Direct Variational Determination Of The Two-Particle Reduced Density Matrix Constrained To Wave Functions Of Seniority-Zero Class

G.E. MASSACCESI; E.M. HONORE; D.R. ALCOBA; M. VAN RAEMDONCK; A. TORRE; D. VAN NECK; W. POELMANS; P. BULTINCK; L. LAIN; O.B. OÑA; S. DE BAERDEMACKER

Buenos Aires

Conferencia; Molecular Electronic Structure Buenos Aires Conference (MESBA 2016); 2016

Consejo Nacional de Investigaciones Cientificas y Técnicas

One of the most popular methods to approximate the two-electron reduced density matrix (2-RDM) corresponding to an N electron system is the variational approach. Within this technique the 2-RDM matrix elements are subjected to some constraints so that they fulfill the well-known N representability conditions of that matrix.  Recently, we have reported [1] the influence of the P, Q, and G two-index conditions in order to calculate approximated 2-RDM arising from seniority-zero wave functions [2]. The resulting optimization problem has been formulated as a standard semidefinite program (SDP). The aim of this work is to go beyond extending the constraint conditions to T1 and T2 three-index ones [3-5]. Projection of the reduced Hamiltonian onto the seniority-zero space allows to implement the SDP using existing algorithms and to exploit sparse matrix data structures. We report calculations of the ground state potential energy surfaces in selected molecular systems, in each case using a minimal basis set. The results obtained from our proposal are compared with those arising from full seniority-zero class calculations. We show that the use of the three-index conditions provides a significant improvement upon just using the two-index ones. The computational costs required turn out to be affordable.References[1] W. Poelmans, M. Van Raemdonck, B. Verstichel, S. De Baerdemacker, A. Torre, L. Lain, G.E. Massaccesi, D.R. Alcoba, P. Bultinck, D. Van Neck, J. Chem. Theory Comput. 11, 4064 (2015).[2] F. Weinhold, E.B. Wilson Jr., J. Chem. Phys. 47, 2298 (1967).[3] R.M. Erdahl, Int. J. Quantum Chem. 13, 697 (1978).[4] Z. Zhao, B.J. Braams, M. Fukuda, M.L. Overton, J.K. Percus, J. Chem. Phys. 120, 2095 (2004).[5] D.A. Mazziotti, Phys. Rev. A 72, 032510  (2005).