Orbital-aware approximations to high-order RDM calculations

In this work, we analyze the structure of higher-order reduced density matrices (RDMs) from the perspective of correlated electron transition processes. We introduce the orbital overlap degree (OOD) as a quantitative measure of the overlap between creation and annihilation orbital indices in individual RDM elements. Systematic analysis of representative strongly correlated systems reveals a strong correlation between the OOD and the magnitude of RDM elements. Motivated by this observation, we develop an orbital-aware (OA) approximation for calculating higher-order RDMs, i.e., oa4-RDMs, that selectively approximates the evaluation of fourth order RDM elements. The oa4-RDMs can be integrated with RDM-based multi-reference approaches, e.g., the density-matrix renormalized group n-electron valence second-order perturbation theory with oa4-RDMs (DMRG-oa4-NEVPT2). Numerical results for Cr2 and 1,2-dioxetanone show that the OA approximation significantly reduces computational cost while preserving the dominant contributions in strongly correlated calculations, and orbital-type analysis of trans-polyacetylene oligomers demonstrates the general applicability of OOD as a descriptor across different orbital representations.