Helium isoelectronic series

It should be noted that in the case of the helium isoelectronic series (singlet GS of a two-electron system), because only one orbital is sufficient to construct the determinantal wave function and to obtain the density as n(r) — 2[t)r(r)], the minimization over n in Eq. (64) is equivalent to the minimization over ip in Eq. (28). Therefore the HF-KS and HF equations and their eigenfunctions are the same, ipir) = and consequently AT n =... 

Table 2 Comparison of quantum mechanical and density functional correlation energies for the helium isoelectronic series The values for the non-dynamical and dynamical components correspond closely to the already reported values6 for A and E FT, respectively. The last column shows the values obtained using the exact energies (/Aartrees) from Davidson [44]. ...

Table 4.3 Coulomb correlation energies of the helium isoelectronic series Eq (OPM) versus CS (Colie and Salvetti 1975), LDA (Vosko et al 1980), GGA (Perdew et al 1992), MP2 (Ishikawa and Koc 1994) and exact results (Davidson et al 1991). Both the nonrelativistic values Ecnr and the difference between the relativistic numbers and aj-e given (all energies...

Illustrative results obtained by a perturbative evaluation of this functional on the basis of a self-consistent calculation with the exact are given in Table 4.3 and Figures 4.1 and 4.2. Table 4.3 lists the correlation energies of the helium isoelectronic series, separating the nonrelativistic from the relativistic contribution. 

Coulomb correlation energies of the Helium isoelectronic series versus CS [166], LDA... 

Potentials and Total-Energy Components for the Helium Isoelectronic Series. 

Calculations of IIq(O) are very sensitive to the basis set. The venerable Clementi-Roetti wavefunctions [234], often considered to be of Hartree-Fock quality, get the sign of IIq(O) wrong for the sihcon atom. Purely numerical, basis-set-free, calculations [232,235] have been performed to establish Hartree-Fock limits for the MacLaurin expansion coefficients of IIo(p). The effects of electron correlation on IIo(O), and in a few cases IIq(O), have been examined for the helium atom [236], the hydride anion [236], the isoelectronic series of the lithium [237], beryllium [238], and neon [239] atoms, the second-period atoms from boron to fluorine [127], the atoms from helium to neon [240], and the neon and argon atoms [241]. Electron correlation has only moderate effects on IIo(O). 

The correlation energies for free (unconfined) H, He, Li+ and Be++ were well known at that time, and so Gimarc wanted to analyze, in particular, how the correlation energy changes as a function of the box radius for the confined helium atom isoelectronic series. Gimarc performed a number of variational calculations based on the following wave functions ... 

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