A combined semiempirical-DFT study of oligomers within the finite-chain approximation, evolution from oligomers to polymers

A computationally cheap approach combining time-independent density functional theory (TIDFT) and semiempirical methods with an appropriate extrapolation procedure is proposed to accurately estimate geometrical and electronic properties of conjugated polymers using just a small set of oligomers. The highest occupied molecular orbital-lowest unoccupied molecular orbital gap (HLG) obtained at a TIDFT level (B3PW91) for two polymers, trans-polyacetylene--the simplest conjugated polymer, and a much larger poly(2-methoxy-5-(2,9-ethyl-hexyloxy)-1,4-phenylenevinylene (MEH-PPV) polymer converge to virtually the same asymptotic value than the excitation energy obtained with time-dependent DFT (TDDFT) calculations using the same functional. For TIDFT geometries, the HLG is found to converge to a value within the experimentally accepted range for the band gap of these polymers, when an exponential extrapolation is used; however if semiempirical geometries are used, a linear fit of the HLG versus 1/n is found to produce the best results. Geometrical parameters are observed to reach a saturation value in good agreement with experimental information, within the length of oligomers calculated here and no extrapolation was considered necessary. Finally, the performance of three different semiempirical methods (AM1, PM3, and MNDO) and for the TIDFT calculations, the performance of 7 different full electron basis sets (6-311+G**, 6-31+ +G**, 6-311+ +G**, 6-31+G**, 6-31G**, 6-31+G*, and 6-31G) is compared and it is determined that the choice of semiempirical method or the basis set does not significantly affect the results.