Hartree-Fock determinant

Configuration Interaction (Cl) methods begin by noting that the exact wavefunction 4 cannot be expressed as a single determinant, as Hartree-Fock theory assumes. Cl proceeds by constructing other determinants by replacing one or more occupied orbitals within the Hartree-Fock determinant with a virtual orbital. 

The full Cl method forms the wavefunction as a linear combination of the Hartree-Fock determinant and all possible substituted determinants ... 

Practical configuration interaction methods augment the Hartree-Fock by adding only a limited set of substitutions, truncating the Cl expansion at some level of substitution. For example, the CIS method adds single excitations to the Hartree-Fock determinant, CID adds double excitations, CISD adds singles and doubles, CISDT adds singles, doubles, and triples, and so on. 

The Hartree-Fock determinant and all of the substituted determinants are eigenfunctions of Hg these are the solutions to the part of the divided Hamiltonian for which we have a solution. Thus ... 

Studies on Cg show that cyclic cumulenes are not well described by a one-determinant wavefunction. In a valence-CASSCF calculation on cyclic Cg, for example, the Hartree-Fock determinant has a weight of only 0.40. The problem is assumed to be aggravated for larger systems, as the HOMO-LUMO gap diminishes. 

The cluster operator T creates excitations out of the Hartree-Fock determinant and may be written as... 

Diagonal matrix elements of the P3 self-energy approximation may be expressed in terms of canonical Hartree-Fock orbital energies and electron repulsion integrals in this basis. For ionization energies, where the index p pertains to an occupied spinorbital in the Hartree-Fock determinant,... 

As we have written it in Equation (8), the DMRG wave function contains redundant variational parameters. This means that the set of variational tensors f/ni... ij/Hk in the DMRG wave function is not unique, because we can find another set of tensors whose matrix product yields an identical state. This redundancy is analogous to the redundancy of the orbital parametrization of the Hartree-Fock determinant. In the case of the DMRG wave function, we can insert a matrix T and its inverse between any two variational tensors and leave the state invariant... 

If the Hartree-Fock determinant dominates the wave function, some of the occupation numbers will be close to 2. The corresponding MO s are closely... 

Fig. 5.22 Configuration interaction (Cl) promotion of electrons from the occupied MOs (corresponding to the Hartree-Fock determinant) gives determinants corresponding to excited states. A weighted sum of determinants D1, D2, corresponds to a molecule in which the...

This partitioning, when applied in conjunction with the set of canonical Hartree-Fock orbitals (in which is diagonal), corresponds to the Moller-Plesset variant of many-body perturbation theory. A Hartree-Fock determinant, which is an eigenfunction of Pjq, is therefore the natural choice for the zeroth-order wavefunctiond... 

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