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Two new constraints for the cumulant matrix.

Eloy Ramos-Cordoba1, Pedro Salvador1, Mario Piris2

  • 1Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia, Spain.

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New constraints for two-particle cumulant matrices are proposed. These inexpensive conditions help assess and improve electron correlation methods like Piris natural orbital functionals (PNOF) without computational cost.

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Area of Science:

  • Quantum chemistry
  • Computational physics

Background:

  • Two-particle cumulant matrices are crucial for describing electron correlation.
  • Existing methods like Piris natural orbital functionals (PNOF) offer high accuracy but may have limitations.

Purpose of the Study:

  • To introduce novel, computationally inexpensive constraints for two-particle cumulant matrices.
  • To evaluate the consistency of these constraints with existing electron correlation methods, specifically PNOF.

Main Methods:

  • Derivation of constraints from the decomposition of the spin square operator, ⟨Ŝ(2)⟩.
  • Application and testing of these constraints on a series of PNOF functionals.
  • Analysis of local spin components to identify shortcomings in current cumulant expressions.

Main Results:

  • The proposed constraints are stringent and computationally inexpensive.
  • All tested PNOF cumulants satisfy the overall ⟨Ŝ(2)⟩ condition.
  • No PNOF cumulant fully captures the local spin structure for systems dissociating multiple electron pairs.

Conclusions:

  • The new constraints offer a valuable, low-cost tool for developing and validating cumulant structures.
  • Analysis of local spin components highlights areas for improving PNOF, particularly PNOF5.
  • These conditions complement existing N-representability and ⟨Ŝ(2)⟩ criteria.