The Water Forcefield: Importance of Dipolar and Quadrupolar Interactions † Jose ´ L. F. Abascal* and Carlos Vega Departamento de Quı ´mica Fı ´sica, Facultad de Ciencias Quı ´micas, UniVersidad Complutense, 28040 Madrid, Spain ReceiVed: June 7, 2007; In Final Form: August 11, 2007 It is widely recognized that dipolar interactions play a fundamental role in water. Less emphasis is put on the effects dues to the quadrupole moment. The recent calculation of the phase diagram for several rigid, nonpolarizable water models has shown that this is a rather severe test for water potentials. In this work, we analyze the results yielded by popular three-point-charge water models (TIP3P, SPC, SPC/E, TIP4P, TIP4P- Ew, TIP4P/2005, and TIP4P/Ice) and attempt to correlate them with the molecular dipoles and quadrupoles. It is shown that the melting temperatures of the proton disordered ices depend almost linearly on the quadrupole moments. However, the relative stability of ice II with respect to ices III, V, and VI seems to be rather dependent on the ratio of dipolar/quadrupolar forces. Small departures from a given ratio increase the stability of ice II and result in a serious deterioration of the phase diagram. Simple expressions are derived for the dipole and quadrupole moments, which allow us to analyze the effect of these multipole moments in the phase diagram when the rest of the molecular parameters are fixed. Satisfactory results for both the melting temperatures and for the relative stability of the different ices are obtained only when the molecular quadrupole approaches that of the isolated water molecule. Or, expressed in terms of the model parameters, acceptable results require that the negative charge be shifted from the oxygen toward the hydrogen positions by 0.14 Å or more. I. Introduction Water is probably the most studied substance in nature. This is not only a consequence of its importance in our everyday life, but it is also due to its peculiar behavior which makes it the target of a great number of theoretical investigations. Both sources of interest (theoretical and practical) are closely related since many industrial and biochemical processes ultimately rely on its unusual physicochemical properties. Hence, there is interest in an adequate description of the intermolecular interac- tions in water. The complexity of the water properties together with the different possible levels of description have led to the proposal of hundreds of models (see the excellent review by Guillot 1 for a critical analysis of the results yielded by these models). At first, it would seem feasible that an analytical fit of ab initio calculations of the potential energy surface (PES) of water dimers could provide accurate potential functions. 2 Unfortunately, the results did not confirm the expectations. This is because the procedure has a number of limitations. The first is due to the reduced number of points used to represent the potential energy surface. Besides, since the potential energy represents only a small fraction of the total energy of the system, the precision of the calculations may compromise the results. Moreover, calculations based on the water dimer or more complex water clusters do not necessarily give an accurate representation of water in condensed phases. For these reasons, most of the popular water models are still empirical. However, promising results have been recently obtained with more refined electronic calculations. This is the case, for instance, of the MCDHO model 3 obtained from a fit of a refined ab initio single molecule deformation PES. 4 These calculations provide quali- tatively important information on the interactions between water molecules. In fact, some models incorporate features obtained in ab initio calculations. For instance, in the PPC model, 5 the polarization produced by an external field or by other molecules determines the electrostatic terms of the force field, while the short-range interactions are calculated as those in empirical models, that is, they are optimized to reproduce several properties of liquid water at 298 K. Ab initio calculations are also a source of information about the values of the dipole and higher multipole moments of the water molecule in different environments. All of the studies indicate that the mean value of the dipole moment in condensed phases is larger than that of the isolated molecule (1.85 D). However there is a nonnegligible uncertainty in these results. The first estimation of the “experimental” dipole moment of the hexagonal ice Ih (which cannot be directly measured) was 2.6 D, 6 but this estimate has been challenged by several authors. Recent calculations yield the value μ ) 3.09 D. 7 This result is slightly larger than the “experimental” dipole moment of liquid water at 298 K, μ ) 2.95 D, which has been recently reported 8 based on experimental data with some support of ab initio calculations and molecular dynamics results for popular water models. The experimental value is in the upper range of ab initio simulations of liquid water, which give a relatively large spread of values (from 2.43 9 to 2.95 D 10 ) due to the different ways of assignment of the electronic density to individual molecules. It is interesting that the mean μ values calculated in simulations of polarizable water models exhibit a similar range of values. 4,11-13 Thus, a literature survey clearly indicates that the relation between the dipole moments of ice Ih, liquid water, and gas- phase water are μ ice gμ l > μ g . High-quality quantum mechanical calculations such as those performed by Probert and reported in the book by Petrenko and Whitworth 14 show that the contour of the total electron density † Part of the “Keith E. Gubbins Festschrift”. 15811 J. Phys. Chem. C 2007, 111, 15811-15822 10.1021/jp074418w CCC: $37.00 © 2007 American Chemical Society Published on Web 10/06/2007