It is shown that there exists a variational Kohn-Sham density-functional theory, with a minimum principle, for the self-consistent determination of an individual excited-state energy and density. Exact properties of the required functional are ascertained, including a Koopmans theorem. This knowledge allows the employment of an effective potential that gives encouraging numerical results, and also helps to explain the success of a recent perturbation theory and its time-dependent counterpart. 31.15.Ew, 31.50. + w Density-functional theory (DFT) is now in widespread use as an effective approach for ground-state electronic structure calculations. The development of accurate functionals within the popular Kohn-Sham formulation of DFT has enabled us to perform efficient ground-state variational calculations with remarkable accuracy. In Kohn-Sham theory, the simplicity of the three-dimensional electron density is coupled with the use of a relatively small number of orbitals to ensure Fermi statistics, through the use of an auxiliary noninteracting system (see, for instance,There has also been noteworthy progress in excited-state DFT (see, for example, Refs. ). These studies have stimulated us into asking if there exists a variational KohnSham theory for an individual excited state, which is analogous to the ground-state theory, because an affirmative answer implies the possibility that accurate excited-state calculations might be performed routinely, in a manner comparable to today's ground-state calculations. Accordingly, it is our purpose to show that there does indeed exist such a variational Kohn-Sham theory, with a minimum principle, for an individual excited state. In our proof, the necessary universal functional is identified and several of its properties are ascertained for the purpose of approximation. This enables us to actually carry out illustrative self-consistent calculations, and encouraging results are obtained for the systems studied.Consider the Hamiltonian of interestĤ y :whereT is the kinetic energy operator,V ee is the electron-electron repulsion operator, and y͑r͒ is the localmultiplicative attractive potential of interest. Assume we want the energy and density of the kth state ofĤ y . (In this Letter, all interacting and noninteracting states shall be assumed nondegenerate to facilitate the presentation.) For this purpose we start by generalizing earlier excited-state functionals [12,13] and define the universal bywhere both r and r 0 are arbitrary electron densities. In Eq. (2), it is understood that each C is orthogonal to the first k 2 1 states of that Hamiltonian,Ĥ y 0 T 1V ee 1 P N i 1 y 0 ͑r i ͒, for which r 0 is the ground-state density. It follows from the definition of F͓r, r 0 ͔ that E k , the energy of the kth state ofĤ y , is given bywhere r 0 is the ground-state density ofĤ y and r k is the density of its kth state. Analogous with the constrainedsearch proof of the ground-state Hohenberg-Kohn variational theorem, Eq. (3) is true becausewhere the C's are understood to be restric...

ABSTRACT:Various thermodynamic elements of the density functional theory of electronic structure are reviewed and clarified. Detailed argumentation is given for the particular "del dot del" definition of the local kinetic energy density and local temperature. The temperature measures the "nighness" of an electron pair, thus playing a key role in quantitative (exchange and kinetic energy functionals) and qualitative (electron localization functions) tools based on the electron pair density. Two different derivations are given of the Gaussian model for the phase-space distribution function, from which one obtains an approximation to the entropy of the charge distribution. The full thermodynamic description is briefly discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 90: [309][310][311][312][313][314][315][316][317][318][319][320][321][322][323][324][325][326] 2002 Key words: electronic structure; density-functional theory; local temperature; nighness 1. Preface B oth the tone and the substance of the densityfunctional theory (DFT) [1] remind one of classical thermodynamics. For an electronic ground (equilibrium) state, the electron density determines the state of the system, there exists a total energy that is a functional of the state of the system, and there is a minimum energy principle that deter- mines the state of the system [2]. There is a finite ambient temperature version of the theory that in most respects can be handled as a thermodynamics [3]. There is an increasing entropy principle. Furthermore, from place to place within an inhomogeneous system, there is a varying electronic kinetic energy density, from which one may infer the existence of a varying "local temperature."Much already is in the literature about these things. The present work reviews and continues the discussion. We treat a range of aspects in some detail, emphasizing first of all, the question of what is the most appropriate definition of the local temperature. Our review is selective, featuring works from our laboratories since about 1980.

A Coulomb density is special because it determines not only its Hamiltonian but the degree of excitation as well. We derive Euler equations for excited state energies and densities that depend only on the electron density. Unlike existing formulations, additional functions and indices are not required; with these functionals, the equations of excited-state density functional theory strongly resemble those of ground-state theory. A critical analysis of the new functionals is included.

In this third paper of a series [Refs.

The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.