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arXiv:cond-mat/0004409 · Physics Letters A

Calculations of single particle spectra in density functional theory

M. Ya. Amusia, Vasily R. Shaginyan

Published May 1, 2000• 8 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(00)00271-1

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The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from which one can construct the action functional, density functional, the response functions, and excitation spectra of the considered systems, is outlined. In the context of the density functional theory we consider the single particle excitation spectra of electron systems and relate the single particle spectrum to the eigenvalues of the corresponding Kohn-Sham equations. We find that the single particle spectrum coincides neither with the eigenvalues of the Kohn-Sham equations nor with those of the Hartree-Fock equations.
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional equation for the effective interaction, using which one can construct the action functional, density functional, the response functions, and excitation spectra of the considered systems, are discussed. We have also related the eigenvalues of the single-particle Kohn-Sham equations to the real single-particle spectra. We begin with the standard action functional and show that it is useful in calculating the linear response functions via which all physical characteristics of a many-body system can be expressed. It is shown, that function can be causal (retarded), noncausal and advanced ones. This resolves the well known paradox related to the causality and symmetry properties of the response functions and the effective interaction.
We consider the density functional theory from the point of view of one-dimensional two-particle systems, where the particles are either spin-1/2 fermions or spin-0 bosons. The basic equations are derived and applied to the system of two coupled harmonic oscillators. An exact density functional solution is constructed from the exactly known single-particle density for this system. We demonstrate how this solution may be applied to other two-particle systems to calculate the exact single-particle density and energy.