Exact Analytic Total Energy Functional for Hooke’s Atom Generated by Local-Scaling Transformations EDUARDO V. LUDEN ˜ A, DANIEL GO ´ MEZ, VALENTIN KARASIEV, PEDRO NIETO Centro de Quı ´mica, Instituto Venezolano de Investigaciones Cientı ´ficas, IVIC, Apartado 21827, Caracas 1020-A, Venezuela Received 11 December 2002; accepted 10 October 2003 Published online 22 January 2004 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.10858 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  5/3 in the kinetic energy expression and an infinite sum of universal terms of the type  (l+4)/3 , for l = 0, 1, ... , in the electron– electron energy. In all cases, these density-dependent terms are multiplied by their corresponding enhancement factors F 5/3 (r) and {F ee (l ) (r)} l=0  that contain system-specific information. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem 99: 297–307, 2004 Key words: LS-DFT; DFT; Hooke’s atom; local-scaling transformations 1. Introduction T he Hohenberg–Kohn theorem [1] provides an implicit proof of the existence of an energy functional solely expressible in terms of the one- particle density. It does not give, however, a sys- tematic procedure for constructing this functional. In fact, the spectacular development of density functional theory (DFT) is due more to the ability of researchers to advance ad hoc functionals—which incorporate important physical aspects and comply with several known asymptotic and scaling condi- tions [2– 4]—rather than to a systematic application of some well-established prescription. In Levy’s constrained-search method [5], the ba- sis is laid for an implicit constructive approach to the formulation of the energy functional. In Levy’s Correspondence to: E. V. Luden ˜ a; e-mail: eludena@ivic.ve International Journal of Quantum Chemistry, Vol 99, 297–307 (2004) © 2004 Wiley Periodicals, Inc.