Hartree-Fock calculations reference configurations

This procedure suffers from a high degree of arbitrariness in the choice of just which configurations are deemed important. The calculation can be made somewhat more objective by including all excitations between a subset of occupied MOs and a subset of vacant orbitals. (These excitations are subject to certain restrictions as to multiplicity or order of excitation.) The orbitals chosen for the excitations are referred to as the active space , and the method is dubbed Complete Active Space Self Consistent Field (CASSCF) - ". Both MCSCF and CASSCF provide a certain fraction of the correlation energy, relative to a single configuration, Hartree-Fock, calculation. 

Often configuration interaction calculations are performed after an initial Hartree-Fock calculation. In such cases the one-electron creation and annihilation operators would refer to eigenfunctions of the Fock operator, and the Fock operator would have a simple form similar to that shown in equation (53). 

In the most recent version of the energy-consistent pseudopotential approach the reference data is derived from finite-dilference all-electron multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian. As an example the first parametrization of such a potential,... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Apparently, a large number of successful relativistic configuration-interaction (RCI) and multi-reference Dirac-Hartree-Fock (MRDHF) calculations [27] reported over the last two decades are supposedly based on the DBC Hamiltonian. This apparent success seems to contradict the earlier claims of the CD. As shown by Sucher [18,28], in fact the RCI and MRDHF calculations are not based on the DBC Hamiltonian, but on an approximation to a more fundamental Hamiltonian based on QED which does not suffer from the CD. At this point, let us defer further discussion until we review the many-fermion Hamiltonians derived from QED. 

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