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. Int J Quantum Chem, 2008