  We study the Hubbard model at half band-filling on a Bethe lattice with
infinite coordination number in the paramagnetic insulating phase at zero
temperature. We use the dynamical mean-field theory (DMFT) mapping to a
single-impurity Anderson model with a bath whose properties have to be
determined self-consistently. For a controlled and systematic implementation of
the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT.
In FE-DMFT the onset and the width of the Hubbard bands are adjusted
self-consistently but the energies of the bath levels are kept fixed relatively
to both band edges during the calculation of self-consistent hybridization
strengths between impurity and bath sites. Using the dynamical density-matrix
renormalization group method (DDMRG) we calculate the density of states with a
resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to
0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the
density of states and the gap is superior to those obtained with other
numerical methods in previous DMFT investigations. We find that the Mott gap
closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we
observe prominent shoulders near the onset of the Hubbard bands. They are the
remainders of the quasi-particle resonance in the metallic phase which appears
to split when the gap opens at $U_{\rm c}$.
