  Correlated band theory implemented as a combination of density functional
theory with exact diagonalization [DFT+U(ED)] of the Anderson impurity term
with Coulomb repulsion $U$ in the open 14-orbital $5f$ shell is applied to
UTe$_2$. The small gap for $U$=0, evidence of the half-filled $j=\frac{5}{2}$
subshell of $5f^3$ uranium, is converted for $U$=3 eV to a flat band semimetal
with small heavy-carrier Fermi surfaces that will make properties sensitive to
pressure, magnetic field, and off-stoichiometry, as observed experimentally.
The predicted Kondo temperature around 100 K matches the experimental values
from resistivity. The electric field gradients for the two Te sites are
calculated by DFT+U(ED) to differ by a factor of seven, indicating a strong
site distinction, while the anisotropy factor $\eta=0.18$ is similar for all
three sites. The calculated uranium moment $<M^2>^{1/2}$ of 3.5$\mu_B$ is
roughly consistent with the published experimental Curie-Weiss values of
2.8$\mu_B$ and 3.3$\mu_B$ (which are field-direction dependent), and the
calculated separate spin and orbital moments are remarkably similar to Hund's
rule values for an $f^3$ ion. The $U$=3 eV spectral density is compared with
angle-integrated and angle-resolved photoemission spectra, with agreement that
there is strong $5f$ character at, and for several hundred meV below, the Fermi
energy. Our results support the picture that the underlying ground state of
UTe$_2$ is that of a half-filled $j=\frac{5}{2}$ subshell with two half-filled
$m_j=\pm\frac{1}{2}$ orbitals forming a narrow gap by hybridization, then
driven to a conducting state by configuration mixing (spin-charge
fluctuations). UTe$_2$ displays similarities to UPt$_3$ with its $5f$ dominated
Fermi surfaces rather than a strongly localized Kondo lattice system.
