The emission of negative cluster ions produced by the impact of similar to 60 MeV Cf-252 fission fragments on a (LiF)-Li-7 polycrystalline target is analyzed. The negative ion mass spectrum is dominated by the ((LiF)-Li-7)(n)F- series, n = 1 to similar to 30. The desorption yield distribution of the ((LiF)-Li-7)(n)F- members has a maximum at n = 2 and then decreases as the sum of two exponentials whose decay parameters are k(Fast) = 0.9 and k(Slow) = 0.08. These k values are the same as those observed for the positive series and close to others obtained for condensed gas targets. Relative cluster ion stabilities, deduced from the experimental ion abundances for the (LiF)(n)F- series, are proposed to be correlated with theoretical Structures according to their internal energy by using the deviation plot (D-plot) methodology. A pool of candidate cluster structures was generated using a genetic algorithm and further analyzed and optimized using density functional theory (DFT) with the hybrid functional B3LYP (DFT/B3LYP) and Moller-Plesset perturbation theory (MP2). For the small Clusters (n = 1 to 2), the most stable structures are found to be linear, whereas the larger clusters (n = 4 to 6) present cubic or polyhedral structures. Fragmentation energies, ionization potentials, and relative stabilities are reported for the most abundant families of the (LiF)(n)F- and (LiF)(n)(-) series.