Spin projected extended Hartree‐Fock equations

The (spin projected) extended Hartree‐Fock equations are derived and discussed in the general (“many λ i ”) case. The derivation is based on the corresponding generalized Brillouin theorem, substituting in its expression the spin projected DODS Slater determinant as a linear combination of determinants. The expressions obtained for the elements of the different matrices ε cd ( c = a or b , and d = a or b ) occurring in the equations are analyzed. The transformation of the equations into the form of a pseudoeigenvalue problem and the LCAO form of the equations are given, too. Finally the relation to the Goddard's GF equations is discussed in detail.