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arXiv:cond-mat/0003277 · Physica Scripta

Description of Dynamic Properties of Finite Electron Systems in Density Functional Theory

M. Ya. Amusia, Vasily R. Shaginyan

Published Jan 1, 2003• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1238/physica.regular.068ac0010

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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.
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.
A new approach for the calculation of the linear response of both the ground and thermal-equilibrium states of many-electron systems is proposed via an integral formulation of the density-functional theory. Based on the path-integral representation of the one-particle Green's function, the frequency-dependent linear-response function for the Kohn-Sham noninteracting system is expressed as an explicit functional of the Kohn-Sham local potential, instead of the summation over the single-electron orbitals. Thus the dynamic linear density response can be determined as the solution of self-consistent equations which only need as input the total electron density of the ground or the equilibrium state. Exchange and correlation effects are incorporated. Because orbitals are not employed, the formulation provides the possibility for calculations of linear-response properties, such as dynamic polarizability and photoabsorption cross sections of systems with very many electrons. The present formulation can also be applied to general fermions.
First principles calculations of many-body systems represent an important tool for investigating the properties of real materials. This work describes the effective action formalism as a rigorous theoretical framework for the development for such calculations. Similar to density-functional theory the effective action formalism reduces the analysis of an interacting many-body system to a self-consistent solution of single-particle equations. This formalism is free of the limitations of the conventional density-functional theory. It is equally applicable for the analysis of ground as well as excited state properties. The formalism is illustrated by constructing density and spin-density based description of nonrelativistic many-electron system. This leads to an explicit diagrammatic expressions for the exchange-correlation functional and provides a systematic density based analysis of one-electron propagators and many-body excitation energies. Numerical results for the excitation energies for several closed shell atoms are presented. ^
We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We illustrate the formalism for the case of a particle-density based description of a nonrelativistic many-electron system. We obtain a simple diagrammatic expansion of the exchange-correlation functional in terms of Kohn-Sham single-particle orbitals and energies; develop systematic Kohn-Sham formulation for one-electron propagators and many-body excitation energies. This work is ideally suited for practical applications and provides a rigorous basis for a systematic development of the existing body of first-principles calculations in a controllable fashion.
The most of the experimental measurable quantities in many-body electron system, such as the optical absorption, luminescent spectra and exciton effect, are related to the excitation states description. The density functional theory with local density approximation (DFT-LDA) as a ground state theory, i.e. the solutions based on the Kohn-Sham equation is a powerful tool for studying the ground state properties in many-particle systems. However, the first principles computation of excited states is more complexity than ground-state calculations. A key problem is that the exchange-correlation interaction in excited states is differ from the ground-states. In recent years, nevertheless, several electronic-excitation theories have been developed. The most important theoretical and computational method include the many-body perturbation theory which is based on the quasi-particle concept and the Green function equation, the time-dependent DFT and the Bethe-Salpeter equation for describing the electron-hole interaction. Among them the central ingredient is an electron's self-energy operator Σ that describes the exchange correlation effect beyond Hartree approximation. The implementations of the above theories are unavoidable to introduce some of approximations. A good approximation for Σ is the GW approach by Hedin. It is shown from computation simulations for many real condensed matter systems that the GW approach is a successful method for electronic-excitation problems. Another effective method for excited-states is so-called screen-exchange local-density approximation (sX-LDA). It is a combination of LDA and Hartree-Fock (HF)theory, in which the intrinsic local screen-exchange interaction has been replaced by a non-local one and a generalized Kohn-Sham equation (GKS) is given. Based on a PWscf package, the sX-LDA-PWscf method has been tested and indicates that an available approach for treating band-gap problem in semiconductors. In this paper, the many-body theories for the excitation process, its development and signification are reviewed. The relation and differences consist in different theoretical methods are discussed. On the based of above discussions, the applications of many-body theory to the band-band transition (band-gap underestimation problem) and exciton effect in semiconductors are presented.