Implementazione, all'interno del codice CRYSTAL, del metodo di Inversione Diretta del Sottospazio Iterativo per ottimizzazioni di Geometria (GDIIS) per solidi cristallini.

In theoretical chemistry the geometry optimization is one of the essential aspects and many studies have been dedicated to it. For this reason in this thesis, among several optimization methods, we decided to study the GDIIS method and to apply it to the geometry optimization of crystals. The GDIIS method is the direct inversion in the iterative subspace (DIIS) algorithm adopted to geometry optimization. Usually it is found to be quite efficient in the quadratic vicinity of a minimum. In literature we found that the efficiency of the algorithm is shown by a dramatic decrease of optimization steps needed to reach convergence criteria. In general it is based on a linear interpolation and extrapolation of the available structures that minimizes the length of an error vector. In fact, for each structure we can construct an error vector by using a quadratic approximation to the potential energy surface. The error vector is the displacement and in a quadratic approximation it is a linear combination of individual error vectors. By solving a proper set of equations we can find all the coefficients needed in order to find the new geometry. We want to demonstrate that GDIIS implementation can enhance significantly the studies of many structures, even for large molecules and in particular for optimizing crystals. In fact, we implemented GDIIS in the CRYSTAL code, a program developed by University of Turin for the study of crystalline solid that performs ab initio calculations of the ground state energy, energy gradient, electronic wave function and properties of periodic systems.