L. Wilk

We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density approximation to the exchange-correlation energy functional. By accurately recalculating the RPA correlation energy as a function of electron density and spin polarization we demonstrate the inadequacies of the usual approximation for interpolating between the para- and ferro-magnetic states and present an accurate new interpolation formula. A Padé approximant technique is used to accurately interpolate the recent Monte Carlo results (para and ferro) of Ceperley and Alder into the important range of densities for atoms, molecules, and metals. These results can be combined with the RPA spin-dependence so as to produce a correlation energy for a spin-polarized homogeneous electron gas with an estimated maximum error of 1 mRy and thus should reliably determine the magnitude of non-local corrections to the local spin density approximation in real systems.

The new, accurate, correlation energy of the spin-polarized homogeneous electron gas due to Vosko, Wilk, and Nusair, based on the "exact" Monte Carlo calculations of Ceperley and Alder, is used to evaluate the cohesive energies of the alkali metals Li, Na, K, and Rb. The new cohesive energies for Li, Na, K, and Rb are 129, 90, 72, and 57 mRy, which differ from experiment by +7, +7, +3, and -7 mRy, respectively, and are approximately 8 mRy larger than those obtained by Janak, Moruzzi, and Williams. Of particular note is the significant improvement in the agreement between theory and experiment for Rb.

Total and ionisation energies have been calculated for a number of simple atoms using spin density functional theory in the local-spin-density approximation (LSDA) as well as by methods that attempt to correct it for electron self-interaction effects. The LSDA total energies using the new improved results of Vosko et al. (1980) for the correlation energy of a spin-polarised homogeneous electron gas are further from experiment than those based on other frequently used, but less accurate, parameterisations. On the other hand ionisation energies are improved and compare as well with experimental as the self-interaction corrected results. By using the transition-state concept the authors examine the non-local correction to the LSDA single-particle potential of a valence electron and show that it can be relatively large.

A new selfinteraction-corrected local correlation energy functional is constructed to conform with the exact limiting behaviour in both one-electron systems and N-electron systems (N to infinity ) with slowly varying densities. It is combined with an exact treatment of exchange to selfconsistently calculate correlation energies, ionisation potentials, electron affinities, spin and number densities and diamagnetic susceptibilities for a number of atoms and ions. The results are compared with those from the Stoll-Pavlidou-Preuss (SPP) and the Perdew-Zunger (PZ) selfinteraction corrected forms as well as the Kohn-Sham (KS) form. For most of the above properties the new form is either as good as or better than the others. The authors conclude that for physical quantities that can be expressed as differences of energies or differences of spin up/down densities the exact exchange plus local correlation method is a viable and much simpler alternative to large configuration-interaction calculations for atoms and ions, especially for those with N>or=15.

Numerical calculations of the Helmholtz free energy $F$ to $O({\ensuremath{\lambda}}^{2})$ and $O({\ensuremath{\lambda}}^{4})$ from all the diagrams have been carried out in the high-temperature limit without making the leading-term approximation for a monatomic face-centered cubic crystal with nearest-neighbor central-force interactions. The numbers obtained for some diagrams and the total $F({\ensuremath{\lambda}}^{4})$ can differ by as much as 47 and 33%, respectively from those obtained in the leading term approximation, indicating that this approximation is not very good as far as absolute magnitudes are concerned. However, the ratio $\frac{F({\ensuremath{\lambda}}^{4})}{F({\ensuremath{\lambda}}^{2})}$ is nearly the same as in the leading-term approximation, indicating that the convergence of the perturbation expansion is satisfactory up to one third of the melting temperature. Finally, the improved-self-consistent (ISC) scheme of selecting the most important diagrams is probably as good as doing perturbation theory to order ${\ensuremath{\lambda}}^{4}$.