An interlacing theorem in simple molecular-orbital theory

Abstract

By connecting two identical bivalent constituent fragments in two different ways S and T isomers are obtained. The following interlacing theorem: s₁⩽ t₁⩽ t₂⩽ s₂⩽⋯⩽ s_2k–1⩽ t_2k–1⩽ t_2k⩽⋯⩽ s_2n–1⩽ t_2n–1⩽ t_2n⩽ s_2n is proved, where s_j and t_j, j= 1, 2,…, 2n, stand for the molecular orbital energies (calculated within the simple tight-binding approximation) of the S and T isomers, respectively. In addition, some new topological functions are studied and a number of statements concerning the location of their zeros as well as their relation to the location of the s_j and t_j are deduced.