This work demonstrates the feasibility and applicability of the theory of extended multiphonon electron transitions for the description of nonlinear optical properties of polymethine dyes using quantum chemistry and model calculations. The transformation of a strong one-photon absorption band in dye monomers to a weak two-photon absorption band is rationalized from the electron-nuclear resonance condition. The power law fitting of the results of quantum chemical computations of nonlinear optical properties allows the predicting of the shift of the corresponding Egorov-like resonance curve to the shortest dye in the vinylogous series of dye monomers. The results presented provide an insight and guide for the rational molecular design and application of polymethine dyes.