Correlation energy, correlated electron density, and exchange-correlation potential in some spherically confined atoms

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We report correlation energies, electron densities, and exchange-correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be2+, and Ne atoms. The variation of the correlation energy with the confinement radius Rc is relatively small for the He, Be2+, and Ne systems. Curiously, the Lee–Yang–Parr (LYP) functional works well for weak confinements but fails completely for small Rc. However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing Rc. This effect is less pronounced at the density-functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small Rc. The standard exchange-correlation potentials exhibit significant deviation from the “exact” potential obtained by inversion of Kohn–Sham equation. The LYP correlation potential behaves erratically at strong confinements ​
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