Correlation energy doubly excited configurations

Specifically, tetra-excited states are responsible for the cancellation of the incorrect N2 behaviour of the CI-SD, as well as, for the further reduction of the correlation energy. Due to truncation of the MB-RSPT at the third order the effect of doubly excited configurations are not included fully and, of course, the higher excited configurations are omitted completely. 

Table 5. Valence shell correlation energy in H2O1) given by MB-RSPT treatment116) and the INO-CI calculations96) including all singly and doubly excited configurations (Cl-SD)...

As we already know from the foregoing sections, the dominant part of the correlation energy is due to doubly excited configurations. It is therefore natural that attempts were made to develop such a procedure, which would pick up the contributions of doubles from the higher... 

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. 

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