Molecular dynamics simulations of rigid and flexible water models: Temperature dependence of viscosity J.S. Medina a , R. Prosmiti a,⇑ , P. Villarreal a , G. Delgado-Barrio a , G. Winter b , B. González b , J.V. Alemán c , C. Collado c a Instituto de Física Fundamental (CSIC), Serrano 123, 28006 Madrid, Spain b SIANI, ULPGC, Edif. Polivalente, 35017 Las Palmas de G. Canaria, Spain c Facultad de Ciencias del Mar, ULPGC, Campus Universitario de Tafira, 35017 Las Palmas de G. Canaria, Spain article info Article history: Received 27 April 2011 In final form 3 July 2011 Available online 13 July 2011 Keywords: Molecular dynamics simulations Liquid water models Viscosity calculations abstract Molecular dynamics (MD) simulations are carried out on a system of rigid or flexible water molecules at a series of temperatures between 273 and 368 K. Collective transport coefficients, such as shear and bulk viscosities are calculated, and their behavior is systematically investigated as a function of flexibility and temperature. It is found that by including the intramolecular terms in the potential the calculated viscos- ity values are in overall much better agreement, compared to earlier and recent available experimental data, than those obtained with the rigid SPC/E model. The effect of the intramolecular degrees of freedom on transport properties of liquid water is analyzed and the incorporation of polarizability is discussed for further improvements. To our knowledge the present study constitutes the first compendium of results on viscosities for pure liquid water, including flexible models, that has been assembled. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Understanding the structure and dynamics of water clusters and of bulk water is crucial in many areas of science, such as phys- ics, chemistry, material science and biology [1,2]. As a result, liquid water has been the subject of intense research, experimental and theoretical, for many decades. However, recent interpretation of X-ray absorption, X-ray Raman, and X-ray emission spectroscopy experiments has been quite controversial [3–8], with the local structure in liquid water being still a subject of debate, and many of its dynamical properties are not yet well understood [9]. Theoretical water models and computational simulations have played an important role in the interpretation of experimental measurements and in understanding its physical properties (see Refs. [10–13] and references therein). In a recent review by Paesani and Voth [14] various computer modeling simulations, providing a comprehensive representation of water properties at molecular level, have been reported with a particular emphasis on theoretical and computational methodologies that combine a proper quantum–mechanical treatment of the nuclear dynamics with an accurate description of the potential surface. Over the last 40 years, numerous water models, depending on the problem to handle, have been developed ranging from empirical ones, with parame- ters fitted to experimental data [15–19], to ab initio, which have been parametrized using the results of quantum chemistry calcula- tions mainly of the water dimer and larger clusters, [20–27] or have been computed ‘‘on the fly’’ from first-principles density functional approaches. [11,28,29] In general, as the degree of com- plexity of the model increases, the computational requirements are also increasing, and it is important to understand the role played by each new added or reparametrized potential term (e.g. electro- static, Van der Waals, intramolecular and polarization). Such im- proved models should reproduce better more properties of water, and as there is still a long way from calculating properties of any water model in understanding the real behavior of the liquid water, a systematic study by employing different interaction potentials is a rational route to follow. In this work, we undertake an examination of collective trans- port properties for pure liquid water, such as shear and bulk vis- cosities. The shear viscosity of a liquid is a measure of the shear stress relaxation, and when viscosity increases strongly with low- ering temperature the behavior is attributed to a rapidly increasing relaxation time, and the onset of slow dynamics. A physical inter- pretation of both shear and bulk viscosities in terms of molecular motion, given by Temkin [30], associates the shear viscosity only with the translational motion of the molecules, while the bulk vis- cosity is related with both rotational and vibrational intermolecu- lar degrees of freedom. Thus, it is interesting to study in detail the direct dependence of the viscosities on molecular interaction by both experiment and theory. Further, the shear and bulk viscosities are important properties especially in bio-simulations, [31,32] and 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.07.001 ⇑ Corresponding author. E-mail address: rita@iff.csic.es (R. Prosmiti). Chemical Physics 388 (2011) 9–18 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys