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