Explain nonconvergence of cCCSD equations for larger molecules

Determine why the cluster coupled-cluster singles-and-doubles equations fail to converge for the larger linear polyenes and establish conditions or modifications that restore convergence.

Background

The authors report that they were unable to converge the cCCSD equations for larger molecules, including the larger linear polyenes. Although the iterations oscillated around energetically reasonable values, the source of the nonconvergence was not identified.

This remains an unresolved methodological issue because cCCSD converged for the smaller molecular systems and for the Hubbard model with relaxed orbitals. Understanding the cause is necessary to assess the robustness of the cluster coupled-cluster approach for large strongly correlated systems.

References

It is unclear whether this convergence issue would persist with a more robust implementation, and we intend to explore this in the future with a production-level SCC code.

— Selected Coupled Cluster Guided by Selected Configuration Interaction  (2609.10829 - Cho et al., 9 Sep 2026) in Section 4.3, “Stretched Circumcoronene”

We were unable to converge the cCCSD equations for the larger molecules, in the case of the linear polyenes, the energy of the iterations were oscillating around reasonable values. For example, the C${12}$H${14}$ correlation energies were around -0.2133 Ha and the C${16}$H${18}$ energies were around -0.2863 Ha, both are just below the 2cCASCI which is consistent with the smaller polyenes. We are not sure why the cCCSD equations are not converging and will leave it to future investigations.

— Examination of Cluster Based Methods to Fermionic Systems  (2609.08773 - Keyes et al., 8 Sep 2026) in Section 5, Results and Discussion, paragraph discussing Table 3