Cálculo de la Energía y la Densidad Electrónica de Átomos Resolviendo la Ecuación de Euler-Lagrange Obtenida a Partir de Funcionales Aproximados para la Energía

Abstract

The present work focuses on the Orbital Free Density Functional Theory (OF-DFT). Using approximations for the kinetic, exchange, and correlation energy functionals, we can deduce the corresponding Euler-Lagrange equations to minimize the entire energy functional with regards of the electronic density. This equations are solved numerically using the central potential for isolated atoms, both with balanced and unbalanced spin, to obtain the electronic density that minimizes the energy functional, and therefore corresponds to the ground state of the atoms. Results are presented for the electronic density and the energy, and a bibliographical revision is presented for the possible reasons of some convergence errors that were met during the resolution of the equations. This work serves as an illustration for this kinds of research, but in the future the approximated functionals must be selected carefully to avoid this problems.