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,... 

We compare the performance of a variational CAS-SDCI with its size-extensive version (SC) CAS-SDCI and the standard size-extensive CCSD. Additionally, we correct CCSD using the non size-extensive T and T amplitudes yielded by a cluster analysis of the CAS-SDCI wavefunction and also using the size-extensive and T amplitudes coming from (SC) CAS-SDCI. 

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

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

Another way to exploit the complementarity of Cl and CC approaches was explored earlier by Meissner et al. [10]. Instead of using Cl as a source of higher-than-pair clusters and correcting CCSD, it exploits the CC theory to correct the MR CISD results. In the spirit of an earlier work on Davidson-type corrections for SR CISD [10], Meissner et al. formulated a CCSD-based corrections for both SR [72] and MR [74] CISD. The latter was later extended to higher lying excited states [73]. 

Let us, finally, reiterate that, similarly as the MR CISD method can serve as an external source for correcting CCSD approaches, we can conversely use CCSD to formulate Davidson-type corrections for MR CISD, both for the lowest-lying [72,74] and the higher-lying states [73]. 

Perhaps the most severe test of the proposed scheme was encountered in our study of the radicaloid mode of benzene dissociation or, equivalently, a recombination of two allylic radicals [67]. Since the separated limit involves open shell subsystems, standatrd CCSD approaches an incorrect channel. However, when VB corrected CCSD is used, we obtain practically the FCI result. 

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 CAS FCI or SOCI corrected CCSD results represent a definite improvement over the standard SR CCSD results. Nonetheless, for a given choice of the active-space, the performance of the ASTQ CCSD approaches deteriorates with the increasing size of the basis set. This is easily understood, since the external source does not include excitations out of the active-space, which are more important for larger basis sets. We should also mention that computationally much more demanding CAS SCF wave functions are about as effective as CAS FCI ones (cf., e.g., Tables II and III of [33]). 

ZPV corrected CCSD(T) basis set limit including estimates for correlation beyond CCSD(T) and relativistic effects. 

ZPV corrected CCSD/d-aug-cc-pVQZ result including relativistic and pure vibrational corrections. 

---