Looking at the literature, one finds that, in atomic and molecular physics, comparatively little interest has so far been devoted to the GHF­ scheme, and the purpose of this paper is to try to focus the interests of some quantum chemists to this rather interesting problem of looking for the "absolute minimum" of the original Hartree-Fock method. (P. -O. Li:iwdin and I. Mayer, Ref. 5, p. 93. ) In view of the complexity of quantum mechanical equations of motion describing atomic, molecular, and solid state phenomena - even when modelling very small systems at the nonrelativistic level within the Born­ Oppenheimer approximation - one is obliged to introduce rather drastic approximations in order to proceed. The standard approach in the in­ vestigation of the molecular electronic structure is then to rely on the so-called ab initio electronic model Hamiltonian H, which is defined on a suitable finite-dimensional subspace WN of the infinite-dimensional N-electron component of the Fock space F, and to look for the solu­ tions of the time-independent Schrodinger equation associated with this model Hamiltonian. The space WN then represents a vector space of N-linear alternating forms, built as the antisymmetrized tensor product of the one-electron space WI, which in turn is spanned by a chosen set of nonorthogonal atomic spin orbitals (ASOs) IXA) == IA)A=I, . . . ,M, defining a given ab initio model.