The generator coordinate Hartree-Fock method

During the 1976 Sanibel Symposia, we introduced the GC Hartree-Fock (GCHF) method. This approach is based on choosing as the one-electron function the continuous superpositions 

The discretization in the first applications for atoms was through the technique called ID [10,16], which includes a relaheling of the generator coordinate space, i.e. 

Then the generator coordinate fi is discretized (for each symmetry) in an equally spaced mesh / so that 

In equation (27) N is the number of discretization points, an option which defines the size of the basis set, and A/2 the numerical integration interval. 

The very first application of the GCHF method was for the construction of universal atomic basis sets [17], culminating with very accurate Gaussian (GTO) and the construction of Slater (STO) bases for neutral and charged, ground and excited states for atoms H to Xe (see Ref. [18] and references therein). Contracted GTO sets were also introduced [19,20]. The extension of integral transforms other than for Is functions (Section 3) was also presented [21]. 

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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. 

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