  We report ab-initio calculations of the phonon dispersion relation on the
bulk and single layer of SnO and PbO. We identify Raman active modes and
infrared active modes at the zone center {\Gamma} point. In agreement with
experimental observations of Raman spectroscopy measurement, we find that A1g
mode is higher in frequency than that of Eg mode. Moreover, the reason behind
the shift of A2u mode to higher frequency for monolayer of both SnO and PbO is
revealed from our calculations. We also find that long-range Coulomb
interaction enhances the dielectric constant and Born effective charges in bulk
SnO and bulk PbO, compared to their monolayer. Here, we observe avoided
crossing or Landau degeneracy between longitudinal acoustics (LA) and low
energetic transverse optical (TO) modes in bulk form of both SnO and PbO.
Additionally, monolayer SnO also shows low energetic Raman modes (Eg and A1g)
of same frequency as bulk. As a result, we notice avoided crossing between LA
and TO modes in monolayer SnO. Interestingly, higher Born effective charge and
low dielectric constant enhances self-force constants and the interatomic force
constants (IFCs) between the M-O bonds. The enhanced force constants give rise
to higher vibrational frequency of phonon modes for monolayer PbO. Our studies
reveal that due to avoided crossing between two degenerate bands, the phonon
dispersion near high symmetry X point lowers specific heat and vibrational
entropy in bulk SnO, bulk PbO and only in monolayer SnO upto temperature 150 K.
Moreover, the large mass difference between Pb and Oxygen atoms and absence of
interlayer van der Waal interactions give rise to high phonon vibration which
reduces the occurrence of band crossing between two degenerate energy levels.
The absence of avoided crossing leads higher specific heat and vibrational
entropy in monolayer PbO at low temperatures.
