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Using a genetic algorithm together with DFT computations, the stable isomers of Lin+1Fn (n = 2 ~ 17) are obtained. It is found that the Li3F2 is a planar structure, and starting at n = 3, Lin+1Fn adopt three-dimensional configurations with a terminal Li atom or vacancy of F atom. As the cluster sizes increase, the geometries of Lin+1Fn develop, first with cube-like and tubular structures, then forming cage-like arrangements, and eventually favoring rock-salt configurations. The Lin+1Fn (n = 3, 5, 8, 11, 13 and 15) are especially stable and magic number clusters. Low ionization potentials are acquired for Lin+1Fn due to the weakly bonded odd electrons of Li atoms. Particularly, the AIP/VIP for Li14F13 and Li17F16 are only 2.68/2.75 eV and 2.77/2.97 eV, respectively, which indicate that they can be looked as superalkali clusters. Meanwhile, the particularly large hyperpolarizabilities (3237157.14 a.u. and 716489.10 a.u.) for these two isomers are also obtained. According to the electronic structure analysis, Li atoms donate their 2s electrons to the 2p orbitals of F atoms, forming Li–F ionic bonds. Additionally, the spectral properties and the reactivities for the magic number clusters are further investigated. [ABSTRACT FROM AUTHOR]