Relationship between Unrestricted and Extended Hartree-Fock Wave Functions as Function of Number of Electrons

The justification of the use of unprojected many-electron wave functions for solids and large molecules is examined from the point of view of an extended Hartree-Fock method in the one-$\lambda$ approximation presented in previous papers. It is shown that, in the limit of a large number of electrons, the Hartree-Fock operators are the same for the projected and unprojected case. It is further shown that the expectation value of purely spatial operators for the projected and unprojected functions are equal in this limit. Graphs of the differences of the relevant quantities as a function of number of electrons are given.