The anti-resonance phenomenon in preresonance Raman scattering is investigated on the basis of the direct Taylor expansion of the electric dipole transition moments in vibrational Raman tensors with respect to vibrational normal coordinates. A time-dependent density functional theory treatment is applied to compute the anti-resonance of a nontotally symmetric vibrational model for naphthalene molecules, and the model spectra agree favorably with experiment. This direct evaluation approach may provide a method of predicting anti-resonance and studying its origin.