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

The isotope effect in the melting temperature of ice Ih has been studied by free energy calculations within the path integral formulation of statistical mechanics. Free energy differences between isotopes are related to the dependence of their kinetic energy on the isotope mass. The water simulations were performed by using the q-TIP4P/F model, a point charge empirical potential that includes molecular flexibility and anharmonicity in the OH stretch of the water molecule. The reported melting temperature at ambient pressure of this model (T = 251 K) increases by 6.5+-0.5 K and 8.2+-0.5 K upon isotopic substitution of hydrogen by deuterium and tritium, respectively. These temperature shifts are larger than the experimental ones (3.8 K and 4.5 K, respectively). In the classical limit, the melting temperature is nearly the same as that for tritiated ice. This unexpected behavior is rationalized by the coupling between intermolecular interactions and molecular flexibility. This coupling makes the kinetic energy of the OH stretching modes larger in the liquid than in the solid phase. However the opposite behavior is found for intramolecular modes, which display larger kinetic energy in ice than in liquid water.