Hartree-Fock theory was the first successful ab initio approach to the calculation of electronic structure. Unlike semi-empirical methods, Hartree-Fock theory does not depend on any adjustable parameters. We have seen an example of such parameters in the use of beta, the resonance integral, in Huckel theory. Hartree-Fock theory is based on calculation of Coulombic effects from first principles using two types of electron-electron repuslsion integrals. The Hartree apptoximation is a an orbital approximation that permits us to write the many electron wavefunction as product of one electron wave functions. Later this idea was refined by Slater using a determinant as the wave function. The so-called Slater determinant ensures that the wave function is always anti-symmetric with respect to electron exchange. The Hartree-Fock equatoins are a set of linear single electron equations. The energy of each electron solved in the field of all of the other electrons. This method requires iterations to achieve a self-consistent field. The greatest challenge for Hartree-Fock theory is the description of electron-electron repulsion. The electron-electron repulsion was written as part of a one-electron operator by using Coulomb and exchange integrals.
Applications of Hartree-Fock theory
Configuration interaction
The iterative solution of the equations using the Fock operator provides a good value for the energies of the occupied molecular orbitals (MOs). However, the unoccupied MOs are not very accurate. This means that Hartree-Fock theory is appropriate for the calculation of ground state energies and other properites, but it is not well-suited to spectroscopy. The method for obtaining more accurate eneriges of the unoccupied levels is to permit them to be occupied using alternative configurations. This method is known as configuration interaction. One can carry out configuration interaction for singles meaning that each electron in the occupied orbitals can be promoted to each of the unoccupied orbitals. Configuration interaction at the level of doubles means that all possible sets of two electrons are promoted from the occupied orbitals to each of the unoccupied orbitals. These methods are nown as multi-determinant methods, where each configuration corresponds to another determinant.
