The concept of a “consistent,” Kohn-Sham (KS) density functional theory (DFT) is discussed, where the functional is able to provide good total energies and its self-consistent potential is such that the KS eigenvalues correspond to accurate approximations to the principal ionization potentials for the molecule. Today, none of the vast number of DFT approximations show this property. The one exception is the ab initio dft method built upon the optimized effective potential strategy for exchange and correlation. This qualifies as a DFT method because it represents the correlated density as a single determinant and by imposing that condition, generates local exchange and correlation operators which are used in self-consistent solutions of the orbitals and eigenvalues. Such a “consistent” DFT shares many of the properties of the Dyson equation, but without its frequency dependence and associated complications. The relationship between ab initio dft based on MBPT2 functional and GW method is discussed. Ab initio dft provides a self-consistent, frequency independent, effective independent particle alternative with a local correlation potential.
Increasing the applicability of density functional theory. III. Do consistent Kohn-Sham density functional methods exist?
Prakash Verma, Rodney J. Bartlett; Increasing the applicability of density functional theory. III. Do consistent Kohn-Sham density functional methods exist?. J. Chem. Phys. 7 October 2012; 137 (13): 134102. https://doi.org/10.1063/1.4755818
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