Abstract
A fundamental weakness of density functional theory (DFT) is the difficulty in making systematic improvements to approximations for the exchange and correlation functionals. In this paper, we follow a wave-function-based approach [N.I. Gidopoulos, Phys. Rev. A 83, 040502 (2011)] to develop perturbative expansions of the Kohn–Sham (KS) potential. Our method is not impeded by the problem of variational collapse of the second-order correlation energy functional. Arguing physically that a small magnitude of the correlation energy implies weak perturbation and hence fast convergence of the perturbative expansion for the interacting state and for the KS potential, we discuss several choices for the zeroth-order Hamiltonian in such expansions. Our first two choices yield KS potentials containing only Hartree and exchange terms: the exchange-only optimized effective potential (xOEP), also known as the exact-exchange potential (EXX), and the Local Fock exchange (LFX) potential. Finally, we choose the zeroth order Hamiltonian that corresponds to minimum magnitude of the second order correlation energy, aiming to obtain at first order the most accurate approximation for the KS potential with Hartree, exchange and correlation character.
Highlights
Electronic structure calculations are becoming indispensable in many areas of modern science, with applications spanning fields from drug discovery [1] to superconductivity [2]
In traditional density functional theory (DFT) perturbation theory (PT) the KS potential is obtained from a perturbative expansion of the total energy functional, they are of the same order
We emphasize again the conceptual shift between the two theories: in DFT perturbation theory (DFT PT), the KS potential is obtained by minimizing the total energy of the system, while in the present wave function theory (WFT) method the KS potential is obtained by minimizing the energy difference TΨ [v]
Summary
Electronic structure calculations are becoming indispensable in many areas of modern science, with applications spanning fields from drug discovery [1] to superconductivity [2]. In order to overcome these limitations, and to satisfy the growing demands for more accurate electronic structure calculations, on larger and more complicated systems, it is important to gain new insights Such insights can be obtained from the integration of DFT with WFT [6,7,8,9,10,11,12,13]. They enabled Gorling and Levy to formulate DFT perturbation theory (PT) [19,20], and Bartlett and co-workers to develop ab initio DFT [8] In these approaches, the correlation energy is approximated from second-order PT (or higher) and the KS potential is determined using the optimized effective potential (OEP) method [21,22].
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