Given the primordial role that water plays in life and our everyday lives, the development of high quality interaction potentials for this ubiquitous material is of great interest. Such models can be obtained "on the fly," as in Carr-Parrinello simulations, 1 or by fitting the results of high level ab initio calculations for clusters to an analytical expression. 2 Another route is to use an empirical potential whose parameters are fine tuned so as to reproduce experimental properties. 3 Once

more »

... potential energy surface ͑PES͒ is known computer simulations can be performed using either classical or quantum statistical mechanics to describe the probability density distribution of the molecules on this PES. Evidence that nuclear quantum effects in water are important is steadily growing. 4-8 If the PES is obtained from first principles calculations then, since one is obtaining the true PES ͑although in an approximate manner͒, it is clear that quantum statistical mechanics should be used to describe the motion of the nuclei. In the case of empirical potentials one can use either classical or quantum statistical mechanics, depending on whether the potential parameters were obtained to reproduce experimental properties of water within classical or quantum simulations, respectively. Recently we have proposed two empirical potentials: the TIP4P/2005 ͑Ref. 9͒ to be used in classical simulations and TIP4PQ/2005 10,11 to be used in path-integral ͑PI͒ simulations. Both of these models are rigid and nonpolarizable. In this note we shall focus on the heat capacity C p at constant pressure along the p = 1 bar isobar for the two aforementioned models. For the TIP4P/2005 model the values of C p obtained from classical simulations for ice I h and water have been reported previously. 12,13 For TIP4PQ/2005 we shall calculate C p using the simulation results for the enthalpy taken from our recent work on the ice phases 10 and water. 11 These were obtained from PI simulations of water ͑ice͒ using 300 ͑432͒ molecules and isotropic ͑anisotropic͒ NpT ensemble simulations. The Lennard-Jones part of the potential was truncated at 8.5 Å, adding long range corrections to both the energy and pressure, and using Ewald sums. The rigid-body rotational propagator was taken from the work of Müser and Berne. 14 For the fluid phase we used P = 7 replicas, and for ice I h the number of replicas was selected such that PT Ϸ 1500 K. The heat capacity is obtained as the first derivative of the enthalpy with respect to the temperature at constant pressure. The enthalpies of the fluid phase ͑for seven temperatures͒ 11 have been fitted variously to either a second or third order polynomial. For ice I h the enthalpies ͑at T = 77, 100, 125, 150, 200, 250, and 273 K͒ have been fitted to the expression H = a + bT 2 + cT 3 . This expression satisfies the third law of thermodynamics and provided an excellent description of the experimental enthalpies 15 of ice I h up to the melting temperature. In Fig. 1 the experimental 15 and TIP4PQ/2005 PI results for the heat capacity of ice I h and water are presented. By including nuclear quantum effects it is, for the first time, possible to describe the C p of ice I h and liquid water over a broad range of temperatures. On the other hand, results from classical simulations of TIP4P/2005 fail in describing C p for all temperatures considered in this work. Although the failure of the classical treatment at low T was expected ͑such a treatment does not satisfy the third law so C p is not zero at 260 270 280 290 300 T (K) 0 4 8 12 16 20 24 C p (cal mol -1