Configuration interaction size extensivity

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

In this work we are concerned with the dressing method known as Size-Consistent Self-consistent Singles and Doubles Configuration Interaction, usually abbrebiated to (SC) SDCI [8]. This method can be considered as a generalization of the CEPA-3 formalism, as has been shown elsewhere [8,35]. It provides size-extensive roots and... 

Simons, J., Size extensivity correction for complete active space multiconfiguration self-consistent-field configuration interaction energies, J. Phys. Chem. 93, 626-627 (1989). 

Presently, the widely used post-Hartree-Fock approaches to the correlation problem in molecular electronic structure calculations are basically of two kinds, namely, those of variational and those of perturbative nature. The former are typified by various configuration interaction (Cl) or shell-model methods, and employ the linear Ansatz for the wave function in the spirit of Ritz variation principle (c/, e.g. Ref. [21]). However, since the dimension of the Cl problem rapidly increases with increasing size of the system and size of the atomic orbital (AO) basis set employed (see, e.g. the so-called Paldus-Weyl dimension formula [22,23]), one has to rely in actual applications on truncated Cl expansions (referred to as a limited Cl), despite the fact that these expansions are slowly convergent, even when based on the optimal natural orbitals (NOs). Unfortunately, such limited Cl expansions (usually truncated at the doubly excited level relative to the IPM reference, resulting in the CISD method) are unable to properly describe the so-called dynamic correlation, which requires that higher than doubly excited configurations be taken into account. Moreover, the energies obtained with the limited Cl method are not size-extensive. 

Another important development was the reahzation of the importance of the size-consistency and size-extensivity in the studies of associative or dissociative chemical processes by Primas [67], as well as his clear delineation of the relationship between the configuration interaction and the exponential coupled-cluster Ansatze. 

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