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This is an analytical investigation of well-known 10–12 potential of hydrogen–hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6–12 Lennard–Jones potential in case of this type of bond. Though the results are illustrated in many text books and literature, an analytical analysis for these potentials is missing almost everywhere. The power laws are valid for small radial distances, which are calculated to some extent. The internuclear separation as well as the binding energy of the hydrogen molecule are evaluated with success.