Generation of serber-type functions by the projection operator method

✍ Scribed by R. Paunc

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 341 KB
• Volume: 46
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(77)80619-2

✦ Synopsis

The projection operator method is used and a suitabte set of trial functions is suggcstcd. The projections of these functions are finearly independent.

The br~nci~in~d~~r~rn Serber-functions are obtained from the projected functions by a Schmjdt-ortllo~on~lization procedure.

The Scrber-type spin eigenfunctions are built up from pair-spin-functions, where each pair-functicn is either a singlet or a triplet. Carrington and Doggett [ 11 have shown that it is sufficient to consider the all-tripiet wavefunctions~ as the remaining ones can simply be obtained by interposing the singlet fur:ctions in all possible ways.

Different algorithms have been suggested for the Lonstruction of Serber-type spin-functions. One tan set up recursion formulas, which generate the N-eiectron functions fro-m the $V--2)-electron functions; this method has the disadvantage that one has to store a large amount of information. Ruedenberg et al. [2; suggested the diagonahzation of the S2 matrix, when the latter is set up in the basis of geminai spin-product functions, i.e. products of two-electron rpin eigenfunctions. Recently a direct method was proposed [3] in which one can cakulate directly the coefficient of any geminal spin-product in a given Serber-function.

A different type of approach was used successfully in the case of simple spin-functions. One starts from an appropriate trial function and projects from it the s2 eigpnfunction [4]. In the present note, the F,ojection operator method is extended to the case of Serher-type functions. One can take over many features from the derivation t If the usual projection operator method, but there wi:l be obvious differences. As the :;rojeztion opemutor method has some advantages as