A new procedure is developed for calculating the best wavefunction for anNhyphen;electron atom in terms ofNonehyphen;electron orbitals which are eigenfunctions ofl2, lzandsz. This is a special case of a method for calculating the best wavefunction in terms ofNorbitals unrestricted in angular momentum but restricted in spin component and is thus a partial generalization of Louml;wdin's EHF method. We calculate approximate spatial eigenfunctions ofHusing the functionPHgr;lsqb;agr;,lgr;rsqb;thinsp;equals;thinsp;Dlgr;lgr;lsqb;agr;rsqb;ithinsp;equals;thinsp;1kdgr;iPiphgr;,wherephgr;is a product ofNspatial orbitals and where thePiare thekpermutations out of whichklinearly independent projections onto the Young tableaulsqb;agr;,lgr;rsqb;can be obtained. The method gives an improvement to each of Goddard's GI solutions in such a way that they all give the same energy when fully minimized, while only involvingkminus;1additional parameters. For Li atom there is only one additional parameter and calculations are performed using Goddard's GI and GF orbitals, obtaining small improvements in the energy. An energy of minus;7.4477076 a.u. is obtained.
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