Modified bielectronic potential method for correlation energy

Abstract

AbstractsLowdin's correlation potential formalism has been used to define a modified bielectronic potential, allowing one to calculate the exact electronic energy, given the Hartree-Fock wave function. This modified potential is in principle peculiar to each electronic system, and is defined by a correlation factor depending on the interelectronic distance r I 2 . The explicit calculation of the correlation factor has been performed for some two-electron atoms, in the 1's and 23S states, and for the beryllium atom. Examination of the results so obtained leads us to conclude in favor of the nonexistence of a universal modified bielectronic potential.Le formalisme du potentiel de corrklation de Lowdin a CtC utilisk pour dkfinir un potentiel bielectronique modifit, permettant de calculer I'tnergie tlectronique exacte au moyen de la fonction d'onde Hartree-Fock du systeme envisagk. Le potentiel modifit est, en principe, propre a chaque systeme tlectronique, et s'exprime au moyen d'un facteur de corrklation, fonction de la distance intertlectronique rI2. Les rtsultats du calcul explicite du facteur de corrtlation de quelques atomes bitlectroniques, dans les Ctats 1's et z3S, et de I'atome de bkryllium, sont prtsentts dans cet article. Leur examen nous amkne a conclure a la non-existence d'un potentiel bielectronique modifik universel.Lowdin's Formalismus zum Korrelationspotential wurde hier benutzt, um ein verandertes bielektronisches Potential zu beschreiben, das es ermoglicht, die genaue elektronische Energie mittels der Hartree-Fock-Wellenfunktioneines bestimmten Systemszu berechnen. DiesesverandertePotential ist, im Prinzip, jedem Elecktronensystem eigen, und ist bestimmt durch einen Korrelationsfaktor abhangig von der interelektronischen Distanz r12. Ausdriickliche Berechnungen des Korrelationsfaktors einiger bielektronischen Atorne im Zustand 1's und 23S, und des Berylatoms, werden hier gezeigt. Die Beobachtung dieser Resultate bringt uns zur Scblussfolgerung der Nicht-Existenz eines universalen veranderten Potentials.

Energy Density Functional Theory of Many-Electron Systems

“…];e(r12) for the groundstate helium atom whose Hartree-Fock state is that of Roothaan et al, 1960) and the exact one, is the six-term function of Hylleraas (1929). Further investigation on the topology of the Coulomb hole for ground and excited states of the helium atom and He-like ions have been carried out by Lester and Krauss (1964), Curl and Coulson (1965), Benesch (1972), Boyd and Coulson (1973), Banyard and Seddon (1973), Boyd and Katriel (1974) Moiseyev et al (1977), Rehmus and Berry (1979), Ros (1979), Ruelle (1979), Boyd and Yee (1982), and Ugalde and Boyd (1986). ( 4.2-43), the total, area lying under the 2.~e( T12)-curve is zero.…”

“…Alternatively, one can formally introduce the concept of the so called "correlation potential" F eorr , (Lowdin, 1969) (4.2-88) Equation (4.2-88) gives the definition of Feorr , whose existence was proved by Lowdin (1969) (for further discussions see McWeeny (1976); Ruelle (1979); Wilets et al (1980); Baiwen et al (1984); Laforgue (1985) and references therein). As follows from Eq.…”