International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Steeplechase for 2-RDM approximationsMauricio Antonio Rodríguez Mayorga
Universitat de Girona, Spain
Coauthor(s) : E. Ramos-Cordoba, M. Via-Nadal, M. Piris, E. Matito
In this work, we will present some tests that we have performed to analize the goodness of second-order reduced density matrices approximations (2-RDM) when the effects of correlation become important. The approximations studied are used to construct functionals in natural orbital functional theory [1-3]. The battery of tests presented here include: the delocalization index, the calculation of the 2-RDM trace, the termwise error for diagonal elements and for the whole matrix, the fulfillment of some N-Representability [2,4] 4conditions, the attainment of symmetry properties and magnitudes related to the intracule density. Unlike common tests that are based on the reproduction of the electronic energy, this battery of tests offer a wide variety of assessments that permit to check relevant features of the 2-RDM that are normally not put into test. To tune the correlation effects and dispose of a wide range of correlation regimes, we have chosen the Harmonium atom (HA) model  as our reference system. In HA, the effects of correlation are driven by one single parameter called the confinement strength. This model systems provides a realistic description of electron correlation effects and renders itself to analytic solutions for some values of the confinement strength. Harmonium has been used to calibrate DFT functionals  and third-order reduced density matrices .
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