  Using first principles calculations, the energetic stability of
two-dimensional (2D) binary compounds $XY$ is investigated, where $X$ and $Y$
indicate the metallic element from Li to Pb in the periodic table. Here, 1081
compounds in the buckled honeycomb (BHC), buckled square, B2, L1$_0$, and B$_h$
structures are studied. For the compounds that have negative formation energy
in the BHC structure or the compounds that can have the B$_h$ structure, the
phonon dispersions of the 2D structures are also calculated. We demonstrate
that (i) a negative formation energy is neither a sufficient nor necessary
condition for yielding the dynamical stability of 2D compounds; and (ii) if a
compound in the B$_h$ structure has been synthesized experimentally, that in
the BHC structure is dynamically stable.
