  Twelve two-dimensional group-IV monochalcogenide monolayers (SiS, SiSe, SiTe,
GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, and PbTe) with a buckled honeycomb
atomistic structure--belonging to symmetry group P3m1--and an out-of-plane
intrinsic electric polarization are shown to be metastable by three
independendent methods. First, we uncover a coordination-preserving structural
transformation from the low-buckled honeycomb structure onto the lower-energy
Pnm2$_1$ (or Pmmn for PbS, PbSe, and PbTe) phase to estimate {\em energy
barriers} $E_B$ that must be overcome during such structural transformation.
Using the curvature of the local minima and $E_B$ as inputs to Kramers escape
formula, large escape times are found, implying the structural metastability of
the buckled honeycomb phase (nevertheless, and with the exception of PbS and
PbSe, these phases display escape times ranging from 700 years to multiple
times the age of the universe, and can be considered "stable" for practical
purposes only in that relative sense). The second demonstration is provided by
phonon dispersion relations that include the effect of long-range Coulomb
forces and display no negative vibrational modes. The third and final
demonstration of structural metastability is furnished by room-temperature {\em
ab initio} molecular dynamics for selected compounds. The magnitude of the
electronic band gap evolves with chemical composition. Different from other
binary two-dimensional compounds such as transition metal dichalcogenide
monolayers and hexagonal boron nitride monolayers which only develop an
in-plane piezoelectric response, the twelve group-IV monochalcogenide
monolayers with a buckled honeycomb structure also display out-of-plane
piezoelectric properties.
