  The evolution of the electronic structure of BiTeI, a layered semiconductor
with a van der Waals gap, under compression is studied by employing semilocal
and dispersion-corrected density-functional calculations. Comparative analysis
of the results of these calculations shows that the band-gap energy of BiTeI
decreases till it attains a minimum value of zero at a critical pressure, after
which it increases again. The critical pressure corresponding to the closure of
the band gap is calculated, at which BiTeI becomes a topological insulator.
Comparison of the critical pressure to the pressure at which BiTeI undergoes a
structural phase transition indicates that the closure of the band gap would
not be hindered by a structural transformation. Moreover, the band-gap pressure
coefficients of BiTeI are computed, and an expression of the critical pressure
is devised in terms of these coefficients. Our findings indicate that the
semilocal and dispersion-corrected approaches are in conflict about the
compressibility of BiTeI, which result in overestimation and underestimation,
respectively. Nevertheless, the effect of pressure on the atomic structure of
BiTeI is found to be manifested primarily as the reduction of the width of the
van der Waals gap according to both approaches, which also yield consistent
predictions concerning the interlayer metallic bonding in BiTeI under
compression. It is consequently shown that the calculated band-gap energies
follow qualitatively and quantitatively the same trend within the two
approximations employed here, and the transition to the zero-gap state occurs
at the same critical width of the van der Waals gap.
