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


Three hierarchically ordered topological factors, i.e., atom connectivity, centrality, and cyclicity, were found to control the number of self-returning walks (SRWS) associated with every atom in the molecule. The reversal of their order was observed in a few cases where the central location of atoms had a stronger influence than did their connectivity on the number of SRWS. Three atomic topological indices, i.e., the Morgan extended connectivity, the Balaban, Mekenyan, and Bonchev hierarchical extended connectivity, the Randić atomic path code, were found to closely match the ordering of atoms in molecules determined by their number of SRWS. New atomic graph invariants fi = lim SRW/SRWn and ti = fi · SRW2 were specified and may find application in QSAR and QSPR. The ti indices are nonintegers close to atomic valence. The fi indices represent the limit of the number of SRWS of length n for the atom i, SRW, normalized by dividing it by the total number of SRWS for the molecule. In the case of Hückel MO considerations, these invariants were shown to be numerically equal to the partial electronic charges of the lowest occupied molecular orbital (LOMO). A new class of isocodal atoms (atoms having the same number of SRWns) was observed, i.e., atoms that become isocodal only at n ⩾ 1. A number of open questions following from these findings were formulated, including the possibility for a topological modeling of electron correlation. © 1993 John Wiley & Sons, Inc.

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