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Correlation energy of two electrons in the high-density limit
3.W. J. Hehre, L. Radom, P. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory (Wiley, New York, 1986).
18.M. Abramowitz and I. E. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
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We consider the high-density-limit correlation energy in dimensions for the ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the values are strikingly similar, depending strongly on but only weakly on the external potential. We conjecture that for large , the limiting correlation energy in any confining external potential, where .
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