The electron localization function in solid systems: implementing and testing algorithms

The software CRYSTAL is a public ab initio code for solid state chemistry and physics. The risult of QM codes calculations consists in the first instance in the structure and the energy of the systems, from which is possible to derive, through the wave function, physical observables such as the electron density, whose importance lies in the fact that it can be experimentally determined. The electron density can be analysed and partitioned in many ways, for instance using an electron localization function (ELF), first proposed by Becke and Edgecombe in 1990, which in Savin's interpretation can be seen as a measure of the excess of kinetic energy density due to the Pauli exclusion principle. It has proved itself useful for the study of bonds and lone pairs. This thesis aims at the implementation and testing of the algorithms relating to the electron localization function and the integration of the electron density over its basins in the software CRYSTAL. The ELF subroutine already implemented in the code, but not yet made public, has been tested on different solid systems and optimized in order to include additional features such as the 1D calculation along specific directions - e.g. the direction connecting two atoms. The ELF calculation is performed by many molecular codes and some solid state codes, but the peculiarity of CRYSTAL relies in the fact that it uses a basis set composed of atomic orbitals. The main work has been on the ELF basins subroutine, where the ELF basins are partitions of space definined following the gradient of ELF and can be distinguished into two main categories: core basins, accounting for the electron density of the inner shells, and valence basins, accounting for bonds, lone pairs and single electron domains. The last step has been the implementation of a subroutine for the integration of the electron density over the basins, defining the density population in the framework of topological analysis complementary to the one of studies such as Bader's Atoms In Molecules and the Hirshfeld charges. These new steps have been tested on systems such as the diamond and a Mg-faujasite. Future developments would include the use of the crystal simmetry in the calculations, reducing the computing time, as well as a parallelization and a massive parallelization of the procedure.