A computational analysis on the first hyperpolarizability (£]) of 5-6-5 heterocyclic rigid-rod benzobisthiazole-based chromophores and their derivatives has been systematically investigated in this study by the software Gaussian03, in an effort to provide a molecular design criterion for better opto-electonic properties. The specific objectives of this study have been focused on (1) understanding of 5-6-5 heterocyclic rigid-rod chromophores and other similar compounds in nonlinear optical property, (2) control on the nonlinear optical properties through the manipulation of the conjugated composition of the chromophores, (3) understanding the effect of the donor and acceptor of chromophore on the nonlinear optical property. The results show that £] value of a chromophore with its 5-6-5 heterocyclic rigid-rod structure near the acceptor is 30 % higher than the one with the same structure near the donor; this reflects a unique property of 5-6-5 heterocyclic rigid-rod structure quite different from other chromophores. In conjugated chromophores, those having double bonds or thiophenes, which have soft structures or heteroatoms, would offer higher £] values. For example, a 5-6-5 heterocyclic rigid-rod chromophore with 15 double bonds has a £] value up to 1.44 x 10-26esu. In the study of multi-donors and acceptors, from 1 donor- 1 acceptor to 2 donors- 2 acceptors, the difference in £] could be up to 116%; however, this difference reduces to only 5% if the chromophere structure becomes unstable. From the band-resolved analysis, it is found that £] values of chromophores are affected by the electronic donor via its HOMO part, the electronic acceptor via its LUMO part, while the conjugated bridge via its molecular orbital exclusive of HOMO and LUMO, depending on the type and degree of conjugation, i.e., HOMO-2 and LUMO+1 for double bonds and HOMO-2, HOMO-1, and LUMO+1 for phenyl moieties. For the 5-6-5 heterocyclic rigid-rod structure, £] value is mainly affected by those molecular orbital below HOMO, i.e., HOMO-2 for those containing double bonds. Further detailed elucidation on the relation between molecular orbital and molecular structure of chromophores can be ambiguously depicted through analyses of electronic distribution on the molecular orbital.