  We report a facile `metric' for the identification of structurally and
dynamically (positive definite phonon structure) stable inorganic compounds.
The metric considers charge-imbalance within the local substructures in
crystalline compounds calculated using first-principles density-functional
theory. To exemplify, we chose carbon-based nitrides as it provides a large
pool of structurally stable and unstable phases. We showcase how local
structural information related to Wyckoff symmetry uniquely identifies four new
carbon-nitride phases. The metric predicts three new structurally stable phases
of 4 (C)$:$3 (N) stoichiometry, i.e., C$_{4}$N$_{3}$, which is further
confirmed by direct phonon calculations. The structurally stable phases also
satisfy the thermodynamic stability and mechanical stability criteria. New
phases possess extraordinary mechanical properties, similar to diamond, and
show insulating bandgap ranging from optimal, 1.45 eV (optimal) to 5.5 eV
(large gap). The structural, electronic, and optical properties of
Pm(1)-C$_{4}$N$_{3}$, discussed in detail, indicate possible application in
optoelectronic and photovoltaic technologies. The way metric is design, it can
be used to predict stability of any material with three-dimensional bonding
network. The metric was also able to predict structural stability of other
nitride polymorphs with 100$\%$ accuracy. We believe that the proposed `Metric'
will accelerate the search of unknown and unexplored inorganic compounds by
quick filtering of dynamically stable phases without expensive
density-functional theory calculations.
