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

Run R Li1, Marcus D Liebenthal1, A Eugene DePrince1

  • 1Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA.

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|November 7, 2021
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Summary
This summary is machine-generated.

Variational optimization of the two-electron reduced density matrix (2RDM) struggles with strong electron correlation in hydrogen clusters, even with full three-particle N-representability conditions (3POS). A correlation metric shows promise but isn't universally reliable.

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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.