HOMO-LUMO gaps for sub-graphenic and sub-buckytubic species
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Many physico-chemical parameters of molecules are determined by or are dependent upon their HOMOLUMO 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 HOMOLUMO gaps for such molecular -networks corresponding to connected subgraphs of graphene. The result elucidates the general situations (involving larger fragments) for which the HOMOLUMO gap is small.