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

TL;DR

This paper introduces a generalized Kohn-Sham system capable of representing any one-electron density matrix, including those with fractional occupations, thereby broadening the applicability of density functional theory.

Contribution

It proposes a novel generalization of the Kohn-Sham framework that can exactly represent arbitrary one-electron density matrices, including correlated systems with fractional occupations.

Findings

The generalized system can represent any one-electron density matrix.

It allows assigning energies to orbitals similar to Hartree-Fock levels.

Facilitates analysis using conventional energy-based methods.

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 non-interacting particles, is the work horse of the theory. The particular form of the Kohn-Sham wavefunction admits only idem-potent one electron density matrices whereas wavefunctions 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 non-interacting 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 wavefunctions.