Orbital-aware approximations to high-order RDM calculations.

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Higher-order reduced density matrices (RDMs) are crucial for describing electron correlation.
• Analyzing RDMs requires efficient computational methods, especially for strongly correlated systems.

Purpose of the Study:

• To introduce a quantitative measure, the orbital overlap degree (OOD), for analyzing RDMs.
• To develop an orbital-aware (OA) approximation for calculating higher-order RDMs.
• To integrate the OA approximation into existing computational frameworks like DMRG-NEVPT2.

Main Methods:

• Introduction of the orbital overlap degree (OOD) as a descriptor for RDM elements.
• Development of an orbital-aware (OA) approximation (oa4-RDMs) for selective approximation of fourth-order RDM elements.
• Integration of oa4-RDMs with RDM-based multi-reference methods (e.g., DMRG-oa4-NEVPT2).

Main Results:

• A strong correlation was found between OOD and the magnitude of RDM elements in strongly correlated systems.
• The OA approximation significantly reduces computational cost while retaining dominant contributions.
• Demonstrated general applicability of OOD across different orbital representations using trans-polyacetylene oligomers.

Conclusions:

• The OOD is a valuable descriptor for understanding RDM structure and electron correlation.
• The OA approximation offers a computationally efficient approach for higher-order RDMs in strongly correlated systems.
• The developed methods enhance the accuracy and feasibility of electronic structure calculations.