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⩽⋯⩽ s2k–1⩽ t2k–1⩽ t2k⩽⋯⩽ s2n–1⩽ t2n–1⩽ t2n⩽ s2n is proved, where sj and tj, 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 sj and tj are deduced.