Recall distance dependence of common intermolecular interactions

• Charge–charge interaction: $U_{q-q} \,\propto\, \frac{1}{r}$
• Charge–dipole interaction: $U_{q-\mu} \,\propto\, \frac{1}{r^2}$
• Dipole–dipole interaction (fixed orientation): $U_{\mu-\mu} \,\propto\, \frac{1}{r^3}$
• Average dipole–dipole interaction for freely rotating polar molecules (Keesom interaction): $\langle U \rangle \,\propto\, -\frac{1}{T r^6}$
• Dipole-induced dipole interaction (Debye interaction): $\langle U \rangle \,\propto\, -\frac{1}{r^6}$ and is essentially independent of temperature.
• London dispersion interaction: $U \,\propto\, -\frac{1}{r^6}$ This explains attraction between nonpolar molecules.

Check option A

Statement: The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.

Compare: $U_{q-q} \propto \frac{1}{r}, \qquad U_{q-\mu} \propto \frac{1}{r^2}$

Since $1/r^2$ goes to zero faster than $1/r$, the charge–dipole interaction approaches zero more rapidly, not charge–charge.

Therefore, A is false.

Check option B

Statement: The average potential energy of two rotating polar molecules that are separated by a distance $r$ has $1/r^3$ dependence.

For freely rotating polar molecules, the thermal average dipole–dipole interaction is: $\langle U \rangle \propto -\frac{1}{T r^6}$

So it does not vary as $1/r^3$.

Therefore, B is false.

Check option C

Statement: The dipole-induced dipole average interaction energy is independent of temperature.

Debye interaction (dipole-induced dipole) has the form: $\langle U \rangle \propto -\frac{1}{r^6}$

It does not involve temperature explicitly.

Therefore, C is true.

Check option D

Statement: Nonpolar molecules attract one another even though neither has a permanent dipole moment.

This is due to London dispersion forces, arising from instantaneous dipole-induced dipole interactions.

Therefore, D is true.

Final conclusion

Correct statements are: $\boxed{C,\ D}$

Comparison with stored correct answer

Stored answer: C, D

My derived answer matches the stored answer.