It is required that molecules with a given graph and with covalent, coordinate-covalent, and ionic bonding contain closed-shell atoms. This requirement results in an equation for each atom, which states that the number of valence electrons pertaining to it before bonding, plus those made available to it in the bonding processes, close its valence shell. Solving the equations results in identifying the atoms and the bond orders of the Lewis diagrams. The algebraic procedure can identify new species. Some of them may be considered impossible (for instance, with high steric strain), or may be transitory, or may be found only under the most unusual conditions. Lists of triatomic molecules, clusters, and resonances found by solving the equations is presented. Closed-shell molecules lie on parallel planes in their chemical spaces, namely those on which isoelectronic molecules are located.
Geach, Jonathan; Walters, Chris J.; James, Bryan; Caviness, Ken E.; and Hefferlin, Ray, "Global Molecular Identification from Graphs. Main-group Triatomic Molecules" (2001). Faculty Works. 1.