Single/double excitation configurational size consistency

The method of single- and double-excitation configuration mixing is not size-consistent. The method remains size-inconsistent even if a multi-configurational reference function is used. For a configuration mixing calculation, with... 

R. J. Bartlett and I. Shavitt, Determination of the Size-Consistency Error in the Single and Double Excitation Configuration Interaction Model, Int. 

In their study of the lowest part of the Ceo Hubbard spectrum, FKS carried out single and double excited configuration interaction (SDCI) calculations. These were based on an appropriate set of reference configuration state functions constructed by means of a set of restricted Hartree-Fock (RHF) orbitals. Although, as FHS point out, a SDCI treatment is not size consistent, one can anticipate obtaining significant information with regard... 

The full configuration interaction method [34-36] is exact in the sense that after choosing appropriate atomic basis functions (defining the model in this way), the resulting many-electron wavefunction is an exact eigenfunction of the model Hamiltonian, the computational effort, nevertheless, increases in an exponential manner. Truncation of the full Cl expansion (especially after single and double excitations, CI-SD) considerably reduces the necessary computational resources, but leads unfortunately to the serious problem of nonsize-consistency [37, 38] which makes the results even for medium systems unrealistic. The coupled-cluster method [39, 40] theoretically properly describes extended systems as well, but numerous experiences show the enormous increase of computational work with the size of the system. 

I>aOb, but the number of configurations rapidly becomes very large. Thus if <1>A and Hartree-Fock function plus double excitations, then d>A J B includes double and quadruple excitations relative to the ground-state AB. In order to maintain a consistent description, the pseudostates, Oa for example, must consist of a set of singly excited functions plus further double replacements, i.e. one- and three-fold excitations relative to the Hartree-Fock ground state of A. Structures a b for the dimer consequently include two-, four- and six-fold excitations. In essence, one requires that the AB wavefunctions fulfil the condition of size consistency. 

The coupled cluster method is the Cl method based on this wavefunction. One of the noain advantages of this method is to ensure size consistency (see Sect. 3.3) in the selection of electron configurations. In coupled cluster methods, the coupled-cluster singles and doubles (CCSD) method terminates f up to the double excitation... 

PeyerimhofT, S. D. and Buenker, R. J., Cl Calculations of vertical excitation energies and oscillator strengths for Rydberg and valence states of molecules, in Excited States in Chemistry C. A. Nikolaides and D. R. Beck (Eds.), Reidel, Dordrecht, 1978, p. 79. A survey of calculations of the electronic spectra of molecules using multireference doubleexcitation Cl (MRD-CI). MRD-CI includes single and double excitations relative not only to the Hartree-Fock wave function (Yq) but also relative to other important configurations (which may themselves be doubly excited with respect to Tq). Thus MRD-CI effectively includes higher than double (e.g., quadruple) excitations from Yg and hence can be essentially size consistent for moderate sized molecules. Other articles found in this book are also recommended. 

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