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. RodriÌ guez-Mayorga, E. Ramos-Cordoba, F. Feixas and E. Matito, Phys. Chem. Chem. Phys., 2017, 19, 4522.
