The structure, bonding nature, and stability properties of several anhydrous and hydrate In-, Gd-, and Yb-carboxylates (M-CBX) and β-diketonates (M-BDK) used in neutrino liquid scintillator detectors have been investigated in two liquid scintillator (LS) solvents by density functional theory (DFT). Bonding energy and quantum theory of atoms in molecule (QTAIM) analyses reveal that the order of stability of these complexes is M-acetylacetone (M-ACAC)>M-tetramethyl-heptane-3,5-dionate (M-THD)>M-ethyl-hexanoate (M-EHA)≈M-methyl-valerate (M-MVA)≈M-tri-methyl-hexanate (M-TMHA) in LS solvent, while for the same ligand, binding energies increase in the order of Gd-L<Yb-L<In-L, which is inversely related to the metal ionic size. Therefore, In(ACAC)3 with better stability property might be more suitable for neutrino experiments than other metal-complexes. QTAIM study also shows that although electrostatic interaction dominates the metal-ligand bonding in In-, Gd-, and Yb-CBX complexes, some slight covalent character can be found in the In-CBX complexes. Calculated changes of Gibbs free energy (ΔG) of the solvent extraction reactions reveal that the products of the solvent extraction are mainly hydrated compounds. Therefore, more sophisticate method should be used to synthesize anhydrous complexes, which are supposed to have better solubility in LS solvent. The calculated ΔG values of potential dehydration reactions show that only limited types of hydrate Gd- and Yb-complexes can dehydrate in the gas phase at room temperature, while the situation is different in LS solvent. It is expected that our calculations can provide some useful information for future neutrino detection, radiochemical composition study of earth, and some other applications involving neutron capture.