STUDY THE CORRELATION ELECTRONIC SYSTEMS INHOMOGÉNOS SIMPLESummary: The treatment of the electronic correlation in a system of three or more interacting particles is still today a challenge from the theoretical point of view, and avai1cesrnetodoiógicClspara its resolution are very important for its potential application in various fields of physics such as fhka! óríllc'a, molecular, nuclear or solid state. This thesis seeks to improve understanding of the properties of the correlation and electronic systems. We have used different techniques, ab initio, commonly used in the invcstigación today, través.de which we have tried to capture conveniently various manifestations which leads la.correlacjón electronics. The principipal tool has been used formalism Kohn-Sham of the theory of functional density (DFT), which offers simultáneamel I1nmarco theoretical exact methodology and a practical resolution but inevitably we introduce a aproximadón for el.funciona exchange correlation ( XC). The different degrees of sophistication of functional XC respond fundarmentalmente an attempt including the nature no-local of correlation and eliminate errors autointeracción of Hartree with the use of a treatment exact exchange. Among the various approaches quehemos considered are the functional approximation local creeks approximation explícitameJ no-local through a process of averaging of densities, and shapes based on a direct approximation of the theory microscopopica defined within the framework of the theory of functional dependent time (TDDFT) for the Coulomb correlation with the exact description of the exchange. We have also employed, but only in the seunda part of the thesis, functional approximations of the DFT semivocales which include units in the density gradients, and the solutions obtained by the method of interaction and Hartree - Fock configurations, we have served to conduct a comparative study of different results.
