Fractional charge effects in calculations of ground-state energy of hydrogen molecules by local density approximation

Abstract

Density Functional Theory is a very successful computational approach to solve multi-electron systems. It simply treats electrons in atoms, molecules and crystals as electron density distribution, and sets up corresponding energy functionals. Many pioneers in this field such as Hohenberg, Kohn and Sham proposed ideas of using homogeneous electron gas systems to estimate the desire properties of the sample, which makes many-body systems much easier to solve. However, computational physicists and chemists have been struggling for the fundamental error of such an approximation method, which deals with the inaccuracy of calculating ground-state energy, band gap and ionization energy. It is known as the Delocalization Error. Delocalization error occurs in charge transfer process when the charge exchange is not integer charge. It lowers the energy calculated by typical approximation methods of Density Functional Theory to a great extent. Over the years, corrections and modifications of those approximate functionals have been made to eliminate the error, whereas the fundamentals of the error remain untold. Recent research has given insights on the size dependence of the problem, which opened a new direction of study on the delocalization error. In this paper, the main theory of density functional theory will be reviewed once, with additional notes to one of the approaches to construct functionals – Local Density Approximation. The fractional charge problem is then demonstrated by appropriate programming code and various system configurations to make analysis on possible geometric dependence appeared. Possibly further investigation of the problem could be taken, for example, extending the system to two-dimensional crystal structure.