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Separation of dynamic and nondynamic correlation.

Eloy Ramos-Cordoba1, Pedro Salvador2, Eduard Matito3

  • 1Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC)., P.K. 1072, 20080 Donostia, Euskadi, Spain. eloy.raco@gmail.com ematito@gmail.com and Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA.

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Summary

This study introduces a new matrix method to separate electron correlation into dynamic and nondynamic components. This approach utilizes natural orbital occupancies for a simplified electron correlation index.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Electron correlation is crucial for accurate computational chemistry methods.
  • Separating dynamic and nondynamic correlation is essential for method development.
  • Existing methods for correlation separation can be complex.

Purpose of the Study:

  • To develop a physically sound matrix formulation for splitting electron correlation.
  • To introduce a simplified electron correlation index based on natural orbitals.
  • To achieve the first separation of dynamic and nondynamic correlation using only natural orbital occupancies.

Main Methods:

  • Utilizing the two-particle cumulant matrix.
  • Employing a measure of deviation from idempotency of the first-order density matrix.
  • Applying these matrices to a two-electron model.

Main Results:

  • A simplified electron correlation index was derived.
  • The index depends solely on natural orbitals and their occupancies.
  • The index successfully decomposes into dynamic and nondynamic correlation parts.
  • A local version of the index was developed.
  • The method accurately accounts for correlation in diverse systems.

Conclusions:

  • The proposed matrix formulation provides a robust method for separating dynamic and nondynamic electron correlation.
  • The derived electron correlation index offers a simplified and versatile tool for computational chemistry.
  • This work presents the first method to distinguish dynamic and nondynamic correlation using only natural orbital occupancies.