Quantum mechanical analysis of kinetic isotope effect

The melting temperature $T_m$ and the boiling temperature of a substance $T_b$ of a substance and it’s isotope are not the same. For example, if we consider water with hydrogen (light water) and hydrogen with deuterium (heavy water), $T_{m,light} = 0 ^{circ} C, T_{m,heavy} = 3.81 ^{circ} C$, and $T_{b,light}=100^{circ} C, T_{b,heavy} = 101.42 ^{circ} C$.

Classical statistical mechanics cannot predict the existence of such differences in phase transition properties, so we have to rely on quantum statistical mechanics. Since this is not an ideal gas, the kinetic energy and potential energy of the system, does not commute, the partition function of the system would be different. How would I go about writing the partition function of such a system, whose potential and kinetic energies do not commute?

Secondly, why is the effect smaller for $T_b$ smaller for $T_m$?

I would appreciate any advice you have for me. Thank you!