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Self‐returning walks and fractional electronic charges of atoms in molecules
Author(s) -
Bonchev D.,
Kier L. B.,
Mekenyan O.
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560460505
Subject(s) - atoms in molecules , atom (system on chip) , molecule , valence (chemistry) , centrality , graph , physics , topology (electrical circuits) , chemistry , combinatorics , mathematics , quantum mechanics , computer science , embedded system
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 f i = lim SRW i n / SRW n and t i = f i · SRW 2 were specified and may find application in QSAR and QSPR . The t i indices are nonintegers close to atomic valence. The f i indices represent the limit of the number of SRWS of length n for the atom i , SRW i n , 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 SRW n s) 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.