Many physico-chemical parameters of molecules are determined by or are dependent upon their HOMO–LUMO gaps, as has become of special interest for conjugated-carbon nano-structures obtained from graphene and its congeners. Here, we deduce an elegant yet simple upper-bound estimate to the HOMO–LUMO gaps for such molecular π-networks corresponding to connected subgraphs of graphene. The result elucidates the general situations (involving larger fragments) for which the HOMO–LUMO gap is small.
- Received March 14, 2015.
- Accepted June 9, 2015.
- © 2015 The Author(s)
Published by the Royal Society. All rights reserved.