Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Strongly correlated electrons present computational challenges due to exponential scaling.
• Reduced-density matrix (RDM) methods offer a way to mitigate these costs.
• Variational two-electron RDM (v2RDM) methods are limited by incomplete N-representability constraints.

Purpose of the Study:

• To develop a machine learning (ML) protocol to improve energy calculations from v2RDM methods.
• To leverage physics-based features derived from N-representability conditions for enhanced accuracy.

Main Methods:

• Utilized violations of partial three-particle N-representability conditions (T1 and T2) as ML features.
• Evaluated these features using only the two-electron reduced density matrix (2RDM).
• Developed an ML protocol to improve energies from v2RDM calculations that enforce only two-particle (PQG) conditions.

Main Results:

• Demonstrated that three-particle N-representability violations can be effectively used as physics-based ML features.
• The ML protocol significantly improved the accuracy of v2RDM energy calculations.
• Achieved substantially improved energies compared to reference values from configuration-interaction calculations.

Conclusions:

• Machine learning, guided by N-representability principles, can overcome limitations in v2RDM methods.
• This approach offers a promising pathway for accurate electronic structure calculations of complex systems.
• The method provides a significant enhancement in energy prediction for strongly correlated electrons.