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Four new forms of the contracted Schrödinger equation and their connection with the second‐order hypervirial condition
Author(s) -
Valdemoro C.,
Tel L. M.,
PérezRomero E.,
Alcoba D. R.
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21576
Subject(s) - hermitian matrix , connection (principal bundle) , order (exchange) , physics , mathematical physics , quantum , schrödinger equation , quantum mechanics , energy (signal processing) , matrix (chemical analysis) , property (philosophy) , mathematics , chemistry , geometry , finance , chromatography , economics , philosophy , epistemology
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