Finite Electronic Systems Research Articles

Dynamical electronic polarizability and the force sum rule

It is shown that a dynamical force sum rule is useful in analyzing the response of a finite electronic system to a uniform electric field that oscillates harmonically in time. The sum rule, which has been used previously in calculations of the response of atoms to electric fields, provides a direct test of electronic polarizability calculations and may lead to useful approximations for the electronic polarizability of metallic microstructures. We apply the sum rule to the case of a small metal sphere in the jellium model, and show that it directly leads to an approximation that is equivalent to the surface-plasmon-pole approximation for the red-shift of the surface plasmon frequency.

New approach to the one-particle Green's function for finite Fermi systems

A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ($n\mathrm{th}$-order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.

Brueckner-Hartree-Fock method for finite electronic systems

A Hartree-Fock-like model where the electrons in their motions are surrounded by exchange-correlation holes is described. Information about the correlation holes may be provided by Bethe-Goldstone type pair functions. An interpretation of the new one-particle equations is given. The theory for Bethe-Goldstone pair functions is shortly reviewed and a simplification is suggested for the case of a Hylleraas basis set. Finally the new method is illustrated for the Li ground state and for diatomic molecules at large internuclear distance.