The z-electron charges in a non-alternant conjugated hydrocarbon alternate in sign along a polymethine chain.
Recent theoretical investigations [ 1,2] have shown that the a, wdisubstituted polyrnethines possess a nurnber of remarkable srelectron characteristics. In the present paper we demonstrate another property of this class of conjugated compounds, namely that in non-altemant rnoiecuIes the x-electron charges alternate in sign along the polymethine chain This rule was certainiy known to earlier researchers (see e.g. ref. [3]), but, to the author's knowledge, no proof of it exists in the available literature.
We shall adopt the same notation and terminology as in ref. 121. Thus the molecular graph of an (II, odisubstituted polymethine R, -(CH), _ 2-$ is denoted by G,-This graph is obtained by joining the subgraphs R, and R2 to the terminal vertices of the path P, _ 2. The subgraphs obtained by deletion of the vertices 1 and n , respectively, from R, and R2 are denoted by R; and Rs. Let RI _ad R, possess iVI and N2 vertices, respectively. 'Ihen the number of vertices in Gn is Nl + N2 f n -2 =N.
Itwillbe assumed that G, represents a non-altemant system such that its fragment R 1 is non-alternant while R2 is alternant". * The situation when both the fragments RI &d R2 are non-aIternant is rather complicated and is d&cussed in the appendix-