Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Direct variational optimization of the two-electron reduced density matrix (2RDM) offers a reference-independent electronic structure description.
• This method naturally captures strong or nondynamic electron correlation effects.
• Satisfying N-representability conditions, like T2, is crucial for accuracy.

Purpose of the Study:

• To investigate the limitations of variational 2RDM methods with N-representability conditions for strongly correlated systems.
• To assess the performance of full three-particle N-representability conditions (3POS) in hydrogen clusters.
• To identify reliable metrics for predicting the accuracy of 3POS calculations.

Main Methods:

• Applied full three-particle N-representability conditions (3POS) to variational 2RDM calculations.
• Performed benchmark calculations on two- and three-dimensional hydrogen clusters.
• Explored various correlation metrics, including the relative squared magnitudes of cumulant two- and three-particle RDMs.

Main Results:

• Failures observed in previous T2 calculations persist even with 3POS conditions for hydrogen clusters.
• The relative squared magnitudes of cumulant RDMs correlate with energy error in hydrogen clusters.
• This correlation metric is not universally applicable across different molecular systems.

Conclusions:

• Variational 2RDM theory with 3POS conditions faces challenges in accurately describing strong correlation in certain systems, like hydrogen clusters.
• A proposed correlation metric can indicate reliability in some cases but lacks universal predictive power.
• Further development is needed to ensure the robustness of reduced-density-matrix theory for diverse electronic structure problems.