  LiV_2 O_4 is one of the most puzzling compounds among transition metal oxides
because of its heavy fermion like behavior at low temperatures. In this paper
we present results for the orbital state and magnetic properties of LiV_2 O_4
obtained from a combination of density functional theory within the local
density approximation and dynamical mean-field theory (DMFT). The DMFT
equations are solved by quantum Monte Carlo simulations. The trigonal crystal
field splits the V 3d orbitals such that the a_{1g} and e_{g}^{pi} orbitals
cross the Fermi level, with the former being slightly lower in energy and
narrower in bandwidth. In this situation, the d-d Coulomb interaction leads to
an almost localization of one electron per V ion in the a_{1g} orbital, while
the e_{g}^{pi} orbitals form relatively broad bands with 1/8 filling. 2The
theoretical high-temperature paramagnetic susceptibility chi(T) follows a
Curie-Weiss law with an effective paramagnetic moment p_{eff}=1.65 in agreement
with the experimental results.
