Semiempirical molecular orbital calculations of 2-(4-dicyanomethylenecyclohexa-2,5-dienylidene)-4,5-ethylenedithio-1,3-dithiole and its analogues, as test molecules towards a highly amphoteric and polar molecule (HAPM) designed on the basis of combination of electron-donating and accepting molecular segments with a pseudo-delocalized electron system were carried out to estimate several molecular parameters, in particular, those regarding the second-order optical nonlinearity, in order to examine a difference between the proposed molecular design and the conventional one for the 'push-pull' type of molecules. Large values of the first molecular hyperpolarizability are obtained for the present molecules, however, it is turned out that the trade-off relation between hyperpolarizability and transparency of a material is also concerned with these materials. This indicates that the proposed molecular design toward HAPM is unique and can be useful to bring about novel materials with remarkable properties.