Limited configuration interaction expansion

We take the initial wavefunctions to be very limited configuration-interaction expansions, containing only s orbitals. Thus, we take as the first wavefunc-tion in the one formed by all single and double excitations generated from the basic configuration [Is ] by substitutions comprising the 2s orbital for the second wavefunction, we span over the 2s and 3s orbitals and for the third one, we use orbitals Is, 2s and 3s. Hence, are all these wavefunctions are full Cl wavefunctions for such bases. Explicitly, these wavefunctions are... 

A posteriori corrections can be developed for calculations performed by using the Brillouin-Wigner perturbation expansion. These a posteriori corrections can be obtained for the Brillouin-Wigner perturbation theory itself and, more importantly, for methods, such as limited configuration interaction or multi-reference coupled cluster theory, which can be formulated within the framework of a Brillouin-Wigner perturbation expansion. 

Let us remark that estimates of 3R can be obtained fi om other approaches to the correlation problem in atoms and molecules, such as, for example, limited configuration interaction or coupled cluster expansions. ... 

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. 

A disadvantage of all these limited Cl variants is that they are not size-consistent.The Quadratic Configuration Interaction (QCI) method was developed to correct this deficiency. The QCISD method adds terms to CISD to restore size consistency. QCISD also accounts for some correlation effects to infinite order. QCISD(T) adds triple substitutions to QCISD, providing even greater accuracy. Similarly, QCISD(TQ) adds both triples and quadruples from the full Cl expansion to QCISD. 

The above expansion of the full N-electron wavefunction is termed a "configuration-interaction" (Cl) expansion. It is, in principle, a mathematically rigorous approach to expressing P because the set of all determinants that can be formed from a complete set of spin-orbitals can be shown to be complete. In practice, one is limited to the number of orbitals that can be used and in the number of CSFs that can be included in the Cl expansion. Nevertheless, the Cl expansion method forms the basis of the most commonly used techniques in quantum chemistry. 

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