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Exact analytic total energy functional for Hooke's atom generated by local-scaling transformations

Abstract:

An analytic closed form for the total energy density functional for Hooke's atom - an artificial two-electron system with harmonic electron-nuclear and Coulombic electron-electron interaction terms - has been constructed by means of local-scaling transformations. This is the first time that an exact density functional is obtained for a quantum mechanical many-electron system containing electron correlation. The density-dependent functional advanced in the present work is strictly variational: It yields the exact value of the total energy of Hooke's atom at the exact density and upper bounds for all other densities. Although the functional is not "universal" it contains the density-dependent term ρ5/3 in the kinetic energy expression and an infinite sum of universal terms of the type ρ(1+4)/3, for Z = 0,1, ∞, in the electron-electron energy. In all cases, these density-dependent terms are multiplied by their corresponding enhancement factors F5/3(r) and {Fee(1)(r)} l=0∞ that contain system-specific information. © 2004 Wiley Periodicals, Inc.