed one, thus demonstrating the importance of this work in order to get a reliable description of electron correlation effects on density properties. As future developments of this work we see the finalization of the implementation, allowing for the calculation of the full density matrix in crystalline systems periodic in 1D, 2D and 3D. This will open the way for further developments such as the calculation of Local-MP2 polarizabilities or the implementation of gradients for geometry optimization at the correlated level.