Effect of length and geometry on the highest occupied molecular orbital lowest unoccupied molecular orbital gap of conjugated oligomers: An analytical Huckel model approach

It is shown that the asymptotic behavior of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap of conjugated oligomers of types M-(M)(N-2)-M and M-(M)(N-2)-M-1 with M = M-1-M-2, where M, M-1, and M-2 are alternant but otherwise arbitrary monomers described by the Huckel Hamiltonian, is ruled by the law Delta(HL)(N)=Delta(HL)(infinity)+const.N-2. On this basis we suggest an approximate expression for the HOMO-LUMO gap as a function of oligomer length, that is exact for minimal-and infinite-length oligomers. Two parameters of this function determine the dependence of Delta(HL)(N) on the oligomer geometry. By comparing the proposed approximation with the exact model results for oligomers of polyene, polyparaphenylene (PPP), and polyparaphenylenevinylene (PPV) (some experimental data and results of more elaborate calculations have been also used for this purpose) the proposed approximation is proven to give a useful estimate of the conjugation length and geometry effect on the HOMO-LUMO gap of the molecules under consideration. Applying our approach to PPP and PPV oligomers, we rederive the geometry effects on the PPP band gap reported previously (however, an important point is taking end effects into account) and predict that the HOMO-LUMO gap of PPV decreases with the increase of the quinoid character of the backbone geometry much more strongly, as compared with PPP. The band gap closing in the infinite chain limit as well as the problem of the existence of discrete in-gap states were also examined, and this analysis has resulted in the formulation of general conditions of the occurrence of the above mentioned situations. Applied to the polymers (infinite oligomers), these conditions allow one to decide whether the gap closing or the existence of in-gap states is possible under the given pi electronic structure of monomer. Since the conditions obtained are expressed in terms of the monomer Green function only, they provide a simple and efficient tool with which to search for new polymer materials with the band gaps desired. (C) 1997 American Institute of Physics.