This study investigates the chemical mechanisms of PN and NS formations in the interstellar medium, comets and the atmosphere of giant planets such as Saturn and Jupiter. The quantum chemical calculations were performed by using the CCSD and CCSD(T) levels of theory. The basis sets used in this study were 6- 311++G(d,p) and 6-311++G(3df,3pd). Geometry optimizations, frequencies and single-point energies were calculated to propose energy diagrams for the chemical mechanisms of PN and NS formations. Transition states were proposed for these chemical mechanisms and their energies calculated. The chemical reaction paths were proposed for the PN formation. The PN molecule may be formed by the 2NH2 + 2PH2, 3NH + 3PH, 2NH2 + 3PH, 4N + 3PH, 4P + 3NH and 4P + 2NH2 reactions. The 4N + PH3 and the 4N + 2PH2 reactions are spin-forbidden. Their probabilities of hopping between the two potential energy surfaces are insignificant by using the Landau-Zenner Theory. For the NS formation, the following chemical reaction paths are energetically favorable: 1NH + 2SH, 3S + 2NH2 and 1NH + 1H2S reactions. The 4N + 2SH - 1NSH reaction is spinforbidden. Using the Landau-Zenner Theory, the probability of hopping between the two potential energy surfaces is unimportant. The chemical mechanisms for the PN and NS formations are presented, which is important for the understanding about the chemistry of the interstellar medium, comets and atmosphere of giant planets.