Article

# Self-Returning Walks and Fractional Electronic Charges of Atoms in Molecules

Virginia Commonwealth University, Ричмонд, Virginia, United States

International Journal of Quantum Chemistry (Impact Factor: 1.43). 01/1993; 46(5):635 - 649. DOI: 10.1002/qua.560460505 Get notified about updates to this publication Follow publication |

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

- [Show abstract] [Hide abstract]

**ABSTRACT:**A proof is presented that the limit of each relative atomic moment (RAM) in tight-binding approximation is equal to the respective squared atomic coefficient in the principal eigenvector. It is also proved that this limit is reached when each higher RAM is obtained from the preceding one by multiplying by the squared largest eigenvalue. Relationships are obtained between the RAM limit and Ruckers' limit of the relative walk counts. Higher molecular branching and cyclicity as well as higher symmetry are shown to favor the convergence. The necessary and sufficient conditions are formulated for a RAM to reach its limit as early as in the second moment. Relationships between different RAMs are obtained for several classes of molecules. - [Show abstract] [Hide abstract]

**ABSTRACT:**Theorems and corollaries are proved and relationships are derived for the atomic and bond moments of energy in molecules and solids or, in terms of graph theory, for the self-returning walks SRWs that begin in graph vertexes and edges, respectively. Topological atomic charges, valencies, and bond orders are introduced by means of the limit distributions of the SRWs. A hierarchical system of topological rules on atomic and bond reactivity is presented proceeding from the alternating positive and negative contributions to the atomic and bond moments. Some light is thus shed on the topological control of chemical reactivity. - [Show abstract] [Hide abstract]

**ABSTRACT:**A recent proof (J. Chem. Inf. Comput. Sci. 1995, 35, 237-242) that the limit of each relative atomic moment in tight binding approximation is equal to the respective squared atomic coefficient in the principal eigenvector is completed.