Molecular Hypergraphs: The New Representation of Nonclassical Molecular Structures with Polycentric Delocalized Bonds

Graph presentation of molecular structures is widely used in computational chemistry and theoretical chemical research.'x2 Molecular structures are represented by graphs where vertices correspond to atoms and edges to chemical bonds. This kind of graph, called a molecular graph,' is the object of study in the theory of ordinary graph^.^ However ordinary graphs do not adequately describe chemical compounds of nonclassical structure. As noted in ref 4 a substantial drawback of the structure theory is the lack of a convenient representation for molecules with delocalized polycentric bonds. Organometallic compounds are one example of such structures.j Organometallic chemistry deals with compounds that have at least one metal-carbon (M-C) bond. This bond may be a simple covalent bond, as for example in Pb(C2Hj)4, but also may be an ionic bond, as for example in Na+CzHj-, or a n-bond, as for example in ferrocene, where iron has bonds with cyclopentadienyls, which are five-electron ligands. In principle any nonsaturated or aromatic organic molecule or radical can be a ligand in metal-carbon bond. Just the same molecule may play roles of different ligands. The variety of M-C bond types and ligands leads to the appearance of a considerable range of organometallic compounds and provides a basis for classification of these compound^.^ In Figure 1, examples of molecular structures for compounds with three-electron ligands are given. Let us consider some of the graph models used for representation of such compounds. In refs 6 and 7 examples of representation for "sandwich" and olefin structures by disconnected molecular graphs (see Figure 2a) are described. Representation 2a does not seem to be illustrative and does not allow us to analyze a structure as a whole, because there are no connections between molecular subgraphs representing individual structural fragments within it. More illustrative but still not devoid of drawbacks are connected molecular graphs where all the vertices corresponding to carbon atoms are connected to the M vertex, which corresponds to a metal atom (Figure 2b). If M = Fe, Ni the valency of the metal atom is equal two. The degree of the M vertex in this case is equal to the number of vertices connected and not necessarily equal to the valency of the M atom. Besides, in both representations the difference between simple covalent and polycentric bonds is obscured.