Diagrammatic Simplification of Linearized Coupled Cluster Theory

Linearized Coupled Cluster Doubles (LinCCD) often provides near-singular energies in small-gap systems that exhibit static correlation. This has been attributed to the lack of quadratic $T_2^2$ terms that typically balance out small energy denominators in the CCD amplitude equations. Herein, I show that exchange contributions to ring and crossed-ring contractions (not small denominators per se) cause the divergent behavior of LinCC(S)D approaches. Rather than omitting exchange terms, I recommend a regular and size-consistent method that retains only linear ladder diagrams. As LinCCD and configuration interaction doubles (CID) equations are isomorphic, this also implies that simplification (rather than quadratic extensions) of CID amplitude equations can lead to a size-consistent theory. Linearized ladder CCD (LinLCCD) is robust in statically-correlated systems and can be made $O(n_{\text{occ}}^4n_{\text{vir}}^2)$ with a hole-hole approximation. The results presented here show that LinLCCD and its hole-hole approximation can accurately capture energy differences, even outperforming full CCD and CCSD for non-covalent interactions in small-to-medium sized molecules, setting the stage for further adaptations of these approaches that incorporate more dynamical correlation.