Abstract
In the usual spin density Kohn-Sham[1,2] (KS) theory, the total ground state energy, E, of a system of electrons moving in an external potential, V(r), is the sum of the kinetic energy of non-interacting electrons with the same spin densities, nσ, the average energy due to the external potential, the Hartree energy, and the exchange-correlation energy, Exc, which is a universal functional of {nσ}. The KS single particle states, φiσ, are obtained by solving a system of Schrodinger-like equations in which the effective potential is the sum of V(r), the Hartree potential, and the exchange-correlation potential, which is the functional derivative of Exc with respect to the nσ(r). This procedure is in principle exact. However, one must make some approximations for the generally unknown Exc[{nσ}] in applying this method.
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Krieger, J.B., Li, Y., Iafrate, G.J. (1995). Recent Developments in Kohn-Sham Theory for Orbital-Dependent Exchange-Correlation Energy Functionals. In: Gross, E.K.U., Dreizler, R.M. (eds) Density Functional Theory. NATO ASI Series, vol 337. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9975-0_9
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