The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function

Is Externally Corrected Coupled Cluster Always Better Than the Underlying Truncated Configuration Interaction?

The short answer to the question in the title is "no". We identify classes of truncated configuration interaction (CI) wave functions for which the externally corrected coupled-cluster (ec-CC) approach using the three-body (T₃) and four-body (T₄) components of the cluster operator extracted from CI does not improve the results of the underlying CI calculations. Implications of our analysis, illustrated by numerical examples, for the ec-CC computations using truncated and selected CI methods are discussed. We also introduce a novel ec-CC approach using the T₃ and T₄ amplitudes obtained with the selected CI scheme abbreviated as CIPSI, correcting the resulting energies for the missing T₃ correlations not captured by CIPSI with the help of moment expansions similar to those employed in the completely renormalized CC methods.

Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD(T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources

We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We use the density matrix renormalization group (DMRG) and heat-bath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H₂O, N₂, and F₂. We find that the triples correction significantly improves upon ecCCSD, and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes against the accuracy of the subsequent CC calculation. In this context, we find that very approximate wave functions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the ecCCSD and renormalized triples combination studied in this work via a well-known wave function diagnostic.

Coupled Cluster Externally Corrected by Adaptive Configuration Interaction

An externally corrected coupled cluster (CC) method, where an adaptive configuration interaction (ACI) wave function provides the external cluster amplitudes, named ACI-CC, is presented. By exploiting the connection between configuration interaction and CC through cluster analysis, the higher-order T₃ and T₄ terms obtained from ACI are used to augment the T₁ and T₂ amplitude equations from traditional CC. These higher-order contributions are kept frozen during the CC iterations and do not contribute to an increased cost with respect to coupled cluster including the single and double excitations (CCSD). We have benchmarked this method on three closed-shell systems: beryllium dimer, carbonyl oxide, and cyclobutadiene, with good results compared to other corrected CC methods. In all cases, the inclusion of these external corrections improved upon the "gold standard" CCSD(T) results, indicating that ACI-CCSD(T) can be used to assess strong correlation effects in a system and as an inexpensive starting point for more complex external corrections.

Symmetric dissociation of the water molecule with truncation energy error. A benchmark study

We use selected configuration interaction with truncation energy error (SCI-TEE) and CI by parts (CIBP) to study the symmetric dissociation of the water molecule with Roos' triple-ζ double polarization basis set and with the Dunning cc-pVTZ basis. The calculations comprise CISDTQ (CI-4x) through CI-8x for H2O at its equilibrium geometry (Req) and up to fifteen times Req. With the Dunning basis our SCI-TEE-8x energies differ from full CI by less than 0.01 mHartree (0.006 kcal mol-1) at all O-H distances, representing the best upper bounds for this system outside Req. We compare our results with those of other relevant ab initio methods finding good agreement with recent DMRG calculations. The non-parallelity error (NPE) for SCI-TEE-6x remains stable below 0.1 mHartree when moving from the Roos to the Dunning orbitals. For the present system, CBS energy errors at the experimental equilibrium geometry and at dissociation can accurately be evaluated as the difference between non-relativistic total electronic energies taken from the literature, and our SCI-TEE-8x energies obtained with Dunning's or Roos' orbitals. In both cases, the difference between CBS energy errors at the equilibrium geometry and dissociation is not smaller than 10 mH, showing that chemically accurate NPE values do not guarantee a chemically accurate potential energy surface.