We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density functional theory.

A misprint was found in the last digit of the parameter C 0 of Table II. The correct value is C 0 0:057 238 4. Moreover, to reobtain exactly Fig. 3, one has to use G 0 0:339 97 (not G 0 0:34 as originally printed). The use of the misprinted values of C 0 and G 0 which appear in the original version of Table II does not affect the results for r s & 30; it does, instead, shift the Wigner crystallization to slightly larger r s .Finally, the text following Eq.(3) has two rather obvious misprints: the factors of 2 and 24 instead of 1=2 and 1=24 in the definitions of 1 and 2 . This is completely harmless: all results and equations of the Letter are based on the correct definition, not on the misprinted one.

Abstract:The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λf∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λf0) mathematically simpler than the physical (λ ) 1) case and can be used to build an approximate interpolation formula between λf0 and λf∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λf∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.