Hartree-Fock method history

Surveying the history of the theory of optical lanthanide spectroscopy, we can discern several main features the usefulness of Lie groups, following their introduction by Racah (1949) the relevance of the method of second quantization, as demonstrated by the use of annihilation and creation operators for electrons and the inability of the Hartree-Fock method and its various elaborations to provide accurate values (say to within 1%) of such crucial quantities as the Slater integrals F (4f,4f) and the Sternheimer correction factors R , for a free ion. The success of the formal mathematics is in striking contrast to the failure of the machinery of computation. This turn of events has happened over a period of time when... 

The time-dependent Hartree-Fock (TDHF) method has a lengthy history as a technique for calculating the electronic excitation energies and transition moments of molecular systems. There are two ways to formulate TDHF theory that look quite different but are in fact equivalent. The formulation used below... 

The DFT method has a long history behind it, which began with Thomas, Dirac, Fermi, etc. At the beginning, the successes were quite modest (the electron gas dieory, known as the Xa method). Real success came after a publication by Jan Andzehn and Ericb Wimmer. The DFT method, offering results at a correlated level for a wide spectrum of physical quantities, turned out to be roughly as inexpensive as the Hartree-Fock proceduie-this is the most sensational feature of the method. 

In the laboratories of the University of Namur, the authors and their colleagues have a long history in the development of methods for the study of one-dimensionaUy periodic systems described quantum-mechanically at the Hartree-Fock and correlation levels using expansions in Gaussian-type atomic orbitals. This work, which was started under the direction of Professor J. M. Andre, led to the creation of the program known as PLH [1]. That program, designed for the study of the structural and electronic properties of linear polymers, evaluated the lattice sums as direct-space expansions. Further work, directed by Professor J. Del-halle, led to the development of an approach that combined direct- and reciprocal-space concepts to yield an Ewald-type method [2], That work appeared in the Ph.D. dissertation of Flamant [3], in a paper that included the present authors [4], and in later publications that are referred to where appropriate in the present communication. 

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