Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices

Hubertus J. J. van Dam
Phys. Rev. A 93, 052512 – Published 23 May 2016
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Abstract

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Finally, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.

  • Received 26 December 2015

DOI:https://doi.org/10.1103/PhysRevA.93.052512

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Hubertus J. J. van Dam

  • Brookhaven National Laboratory, Upton, New York 11973-5000, USA

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Issue

Vol. 93, Iss. 5 — May 2016

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