Theoretical calculation on relationship between molecular structure and band gap of benzo[1,2-b:4,5-b′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document}]dithiophene based homopolymer

In order to guide the synthesis of new materials with low band gaps, quantum-chemical methods have been increasingly applied to predict the band gaps of conjugated polymers. Softwares such as Material Studio, Gauss View, Gauss 03 and Gauss 09 calculation program were used in this paper. Semi-empirical AM1 method was applied to calculate the optimal geometric structure of selected three benzo[1,2-b:4,5-b′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$'$$\end{document}]dithiophene homopolymers, namely PBDTV, H2 and H3. Using the generalized density function theory based on B3LYP/6-31G*, B3LYP/6-311G* and M062X/6-311G* level calculation of polymers’ band gaps. The results indicate that whether there is enough interspace between adjacent subunits, long alkoxy side chain is advantageous to the band gap decrease, and otherwise it will bring steric hindrance to destroy the coplanarity of polymer chain which is disadvantageous to the band gap decrease. The band gaps of polymers mainly depends on the molecular structure, generally speaking, the more coplanarity of main chain, smaller dihedral angle, smaller difference between the bond length of single and double bonds in the main chain, resulting in narrower band gap.