Self-consistent field methods, correlation coefficients

The Kohn-Sham equations are solved in a self-consistent field fashion. Initially a charge density is needed so that Exc can be computed. To obtain the charge density, an initial guess to the Kohn-Sham orbitals is needed. This initial guess can be obtained from a set of basis functions whereby the coefficients of expansion of the basis functions can be optimized just like in the HF method. From the function of Exc in terms of the density, the term xc is computed. The Kohn-Sham equations (Equation 9-50) are then solved to obtain an improved set of Kohn-Sham orbitals. The improved set of Kohn-Sham orbitals is then used to calculate a better density. This iterative process is repeated until the exchange-correlation energy and the density converge to within some tolerance. 

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