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The isotope effect in the melting temperature of ice Ih has been studied byfree energy calculations within the path integral formulation of statisticalmechanics. Free energy differences between isotopes are related to thedependence of their kinetic energy on the isotope mass. The water simulationswere performed by using the q-TIP4P/F model, a point charge empirical potentialthat includes molecular flexibility and anharmonicity in the OH stretch of thewater molecule. The reported melting temperature at ambient pressure of thismodel (T = 251 K) increases by 6.5+-0.5 K and 8.2+-0.5 K upon isotopicsubstitution of hydrogen by deuterium and tritium, respectively. Thesetemperature shifts are larger than the experimental ones (3.8 K and 4.5 K,respectively). In the classical limit, the melting temperature is nearly thesame as that for tritiated ice. This unexpected behavior is rationalized by thecoupling between intermolecular interactions and molecular flexibility. Thiscoupling makes the kinetic energy of the OH stretching modes larger in theliquid than in the solid phase. However the opposite behavior is found forintramolecular modes, which display larger kinetic energy in ice than in liquidwater.

Quantum path integral simulation of isotope effects in the melting temperature of ice Ih