An outlook of the contracted equations formalism and effective combination of the G-particle-hole hypervirial and the hermitian-operator methods

C. VALDEMORO; D.R. ALCOBA; O.B. OÑA; L.M. TEL; G.E. MASSACESSI

Salamanca

Jornada; Jornada científica organizada por el Departamento de Química Física de la Universidad de Salamanca en honor a L.M. Tel; 2013

Universidad de Salamanca

After a brief outlook of the 2-order Contracted Schrodinger and Liouville equations theory [1-3], we focus our attention on the 2-order G-particle-hole hypervirial (GHV) method [4]. In the GHV method one looks for a 2-order G-particle-hole} matrix which is a 2-electron quantum average of the electronic correlation of the N-electron state considered. Then [5], we show the effectiveness of combining the GHV method with the Hermitian Operator (HO) method of Bouten, Van Leuven, Mihailovich and Rosina [6]. Thus, the G-particle-hole matrix corresponding to a given state of an N-electron system contains all the needed data for applying the HO-method which yields a set of energy values corresponding to the spectrum of the system. A preliminary study of the reduction of the computational cost due to the use of the molecular spatial symmetry is also included. The results obtained with this approach in a series of calculations are presented here. [1] Nakatsuji, H., Phys. Rev. A, 14: 41, 1976. Cohen, L., Frishberg, C., Phys. Rev. A}, 13:927, 1976.[2] Valdemoro, C., pg. 275-288. Density Matrices and Density Functionals, Proceedings of the A. J. Coleman Symposium, Kingston, Ontario, 1985, R. Erdahl and V. Smith, eds. Reidel, Dordrecht, 1987.[3] Colmenero, F., Valdemoro, C., Int. J. Quantum Chem., 51:369, 1994.[4] Alcoba, D. R., Valdemoro, C., Tel, L. M.  and Perez-Romero, E., Int. J. Quantum Chem., 109:3178, 2009.[5] Valdemoro, C., Alcoba, D. R., Oña, O. B., Tel, L. M., Perez-Romero, E., J. Math. Chem. A}, 50:492, 2012. [6] Bouten, M., Van Leuven, P., Mihailovich,M. V., Rosina, M., Nucl. Phys. A, 202:127, 1973. Nucl. Phys. A}, 221:173, 1974.