Helium, confined closed-shell

In 1978, Ludena [102] carried out a Hartree-Fock calculation by using a wave function consisting of a single Slater determinant for the closed-shell atoms, whereas he used a linear combination of the Slater determinants for the open-shell atoms. Each Slater-type orbital times a cut-off function of the form (1 — r/R) to satisfy the boundary conditions. Ludena studied pressure effects on the electronic structure of the He, Li, Be, B, C and Ne neutral atoms. The energies he obtained for the confined helium atom are slightly lower than those Gimarc obtained, especially for box radii in the range R > 1.6 au. 

By checking the results from Table II of Ref. [19], we see that for the closed-shell system there are discrepancies between the HF and KS-SIC-OEP-KLI methods. Such differences can be attributed to the basis set used for the HF method, or to the methodology used in the KS approach. The aim of this work is twofold. First, we recomputed the Table II from Ref. [19] by using an optimized basis set for the HF calculation. Second, we compute the lowest triplet state of the confined helium atom by the HF method and its results are compared with those obtained by the KS approach. In this way a reliable comparison between HF and KS is made for the lowest singlet and triplet states of the confined helium atom. 

As in the closed-shell case, we estimate the correlation energy involved in the lowest triplet state of the confined helium atom. In Table 6 we report the total energy obtained from Table IV of Ref. [19], also the HF results from this work, and results obtained from correlated methods. We see that the results obtained with the HF method, coupled with exponent optimization, compete with the other correlated methods, since for some confinement radii our results are below those reported by the other authors. Comparing our Hartree-Fock results with those obtained with 40-terms Hylleraas wave... 

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