Ab initio MP2/6-31G*//HF/6-31G* + ZPE(HF/6-31G*) and MP4SDTQ/6-31(+)G*//MP2/6-31G* + ZPE(MP2/6-31G*) calculations of the potential energy surface (PES) are performed for a series of lithium oxo and thio borates, aluminates, carbonates, and silicates Li(3)AB(3) (A = B, Al, C+, Si+; B = O, S) with 24 valence electrons. It was found that the planar D-3h structure with the bidentate coordination of the cations is most favorable for borates and carbonates. For aluminates and silicates, this structure corresponds to the top of a small inversion barrier, and the global minimum corresponds to the quasi-planar bidentate C-3V structure with a strongly flattened pyramidal anion and noticeable out-of-plane displacements of the cations. For the LiSiO3+ ion, an additional low-lying local minimum was localized; this minimum corresponds to the planar D-3h structure with the monodentate coordination of the cations and approaches in energy (is 1.2 kcal/mol higher) the bidentate isomer. The LiSiO3+ ion was predicted to be not rigid with respect to the cation migration C-3v -> D-3h -> C-3v(''). For the other systems, monodentate structure is evidently less favorable. The equilibrium geometrical parameters, relative energies and decomposition energies of isomers, the frequencies and IR spectral intensities of their normal modes, and characteristics of electron density distribution are determined. The effect of electron correlation on the results of calculations is discussed. The behavior of molecular properties in different series of Li(3)AB(3) molecules and ions is analyzed. The results of these calculations are compared to those of previous calculations for isoelectronic LiAB(3) and Li(2)AB(3) salts. The deformation and polarization of the AB(3) anion in the field of one, two, and three Li+ cations are considered.