The study of the reaction of a Cr atom with H(d)2, N-2, and O-2 is performed in order to obtain an explanation of the different observed reactivities. The reactivity is investigated with the all-electron linear-combination-of-Gaussian-type-orbitals Kohn-Sham density functional theory (LCGTO-KS-DFT). The equilibrium geometries are characterized by their binding energies and harmonic frequencies. For CrH2, the lowest minimum is a quintet bent structure. The binding energy with respect to Cr + H-2 is 6.7 kcal/mol, and the electronic state is B-5(1). For CrN2, the lowest minimum is a septet linear structure. The binding energy with respect to Cr + N-2 is 4.8 kcal/mol, and the electronic state is (7) Sigma(+). For CrO2 several local minima on different potential energy surfaces were obtained. The lowest minimum for CrO2 is a bent structure on the triplet potential energy surface. The binding energy with respect to Cr + O-2 is 125.6 kcal/mol, and the electronic state is B-3(2). A detailed analysis of the molecular orbitals for the most stable structures is given. As the mechanism of the reaction, a two-step charge-transfer process is suggested, were the Cr atom is always the electron donor. The theoretical explanation of some of the available experimental results provides a better understanding of the electronic structure and the reaction mechanism.