We developed the analytic second derivative of the energy for unrestricted Hartree-Fock based on the fragment molecular orbital (FMO) method. We formulated the second order derivative for the separated dimer approximation in both restricted and unrestricted methods, which accelerated the calculations by the factor of 9 for a radical system containing 704 atoms. The accuracy was evaluated for organic radicals in explicit solvent, in comparison to full ab initio results. The method was applied to study the change of IR absorption spectra in the tyrosine oxidation reaction for a polypeptide representing the active part of the photosynthetic reaction center. (C) 2014 Elsevier B.V. All rights reserved.