Externally corrected CCSD

Comparing (SCfCAS-SDCI and Externally Corrected CCSD Methods... 

A different way to approximate SS-MRCC is the so-called externally corrected CCSD (ec-CCSD) [13-17], The ec-CCSD method is based on the Coupled Cluster Approach (CCA). In CCA the exact wavefunction is written in an exponential form,... 

Comparing (SC) CAS-SDCI and externally corrected CCSD methods... 

Our recently developed reduced multireference (RMR) CCSD method [16, 21, 22, 23, 24, 25] represents such a combined approach. In essence, this is a version of the so-called externally corrected CCSD method [26, 27, 28, 29, 30, 31, 32, 33, 34] that uses a low dimensional MR CISD as an external source. Thus, rather than neglecting higher-than-pair cluster amplitudes, as is done in standard CCSD, it uses approximate values for triply and quadruply excited cluster amplitudes that are extracted by the cluster analysis from the MR CISD wave function. The latter is based on a small active space, yet large enough to allow proper dissociation, and thus a proper account of dynamic correlation. It is the objective of this paper to review this approach in more detail and to illustrate its performance on a few examples. 

We first outline the basic idea and origins of the externally corrected CCSD methods in Sect. 2, followed by the formulation and discussion of its special version, the RMR CCSD method, in Sect. 3. In Sect. 4 we present a few illustrative examples and summarize the general conclusions in Sect. 5. 

The basic idea of the externally corrected CCSD methods relies on the fact that the electronic Hamiltonian, defining standard ah initio models, involves at most two body terms, so that the correlation energy is fully determined by one (Ti) and two (T2) body cluster amplitudes, while the subset of CC equations determining these amplitudes involves at most three (T3) and four (T4) body connected clusters. In order to decouple this subset of singly and doubly projected CC equations from the rest of the CC chain, one simply neglects all higher than pair cluster amplitudes by setting... 

As already pointed out in Ref. 13, the externally corrected CCSD is equivalent to (truncated) CCSDTQ with zero-iteration on and T4 amplitudes that are in turn obtained from some external sources. Depending on the source of these amplitudes, we usually deal with only a proper subset of all possible T3 and T4 amplitudes. This subset is fixed in the externally corrected CCSD calculations. The RMR CCSD is then a special case of the general externally corrected CCSD in which the MR CISD wave function is used as the external source. The RMR CCSD method represents in fact a multireference approach in the sense that it is uniquely defined by the choice of the reference space and the fact that the RMR CCSD wave function involves the same number of connected cluster amplitudes as the corresponding genuine MR CCSD, such as the state-universal CCSD employing the same reference space. 

---