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• W2009091818 abstract "The singlet and triplet projections of a two-electron unrestricted Slater determinant (USD) are obtained. Then the $S$, ${{ensuremath{Sigma}}_{g}}^{+}$, etc. projections are considered and a correspondence is found between these functions and those that arise from a special choice of superposition of configurations. In the atomic case ($S$ states), if the variation method is applied to a specific multiconfiguration wave function, one can readily obtain the corresponding USD which is the Roothaan-type solution to the unrestricted, projected Hartree-Fock equations for that case, in a basis {${R}_{mathrm{il}|m|}(r){Y}_{mathrm{lm}}(ensuremath{theta}, ensuremath{varphi}){ensuremath{xi}}_{{m}_{s}}({ensuremath{sigma}}_{s})$, $i=1, ensuremath{cdots}4$ ($i=1, ensuremath{cdots}8$ when $mensuremath{ne}0$); $l=0, 1, ensuremath{cdots}ensuremath{infty}$; $m=ensuremath{-}l, ensuremath{cdots}l$; ${m}_{s}=ifmmodepmelsetextpmfi{}frac{1}{2}$}. Similar results are found for even-$P$ states (${L}_{z}=0$), ${{ensuremath{Sigma}}_{g}}^{+}$ and ${{ensuremath{Sigma}}_{g}}^{ensuremath{-}}$ states. This applies to the ground state as well as to the excited states of the same symmetry type. In this way a value better than $E=ensuremath{-}2.9030$ atomic units may be obtained for the nonrelativistic ground-state energy of the He atom, which means that more than 98% of the correlation energy can be accounted for by a single unrestricted projected Slater determinant. The quantitative effect of the use of spin-mixed spin orbitals is discussed, as well as some problems arising in the theory of unrestricted projected Hartree-Fock equations as applied to excitation processes. The use of a multiconfigurational form of the wave function constitutes only an artifice, and the unrestricted projected Hartree-Fock scheme at the present moment does not represent a reasonable approach to the two- and many-electron problems. Nevertheless, the present results indicate that it may become an alternative worthy of investigation." @default.
• W2009091818 created "2016-06-24" @default.
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• W2009091818 date "1967-02-05" @default.
• W2009091818 modified "2023-10-13" @default.
• W2009091818 title "Unrestricted Projected Hartree-Fock Solutions for Two-Electron Systems" @default.
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• W2009091818 doi "https://doi.org/10.1103/physrev.154.70" @default.
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