This article is devoted to analyze the measures of electron–electron correlation for hydrogen molecule in ground and thermal states in presence of applied magnetic field. It is found that quantum discord is more robust then the entanglement in the sense that quantum discord have significant correlation as compared to the entanglement. It is further discovered that the quantum discord and entanglement can be controlled by thermal and magnetic effects. In addition it is investigated that the decoherence degrades both the entanglement and quantum discord. However, phase damping channels degrades more heavily compared to the amplitude damping. Finally, both the entanglement and quantum discord vanish asymptotically under decoherence, with no ESD is seen.