Analytic second derivatives of the energy with respect to nuclear coordinates are derived for the fragment molecular orbital method combined with the polarizable continuum model. Harmonic frequencies, infrared intensities and normal Raman activities of large molecular systems in solution can be evaluated. Periodic trends on S_N2 chemical reactions are elucidated. The accuracy of the developed method is established in comparison to full calculations without fragmentation. The method is applied to ionic liquids and crambin (PDB: 1CRN). Solvent effects on the vibrational frequencies are discussed.