We examine the vibrational and Raman spectra for Li doped Si nanocrystals using real-space pseudopotentials constructed within density functional theory. We calculate differences in the Raman spectra using the Placzek approximation. The insertion of Li atoms into Si nanocrystals disrupts the Si crystal structure forming a region of Li-Si alloy in which the regular crystal structure is significantly disrupted. The Raman spectrum for this alloy exhibits a Li induced peak at 440-480 cm(-1). We find an accompanying reduction in the size of the dominant bulk-like Si peak at 520 cm(-1). Both of these results are consistent with experiment. Our analysis of the calculated spectrum confirms the utility of using Raman spectroscopy, coupled with first principle computations, to predict the structural and electronic properties of Li doped Si nanocrystals. (C) 2016 Elsevier B.V. All rights reserved.