Quantum chemical simulation of infrared (IR) and Raman spectra for molecules with open-shell, radical, or multiradical electronic structure represents a major challenge. We report analytic second-order geometrical derivatives of the Mermin free energy for the second-order self-consistent-charge densityfunctional tight-binding (DFTB2) method with fractional occupation numbers (FONs). This new method is applied to the evaluation of N-O radical stretching modes in various open-shell molecules and to the prediction of the evolution of IR and Raman spectra of graphene nanoribbons with increasing molecular size. (C) 2016 Elsevier B.V. All rights reserved.