  Magnetic and multipolar ordering in f electron systems takes place at low
temperatures of order 1--10 Kelvin. Combinations of first-principles with
many-body calculations for such low-energy properties of correlated materials
are challenging problems. We address multipolar ordering in f electron systems
based on the dynamical mean-field theory (DMFT) combined with density
functional theory. We derive the momentum-dependent multipolar susceptibilities
and interactions in two ways: by solving the Bethe-Salpeter (BS) equation of
the two-particle Green's function and by using a recently developed approximate
strong-coupling formula. We apply the formalism to the prototypical example of
multipolar ordering in CeB6 using the Hubbard-I solver, and demonstrate that
the experimental quadrupole transition is correctly reproduced. The results by
the approximate formula show good agreement with those by the BS equation. This
first-principles formalism for multipolar ordering based on DMFT has
applications which are beyond the reach of the traditional RKKY formula. In
particular, more itinerant electron systems including 5f, 4d and 5d electrons
can be addressed.
