Topological index as applied to .PI.-electronic systems. IV. On the topological factors causing non-uniform .PI.-electron charge distribution in non-alternant hydrocarbons.
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概要
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The topological factors which cause non-uniform π-electron charge distribution in non-alternant hydrocarbons (NAH′s) are discussed. For estimating and analyzing the net-charge density a novel topological index, topological charge density, <I>Q<SUB>r</SUB></I><SUP>T</SUP>, is proposed. It is defined as <I>Q<SUB>r</SUB></I><SUP>T</SUP>=Re(F<SUB><I>G</I>,<I>r</I></SUB>(1)), the real part of F<SUB><I>G</I>,<I>r</I></SUB>(<I>y</I>)=<I>Δ</I><SUB><I>r</I>,<I>r</I></SUB>(<I>iy</I>)⁄<I>Δ</I>(<I>iy</I>), where <I>Δ</I>(<I>x</I>) is the secular determinant of graph <B>G</B> and <I>Δ</I><SUB><I>r</I>,<I>r</I></SUB>(<I>x</I>) is its adjunct with row <I>r</I> and column <I>r</I> struck out. This quantity <I>Q<SUB>r</SUB></I><SUP>T</SUP>, corresponding to the Coulson net charge density <I>Q<SUB>r</SUB></I>=1−<I>q<SUB>r</SUB></I>, is related with the topological indices \widetilde<I>Z<SUB>G</SUB></I> and \widetilde<I>Y<SUB>G</SUB></I> which are defined in terms of the coefficients of the characteristic polynomial of graph <B>G</B>. As all the newly proposed indices can be enumerated graphically, one can easily estimate the net-charge densities of NAH′s.
- 公益社団法人 日本化学会の論文
著者
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Hosoya Haruo
Department Of Chemistry Faculty Of Science Ochanomizu University
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Yamaguchi Tamie
Department Of Chemistry Faculty Of Science Ochanomizu University
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Gutman Ivan
Institute "Ruder Bo\u{s}kovic," Zagreb
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