Towards Low-Scaling Perturbative Energy Corrections for Efficient MPCC Simulations

In an effort to efficiently model large electronic systems, Shee \emph{et al.} recently introduced a QM-in-QM embedding framework known as Møller–Plesset Coupled Cluster (MPCC), in which a chemically relevant region (fragment) is treated with a high-level coupled-cluster theory, while the rest of the system (environment) is approximated using a lower-level perturbative approach.

Subsequent developments of MPCC employ CC2 for the environmental treatment, whose computational cost scales as $O(N^5)$ and $O(N^3)$ in memory, limiting the applicability of MPCC to large systems.

 

Motivated by prior work demonstrating that tensor factorizations can reduce the computational cost of correlated electronic-structure methods, we study the effect of approximating three-center electron repulsion integrals (ERIs) using the Canonical Polyadic Decomposition (CPD) format combined with a density-fitting ansatz. In this study, we demonstrate the ability of CPD to preserve the accuracy of energies and intermediate tensor quantities within the CC2 method.

 

Furthermore, we show that the resulting CP-CC2 approximation has a limited impact on the MPCC optimization procedure. Taken together, these findings establish a clear pathway toward the development of a fully reduced-scaling CP-CC2 MPCC embedding algorithm.