The dispersion coefficients $C_6$, $C_8$, and $C_{10}$ for hydrogen molecules (${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and HD) in the three lowest pure vibrational states are computed nonadiabatically using a variational approach in Hylleraas coordinates. We also report the scalar static quadrupole polarizability ${\alpha }_2$ and octupole polarizability ${\alpha }_3$ for hydrogen molecules in their ground vibrational states. Comparisons with existing values obtained under the Born-Oppenheimer approximation show that the contribution of nuclear rotational transitions becomes non-negligible for $C_8$ and $C_{10}$ at the percentage accuracy level. This effect is particularly pronounced for ${\alpha }_2$, where nuclear rotational transitions provide the dominant contribution. Specifically, for ${\alpha }_2$ of ${\mathrm{H}}_2$ in the ground state, the contribution from electronic transitions amounts to 17.03, while that from nuclear rotational transitions reaches 58.33, resulting in a total static quadrupole polarizability of 75.36(2).

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• Atomic & molecular structure
• Long-range interactions
• Rotational states
• van der Waals interaction