Ceperley-Alder data

The exact numerical values of r ) and ef(rs) are known, with small statistical uncertainties, for several intermediate values of r from Monte Carlo simulations of the UEG carried out by Ceperley and Alder [112]. Based on these results, several interpolation formulas for e r ) and ef(rs) have been devised to connect the high- and low-density limits [Eqs. (69) and (71)] and simultaneously reproduce the Ceperley-Alder data for intermediate r. Three such parametrizations are widely used in quantum-chemical codes. 

Perdew and Zunger [77] (PZ81) suggested the following parametrization of the Ceperley-Alder data for the spin-compensated and spin-polarized cases... 

The best available analytic representation of the Ceperley-Alder data was devised by Perdew and Wang [114] (PW92)... 

At this stage, the formalism can be implemented in a computer program. The applications described below [15-21] rely on the expansion of the electronic wavefunctions in terms of a large number of plane waves, as well as on the replacement of nuclear bare potentials by accurate norm-conserving pseudopotentials. The Local Density Approximation was used, with the Ceperley and Alder data for the exchange-correlation energy of the homogeneous electron gas. 

Modem functionals include more elaborate expressions for hom( ) (Vosko et al., 1980 Perdew and Zimger, 1981) relying on accurate Quantum Monte Carlo data for the homogeneous electron gas (Ceperley and Alder, 1980). Generalizing to magnetic solids, which is highly relevant for lanthanide materials, is straightforward as one merely has to consider two densities, one for spin-up and one for spin-down electrons, which corresponds to the LSD functional (von Barth and Hedin, 1972), Even more accurate calculations may be obtained by... 

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