  The melting point of ice Ih, as well as the temperature of maximum density
(TMD) in the liquid phase, has been computed using the path integral Monte
Carlo method. Two new models are introduced; TIP4PQ_D2O and TIP4PQ_T2O which
are specifically designed to study D2O and T2O respectively. We have also used
these models to study the "competing quantum effects" proposal of Habershon,
Markland and Manolopoulos; the TIP4PQ/2005, TIP4PQ/2005 (D2O) and TIP4PQ/2005
(T2O) models are able to study the isotopic substitution of hydrogen for
deuterium or tritium whilst constraining the geometry, while the TIP4PQ_D2O and
TIP4PQ_T2O models, where the O-H bond lengths are progressively shortened,
permit the study of the influence of geometry (and thus dipole moment) on the
isotopic effects. For TIP4PQ_D2O - TIP4PQ/2005 we found a melting point shift
of 4.9 K (experimentally the value is 3.68K) and a TMD shift of 6K
(experimentally 7.2K). For TIP4PQ_T2O - TIP4PQ/2005 we found a melting point
shift of 5.2 K (experimentally the value is 4.49K) and a TMD shift of 7K
(experimentally 9.4K).
