Excited States and Electron-Atom Scattering
As has become evident from a vast variety of applications, the Kohn Sham-version  of density functional (DF-)theory  constitutes the most successful many-electron theory for the calculation of electronic ground state properties. The considerable practical virtue of this scheme resides in the fact that it maps the N-electron problem onto a one-particle problem which consists in self-consistently solving N one-particle equations with a strictly local, energy-independent and real-valued potential. The term “local” in that context refers to the property of this potential that it appears as a factor in front of the sought-for solution ψ i (x) as in a Schrödinger equation that describes a true one-particle problem. (Here x stands, collectively, for the real-space coordinate r and the spin variable s of some electron.) The N lowest lying solutions can be used to calculate the total kinetic energy of the system and the charge density ρ(r) which turns out to be expressible as the sum of the square moduli of those N solutions. If, in addition, the exchange-correlation energy per particle, ε xc (r), is approximated by one of the more recent local expressions with gradient corrections [3, 4, 5], one can calculate the total energies of atoms, molecules and solids to an accuracy that appeared to be inconceivable 20 years ago. The foundation of this theoretical framework seemed to suggest that its extension to stationary electronic excitations is impossible. Nevertheless, many naïve applications of the Kohn-Sham scheme to non-ground state situations proved to be surprisingly successful. The objective of the present contribution is to show that the Kohn-Sham theory can be rederived in a form that applies, in fact, to ground states as well as to excited states.
KeywordsLocal Density Approximation SchrOdinger Equation Induce Polarization Slater Determinant Ground State Wave Function
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