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International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'

September 26, 2017 to September 29, 2017
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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Steeplechase for 2-RDM approximations

Mauricio Antonio Rodríguez Mayorga


Coauthor(s) : E. Ramos-Cordoba, M. Via-Nadal, M. Piris, E. Matito


Abstract

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 [5] 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 [6] and third-order reduced density matrices [7].



References

[1] J. Cioslowski, M. Piris and E. Matito, J. Chem Phys. 143 214101 (2015),
[2] M. Piris, Int. J. Quant. Chem. 113 620 (2013).
[3] M. Piris, J. Chem Phys. 141 0044107 (2014).
[4] J. M. Herbert and J. E. Harriman, J. Chem. Phys. 118 10835 (2003).
[5] N. R. Kestner and O. Sinanoglu, Phys. Rev. 128 2687 (1962).
[6] J. Cioslowski and E. Matito, J. Chem. Theory Comput. 7 915 (2011).
[7] M. Rodríguez-Mayorga, E. Ramos-Cordoba, F. Feixas and E. Matito. Phys. Chem. Chem. Phys. 19 4522 (2017).