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 λ→∞, turns out to be, like the
opposite non-interacting Kohn-Sham limit (λ→0) mathematically
simpler than the physical (λ=1) case, and can be used to build an
approximate interpolation formula between λ→0 and λ→∞
for the exchange-correlation energy. Here we extend the exact treatment of the
λ→∞ limit [Phys. Rev. A {\bf 75}, 042511 (2007)] 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.Comment: 11 pages, submitted to J. Chem. Theory Compu