Abstract
Wave‐functions of various spin‐dependent and spin‐free methods are examined from the point of view of the requirements of the exclusion principle and the spin projection. It is shown that the “two‐rowed” or “two‐columned” requirements of the standard Young tableaux are necessary but not sufficient to replace the “antisymmetry” requirement of a wave‐function and to be regarded as exclusion principle. The symmetry adapted wave‐functions which are constructed from the matric basis e may not satisfy the exclusion principle and, hence, their usages are open to question. The appropriate symmetry adapted wave‐functions which satisfied the exclusion principle are given for any pure spin state. We have also shown that the structure operators __N__P for bond functions are spin projectors in the Waller‐Hartree double‐antisymmetrized space only, and should not be used in the Hartree product space. Furthermore, if the corresponding matric operators __P__NP are used in the Hartree product space, then the wave‐functions thus constructed may not be antisymmetric with respect to the permutations of indistinguishable electrons.