Estimation of the HOMO-LUMO Separation

In the quantum theory ·of the electrnnic st:riucture of molecules, · the diffe., rence between the energy of the highest occupied molecular orbital (HOMO) and the energy of the lowest unoccupied molecular orbital (LUMO) the so-called »HOMO-LUMO separation« plays an important role1 • We shall denote this quantity by S. Relatively little has been done tin elucidating the relationship between molecular structure (i. e. molecular topology2•3) and the HOMO-LUMO separation. Thus, in spite of several attempts in the past46, the structural factors which influence S are not yet clear. · In the present work we would like to report a number of new results on S. First we consider alternant conjugated hydrocarbons and analyse their HOMO-LUMO separation as calculated within the framework of the Hiickel molecular orbital method. Non-alternant hydrocarbons and heteroconjugated systems are treated in the Appendix. The molecular graph G will be associated with a conjugated rr-electron system in the usual manner3. For details on graph theory and its applications in the quantum chemistry of conjugated compounds the reader is referred to the books2•3 . Let G be the molecular graph of an alternant hydr·ocarbon with 2ri carbon atoms. Let the characteristic polynomial of G be written in the form