A series of three-coordinate octupolar compounds with varied centers (boron, aluminum, and nitrogen), which exhibit very large effective two-photon absorption cross sections have been theoretically studied. The ground state geometries and electronic structures are obtained using the density functional theory with the B3LYP functional and 6-31G(d) basis set, and the results are comparable to the available experimental determinations. Based on the correct geometrical and electronic structures, the one- and two-photon absorptions are predicted by the ZINDO-SOS method. Among these compounds, the boron (B) and aluminum (Al) centers act as acceptors, while the nitrogen center acts as donor according to the net charge changes during the excitation. It is found that (i) the compounds with boron and aluminum centers show two large two-photon absorption peaks, while the molecule with nitrogen center show only one two-photon absorption peak; (ii) the cross sections of the molecules with B or Al as centers are larger than that of the molecule with nitrogen as center; furthermore, the two-photon absorption cross section of the molecule with Al center is larger than that of the molecule with B center, from this point of view, our theoretical prediction provides for the experiment a good new candidate with large two-photon absorption cross section for further research; (iii) lengthening the conjugation bridge by inserting a benzene ring on the organoborane compounds (forming the investigated molecule B-2) enhances the two-photon absorption cross section, and keeping good transparency at the same time. (C) 2004 American Institute of Physics.