  The Mott transition, a metal-insulator transition due to strong electronic
interaction, is observed in many materials without an accompanying change of
system symmetry. An important open question in Mott's proposal is the role of
long-range screening, whose drastic change across the quantum phase transition
may self-consistently make the transition more abrupt, toward a first-order
one. Here we investigate this effect in a model system of hydrogen atoms in a
cubic lattice, using charge self-consistent dynamical mean-field theory that
incorporates approximately the long-range interaction within the density
functional treatment. We found that the system is well within the
charge-transfer regime and that the charge-transfer gap intimately related to
the Mott transition closes smoothly instead. This indicates that within this
approximation, the long-range screening does not play an essential role in this
prototypical example. We explain this finding by demonstrating analytically
that the obtained insulating phase in this typical case is driven by
short-range physics of large energy scale, and the transition is controlled by
the charge-transfer gap closing, both insensitive to long-range screening.
