The reactivity of a Mo atom with H-2, N-2, and O-2 is investigated with the all-electron Linear Combination of Gaussian Type-Orbitals-Kohn-Sham-Density Functional Theory (LCGTO-KS-DFT) method. We used MoH2 to validate the DFT methodology, comparing with accurate relativistic CI results. After this validation we studied the reaction of a Mo atom with N-2 and O-2 in order to obtain an explanation of the different observed reactivities. The equilibrium geometries are characterized by their binding energies, electronic states, and harmonic frequencies. For MoN2 we found two local minima under the dissociation limit on the quintet surface that are very weakly bonded. For MoO2 we found several local minima on different potential energy surfaces. The lowest minimum for this system is a bent structure on the triplet potential energy surface. A detailed analysis of the molecular orbitals is given. We suggest a two-step charge transfer process as the mechanism of the reaction, and we found that the Mo atom is always the electron donor. The theoretical explanation of the experimental results provide a better understanding of the electronic structure and the reaction mechanism.