Coupled cluster method active space

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

Kowalski K, Piecuch P (2000) The active-space equation-of-motion coupled-cluster methods for excited states The EOMCCSDt approach. J Chem Phys 113 8490-8502. 

In the Fock space coupled cluster method, the Hartree-Fock solution for an iV-electron state, 0), is used as the vacuum. The Fock space is divided into sectors, (m,n), according to how many electrons are added to and removed from 0). Thus, the vacuum is in the (0,0) sector, single ionizations are in the (0,1) sector, one-electron attached states are in (1,0), and (1,1) are single excitations relative to 0). The orbitals are also divided into active, which can change occupation, and inactive, for which the occupation is fixed. All possible occupations of the active orbitals in all possible sectors constitute the multireference space for the system. 

Abstract The block correlated coupled cluster method, with the complete active-space self-consistent-field reference function (CAS-BCCC), has been applied to investigate the bond-breaking potential energy surfaces (PESs) for a C—C bond in two alkanes (ethane and 2,3-dimethyl-butane) and a C=C bond in two alkenes (ethylene and 2,3-dimethyl-2-butene). The results are compared with those from other multireference methods (CASPT2, MR-CISD, and MR-CISD+Q). It is demonstrated that the CAS-BCCC method can provide more accurate PESs for C—C bond-breaking PESs than CASPT2 and MR-CISD. The overall performance of CAS-BCCC is shown to be comparable to that of MR-CISD-pQ for systems under study. 

L. K. Sorensen, T. Fleig, J. Olsen. A Relativistic Four- and Two-component Generalized-active-space Coupled Cluster Method. Z. Phys. Chem., 224 (2010) 671-680. 

L. K. Sorensen, J. Olsen, T. Fleig. Two- and four-component relativistic generalized-active-space coupled cluster method Implementation and application to BiH. /. Chem. Phys., 134 (2011) 214102. 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

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