Generator coordinate Hartree-Fock method

The generator coordinate method (GCM), as initially formulated in nuclear physics, is briefly described. Emphasis is then given to mathematical aspects and applications to atomic systems. The hydrogen atom Schrodinger equation with a Gaussian trial function is used as a model for former and new analytical, formal and numerical derivations. The discretization technique for the solution of the Hill-Wheeler equation is presented and the generator coordinate Hartree-Fock method and its applications for atoms, molecules, natural orbitals and universal basis sets are reviewed. A connection between the GCM and density functional theory is commented and some initial applications are presented. 

Jorge FE, de Castro EVR, Da SUva ABF. A universal Gaussian basis set for atoms cerium through lawrencium generated with the generator coordinate Hartree-Fock method. J Comp Chem. 1997 18(13) 1565-9. 

The mutual avoidance of electrons in helium atom or in hydrogen molecule is caused by Coulombic repulsion of electrons ( Coulomb hole , see above). As we have shown in this Chapter, in the Hartree-Fock method the Coulomb hole is absent, whereas methods which account for electron correlation generate such a hole. However, electrons avoid each other not only because of their charge. The Pauli principle is an additional reason. One of the consequences is the fact that electrons with the same spin coordinate cannot reside in the same place, see p. 33. The continuity of the wave function implies that the probability density of them staying in the vicinUy of each other is small, i.e. 

Osvaldo and I certainly became friends. We later met many times, in Uppsala, Norway, Florida (where 1 had also the privilege to meet Professor Slater 1 believe he and a few others - Hartree, Fock, Bom, Oppenheimer - set the foundations in the 1930s of what we now call quanmm chemistry). I remember specially when, in Rio de Janeiro, during the 6th Escola Latinoamericana de Quimica Teorica in 1988, Osvaldo had very stimulating words on our first results with the generator coordinate method, which I review below. 

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