Four new forms of the contracted Schrödinger equation and their connection with the second-order hypervirial condition

Through the use of an important property of a fourth-order correlation matrix previously reported (Valdemoro, C.; Tel, L. M.; Alcoba, D. R.; Perez-Romero, E.; Casquero, F. J. Int J Quantum Chem 2002, 90, 1555; Alcoba, D. R.; Valdemoro, C. Phys Rev A 2001, 64, 062105) four new equivalent forms of the second-order contracted Schrödinger equation (2-CSE) are obtained. The role played by the energy terms involving these correlation matrices is crucial in the solution of these equations. The relations linking the Hermitian (Yasuda, K. Phys Rev A 1999, 59, 4133) and antiHermitian parts (Mazziotti, D. A. Phys Rev Lett 2006, 97, 142002) of the 2-CSE with these correlation energy terms are analyzed in detail. A discussion of the second-order hypervirial condition is also given here. © 2008 Wiley Periodicals, Inc.Fil: Valdemoro, C.. Consejo Superior de Investigaciones Científicas; EspañaFil: Tel, L. M.. Universidad de Salamanca; EspañaFil: Pérez Romero, E.. Universidad de Salamanca; EspañaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin