Metric-driven search for structurally stable inorganic compounds

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)$:$3 (N) stoichiometry, i.e., C$<sub>4</sub>$N$<sub>3</sub>$, which is further confirmed by direct phonon calculations. The structurally stable phases also satisfy the thermodynamic stability and mechanical stability criteria. New phases possess extraordinary mechanical properties, similar to diamond, and show insulating bandgap ranging from optimal, 1.45 eV (optimal) to 5.5 eV (large gap). The structural, electronic, and optical properties of Pm(1)-C$<sub>4</sub>$N$<sub>3</sub>$, discussed in detail, indicate possible application in optoelectronic and photovoltaic technologies. The way metric is design, it can be used to predict stability of any material with three-dimensional bonding network. The metric was also able to predict structural stability of other nitride polymorphs with 100$\%$ 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.