Recent advances in the theory of the contracted Schrödinger and Liouville-Von neumann equations

C. VALDEMORO; D.R. ALCOBA; L.M. TEL; O.B. OÑA; G.E. MASSACCESI; J.M. OLIVA

El Escorial

Workshop; Convergent Distributed Environment for Computational Spectroscopy (CODECS) 2013 workshop (COST action); 2013

Consejo Superior de Investigciones Cientificas

One of the most recent advances in the theory of the contracted Schrödinger and Liouville-von Neumann equations [1], in which only the anti-Hermitian part of the second-order correlation contracted Schrödinger equation - or the G-particle-hole hypervirial equation (GHV) [2, 3] - is solved, and its joint use with Equations-of-Motion techniques, permit the direct determination of two-electron reduced density and correlation matrices that yield ground- and excited-state energies of atoms and molecules with an accuracy between 0.0003% and 0.2% of their absolute values [2-10]. Here, we give an overview of this method, discuss recent theoretical and computational advances, and present some illustrative applications. References [1] C. Valdemoro, in Density Matrices and Density Functionals, Proceedings of the A.J. Coleman Symposium, Kingston, Ontario, 1985, R. Erdahl and V. Smith (eds.), Reidel, Dordrecht (1987), p. 275. [2] D.R. Alcoba, C. Valdemoro, L. M. Tel, E. Perez-Romero, Int J. Quantum Chem. 109, 3178 (2009). [3] C. Valdemoro, D.R. Alcoba, L. M. Tel, E. Pérez-Romero, Int J. Quantum Chem. 109, 2622 (2009); ibid. 111, 245 (2011). [4] D.R. Alcoba, L. M. Tel, E. Pérez-Romero, C. Valdemoro, Int J. Quantum Chem. 111, 937 (2011). [5] D.R. Alcoba, C. Valdemoro, L. M. Tel, E. Pérez-Romero, O.B. Oña, J. Phys. Chem. A 115, 2599 (2011). [6] C. Valdemoro, D.R. Alcoba, O. B. Oña, L. M. Tel, E. Perez-Romero, J. Math. Chem. 50, 492 (2012). [7] C. Valdemoro, D. R. Alcoba, O. B. Oña, L.M. Tel, E. Pérez-Romero, J. M. Oliva, Chem. Phys. 399, 59 (2012). [8] G.E. Massaccesi, D. R. Alcoba, O. B. Oña, J. Math. Chem. 50, 2155 (2012). [9] C. Valdemoro, D. R. Alcoba, L. M. Tel, Int. J. Quantum Chem. 112, 2965 (2012).[10] D. R. Alcoba, O. B. Oña, C. Valdemoro, L. M. Tel, G. E. Massaccesi, J. Math. Chem. 50, 2478 (2012). [11] M. Bouten, P. Van Leuven, M. V. Mihailovic, M. Rosina, Nucl. Phys. A202, 127 (1973). [12] J. Simons, Adv. Quantum Chem., 50, 213 (2005).