Implications of the unitary invariance and symmetry restrictions on the development of proper approximate onebody reduceddensitymatrix functionals
Abstract
In many of the approximate functionals in onebody reduceddensitymatrix (1RDM) functional theory, the approximate twobody reduced density matrix (2RDM) in the natural orbital representation only depends on the natural occupation numbers. In Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520, Wang and Knowles initialized 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), 10.1103/PhysRevA.97.026501]. This work aims to contribute to the discussion on the following points: (1) one should rather speak of symmetryrestricted 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) symmetryrestricted 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.
 Publication:

Physical Review A
 Pub Date:
 November 2020
 DOI:
 10.1103/PhysRevA.102.052814
 arXiv:
 arXiv:1909.04927
 Bibcode:
 2020PhRvA.102e2814G
 Keywords:

 Physics  Chemical Physics;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 15 pages, 3 figures, 3 tables