Random phase approximation-based local natural orbital coupled cluster theory

Practical applications of fragment embedding and closely related local correlation methods depend critically on a judicious choice of low-level theory to define the local embedding subspace and to account for long-range electrostatic and correlation effects outside the embedding region. Second-order Møller-Plesset perturbation theory (MP2) is by far the most widely used correlated low-level theory; however, its applicability becomes questionable for systems in which MP2 is known to fail, either quantitatively or qualitatively. In this work, we present the random phase approximation (RPA) and the closely related second-order screened exchange (SOSEX) as promising alternatives to MP2 within the local natural orbital-based coupled-cluster (LNO-CC) framework. Through benchmark calculations on noncovalent molecular complexes and crystals, reaction barrier heights, and bulk metals, we demonstrate that RPA- and SOSEX-based LNO-CC at the LNO-coupled-cluster singles doubles triples CCSD(T) level closely match the performance of the corresponding MP2-based approach, while at the LNO-CCSD level they yield significantly faster convergence toward the canonical CCSD limit. The improvement is particularly pronounced for metallic systems as the thermodynamic limit is approached. These results highlight the critical role of the low-level theory in fragment embedding and local correlation methods and identify RPA as a compelling alternative to the commonly used MP2.