A model for an articial hydrogen molecule consisting of two positive on-axis Coulombic centers and two electrons coupled to them inside a double concentric quantum ring is considered.Such a nanostructure is assumed to be under the inuence of external probes like hydrostatic pressure and magnetic eld.By using the adiabatic approximation, the ground state energy is calculated as a function of the outer center line radius and the impurity Coulombic center separation, for dierent values of the hydrostatic pressure and magnetic eld strength.In contrast to the single properties imposed by nature on the actual hydrogen molecule, our model allows us to explore a great variety of properties of the articial hydrogen molecule by changing the ring dimensions.The articial hydrogen molecule energy structure may be tuned by changing the external eld strengths.