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KohnSham equationsThe KohnSham equations are a set of eigenvalue equations within density functional theory (DFT). DFT attempts to reduce a manybody problem for the N particle wavefunction (which depends on 4N variables) to one in terms of the charge density (which depends on 3 variables), using the HohenbergKohn theorems. Thus, one writes the total energy E of the system as a functional of the charge density:
Additional recommended knowledgewhere T is the kinetic energy of the system, V_{ext} is an external potential acting on the system, is the Hartree energy and E_{xc} is the exchangecorrelation energy. The straightforward application of this formula has two obstacles: first, the exchangecorrelation energy is not known exactly (see DFT Approximations for the workaround), and second, the kinetic term must be formulated in terms of the charge density. As was first proposed by Kohn and Sham, the charge density can be written as the sum of the squares of a set of orthonormal wave functions : which are solutions to the Schrödinger equation for N noninteracting electrons moving in an effective potential where the effective potential is defined to be These three equations form the KohnSham orbital equations in their canonical form. This system is then solved iteratively, until selfconsistency is reached. Note that the eigenvalues ε_{i} have no physical meaning, only the total sum, which corresponds to the energy of the entire system E through the equation
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "KohnSham_equations". A list of authors is available in Wikipedia. 