Abstract

The effect of cycles on the HOMO-LUMO separation of alternant conjugated hydrocarbons is examined. A general topological regularity is established, namely that (4m -f 2)-membered con-jugated circuits increase and (4w)-membered conjugated circuits decrease the HOMO-LUMO sep-aration. Möbius cyclcs exhibit an opposite effect. In recent years a graph theoretical technique was developed, which enabled one to analyse and partially understand the dependence of the rr-elec-tron properties of conjugated molecules on molec-ular topology [1]. The HOMO-LUMO separation (i.e. the difference between the energy of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO)) belongs among those ^-electron characteristics of a conjugated system, for which the graph theoretical approach was not very successful. The previously obtained results about the topological properties of the HOMO-LUMO separation are rather limited [2—4]. In the present paper we offer a general topological rule which elucidates the effect of cycles on the HOMO-LUMO separation of alternant conjugated hydrocarbons. An auxiliary graph theoretical polynomial According to the Sachs theorem [1, 5] tho characteristic polynomial of a graph G (with n vertices) is calculated as