Convergence dynamic correlations

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. 

In addition to MP2, MP3, and MP4 calculations, CCSD(T), CASSCF, FOCI (First-Order Configuration Interaction), and sometimes SOCI (Second-Order Configuration Interaction) approaches have been used to ensure the convergence of the results. The complete definitions of the variational spaces used are given in [61,62,63]. Electronically-excited states have been obtained by means of the MC/P method, recently developed in our group [64,65] it couples a variational treatment to deal with the nondynamic correlation effects and a perturbation treatment to account for the dynamic correlation effects as well as the non-dynamic effects not treated at the variational level becanse of their limited contributions to the phenomena investigated. All electronic transitions reported here are vertical transition energies. 

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