The compounds doped with or containing Cr2+ ions are extensively used as optoelectronic and nonlinear optical materials, because they have special optical, magnetic and electric properties. These properties are very closely related to the absorption spectra and zero-field-splitting. The studies of the absorption spectra and zero-field-splitting are very important for realizing the doped microscopic mechanism and understanding the interaction between impurity ions and host crystals, and they may be useful to material designers. The concept of the standard basis adapted to the double group chain is adopted in the strong-field scheme by the crystal field theory. This concept emphasizes the standardization of the basis of the whole 3d4 configuration space including all spin states. Thus, the basis functions can be constructed according to each irreducible representation of the double group and each basis function has a certain expression. Each standard basis adapted to the double group chain can be built from the former by a linear transformation, which forms a basis chain. Thus, the complete energy matrix including spin singlet is constructed for Cr2+ ion in tetragonal symmetry environment in the strong-field-representation by the crystal field theory. The fine structures of absorption spectra and the spin-singlet contributions to zero-field-splitting parameters for BaCrSi4O10 and AgGaSe2:Cr2+ are studied by diagonalizing the complete energy matrix. The fine structures for the two systems and the zero-field-splitting parameters for BaCrSi4O10 are given theoretically for the first time. The fine structures are assigned by the irreducible representation of the group. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are important. The contributions arise from the interaction of the spin quintuplets with both spin triplets and spin singlets via spin-orbit coupling. However, the selection rule of spin-orbit coupling shows that the spin singlets do not affect the quintuplets directly but indirectly via the spin triplets. Thus, all spin states should be considered to obtain more accurate zero-field-splitting values.