Implications of the unitary invariance and symmetry restrictions on the development of proper approximate one-body reduced density matrix functionals

Abstract

In many of the approximate functionals in one-body reduced density matrix (1RDM) functional theory, the approximate two-body reduced density matrix (2RDM) in the natural orbital representation only depends on the natural occupation numbers. In Phys. Rev. A 92, 012520 (2015) Wang and Knowles initialised a discussion of to what extent this simplification is valid, by introducing two different H${}_4$ geometries with identical natural occupation numbers, but different 2RDMs. Gritsenko has argued that this feature is due symmetry [Phys. Rev. A 97, 026501 (2018)]. This work aims to contribute to the discussion on the following points: 1) one should rather speak of symmetry-restricted variants of the universal functional, than saying that the universal functional is symmetry dependent; 2) the unitary invariance of degenerate NOs can lead to large deviations in the 2RDM elements, especially the phase of the NOs; 3) symmetry-restricted functionals are constructed for the H${}_4$ geometries considered by Wang and Knowles, whose structure could serve as guide in the construction of approximate 1RDM functionals.

arXiv comment15 pages, 3 figures, 3 tables

References in corpus (10)

• Quantum marginal problem and N-representability
• The Pauli principle revisited
• Global Method for Electron Correlation
• Relating the pure and ensemble density matrix functional
• Diverging exchange force and form of the exact density matrix functional
• Natural orbital functional for multiplets
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• Long-range interactions and the sign of natural amplitudes in two-electron systems
• Equations of motion for natural orbitals of strongly driven two-electron systems
• Response calculations based on an independent particle system with the exact one-particle density matrix: polarizabilities

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• Electron correlation in the Iron(II) Porphyrin by NOF approximations
• Outstanding Improvement in Removing the Delocalization Error by Global Natural Orbital Functional