Unphysical solutions in coupled-cluster-based random phase approximation and how to avoid them

The direct ring coupled-cluster doubles (drCCD)-based random phase approximation (RPA) has provided an attractive framework for the development and application of RPA-related methods. However, a potential unphysical solution issue recently reported by Rekkedal et al., J. Chem. Phys. 139, 081101, (2013) has raised significant concerns regarding the general applicability of coupled-cluster-based RPA, particularly in small-gap systems where RPA is anticipated to outperform commonly employed second-order perturbation theory. In this work, we elucidate the underlying origin of the multi-solution issue in drCCD and develop both a practical criterion for validating drCCD solutions and improved preconditioners based on level shifting and regularized MP2 methods for stabilizing the iterative solution of the drCCD equation. We demonstrate the robustness and effectiveness of our approach through representative systems-including molecules with stretched bonds, large conjugated systems, and metallic clusters-where standard drCCD iteration encounters convergence difficulties. Furthermore, we extend our approach to various recently developed reduced-scaling drCCD-based RPA methods, thereby establishing a foundation for their stable application to large-scale problems. The extension of our approach to RPA with exchange, quasiparticle RPA, and particle-particle RPA is also discussed.