Publication record · 18.cifr/1965.kohn.kohn-sham-dft

Self-Consistent Equations Including Exchange and Correlation Effects

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W. Kohn (University of California, San Diego), L. J. Sham (University of California, San Diego)

RAI18.cifr/1965.kohn.kohn-sham-dft

Physical Review· 1965· doi:10.1103/PhysRev.140.A1133

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. The equations for the self-consistent field are discussed and it is shown how correlation effects can be incorporated.

density functional theoryKohn-Sham equationsexchange-correlationLDAelectronic structureself-consistent field

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Before this paper, ab initio electronic structure calculations required solving the full many-body Schrodinger equation, which scales exponentially with the number of electrons. Kohn-Sham DFT provided a way to compute ground-state electron densities and total energies at mean-field computational cost. The LDA approximation made XC tractable for real inhomogeneous systems.

Novelty

Kohn and Sham reformulated the many-body electron problem as a set of single-particle equations with an effective local potential that exactly includes exchange and correlation effects through a functional derivative of the XC energy. This replaced the computationally intractable interacting many-body Schrodinger equation with a tractable non-interacting system. The LDA for the XC functional was introduced, making the equations computationally feasible for real systems.

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