Temperature Dependence of the Hydrophobic Hydration and Interaction of Simple Solutes: An Examination of Five Popular Water Models

We examine five different popular rigid water models (SPC, SPCE, TIP3P, TIP4P and TIP5P) using MD simulations in order to investigate the hydrophobic hydration and interaction of apolar Lennard-Jones solutes as a function of temperature in the range between $275 {K}$ and $375 {K}$. For all investigated models and state points we calculate the excess chemical potential for the noble gases and Methane.All water models exhibit too small hydration entropies, but show a clear hierarchy. TIP3P shows poorest agreement with experiment whereas TIP5P is closest to the experimental data at lower temperatures and SPCE is closest at higher temperatures. A rescaling procedure inspired by information theory model of Hummer et al. ({\em Chem.Phys.}258, 349-370 (2000)) suggests that the differences between the different models and real water can be explained on the basis of the density curves at constant pressure. In addition, the models that give a good representation of the water structure at ambient conditions (TIP5P, SPCE and TIP4P) show considerably better agreement with the experimental data than SPC and TIP3P. We calculate the hydrophobic interaction between Xenon particles directly from a series of 60 ns simulation runs.We find that the temperature dependence of the association is related to the strength of the solvation entropy. Nevertheless, differences between the models seem to require a more detailed molecular picture.The TIP5P model shows by far the strongest temperature dependence.The suggested density-rescaling is also applied to the Xenon-Xenon contact-pair configuration, indicating the presence of a temperature where the hydrophobic interaction turns into purely repulsive.The predicted association for Xenon in real water suggest the presence a strong variation with temperature.Comment: 19 pages, 16 figures, revtex4 twocolums, removed typos, accepted for publication in J.Chem. Phy

Heat Capacity Effects Associated with the Hydrophobic Hydration and Interaction of Simple Solutes: A Detailed Structural and Energetical Analysis Based on MD Simulations

We examine the SPCE and TIP5P water models to study heat capacity effects associated with the hydrophobic hydration and interaction of Xenon particles. We calculate the excess chemical potential for Xenon employing the Widom particle insertion technique. The solvation enthalpy and excess heat capacity is obtained from the temperature dependence of the chemical potentials and, alternatively, directly by Ewald summation, as well as a reaction field based method. All three different approaches provide consistent results. The reaction field method allows a separation of the individual components to the heat capacity of solvation into solute/solvent and solvent/solvent parts, revealing the solvent/solvent part as the dominating contribution. A detailed spacial analysis of the heat capacity of the water molecules around a pair of Xenon particles at different separations reveals that the enhanced heat capacity of the water molecules in the bisector plane between two Xenon atoms is responsible for the maximum of the heat capacity observed at the desolvation barrier, recently reported by Shimizu and Chan ({\em J. Am. Chem. Soc.},{\bf 123}, 2083--2084 (2001)). The about 60% enlarged heat capacity of water in the concave part of the joint Xenon-Xenon hydration shell is the result of a counterplay of strengthened hydrogen bonds and an enhanced breaking of hydrogen bonds with increasing temperature. Differences between the two models concerning the heat capacity in the Xenon-Xenon contact state are attributed to the different water model bulk heat capacities, and to the different spacial extension of the structure effect introduced by the hydrophobic particles. Similarities between the different states of water in the joint Xenon-Xenon hydration shell and the properties of stretched water are discussed.Comment: 14 pages, 16 figures, twocolumn revte

How the Liquid-Liquid Transition Affects Hydrophobic Hydration in Deeply Supercooled Water

We determine the phase diagram of liquid supercooled water by extensive computer simulations using the TIP5P-E model [J. Chem. Phys. {\bf 120}, 6085 (2004)]. We find that the transformation of water into a low density liquid in the supercooled range strongly enhances the solubility of hydrophobic particles. The transformation of water into a tetrahedrally structured liquid is accompanied by a minimum in the hydration entropy and enthalpy. The corresponding change in sign of the solvation heat capacity indicates a loss of one characteristic signature of hydrophobic hydration. The observed behavior is found to be qualitatively in accordance with the predictions of the information theory model of Garde et al. [Phys. Rev. Lett. {\bf 77}, 4966 (1996)].Comment: 4 pages, 4 figures, twocolumn Revtex, modified text applied changes to figure 1, 2d, 3,

An OrthoBoXY-Method for Various Alternative Box Geometries

We have shown in a recent contribution [J. Phys. Chem.B 127, 7983-7987 (2023)] that for molecular dynamics (MD) simulations of isotropic fluids based on orthorhombic periodic boundary conditions with "magic" box length ratios of $L_z/L_x\!=\!L_z/L_y\!=\!2.7933596497$, the computed self-diffusion coefficients $D_x$ and $D_y$ in $x$- and $y$-direction become system size independent. They thus represent the true self-diffusion coefficient $D_0\!=\!(D_x+D_y)/2$, while the shear viscosity can be determined from diffusion coefficients in $x$-, $y$-, and $z$-direction, using the expression $\eta\!=\!k_\mathrm{B}T\cdot 8.1711245653/[3\pi L_z(D_{x}+D_{y}-2D_z)]$. Here we present a more generalized version of this "OrthoBoXY"-approach, which can be applied to any orthorhombic MD box. We would like to test, whether it is possible to improve the efficiency of the approach by using a shape more akin to the cubic form, albeit with different box-length ratios $L_x/L_z\!\neq\! L_y/L_z$ and $L_x\!<\!L_y\!<\!L_z$. We use simulations of systems of 1536 TIP4P/2005 water molecules as a benchmark and explore different box-geometries to determine the influence of the box shape on the computed statistical uncertainties for $D_0$ and $\eta$. Moreover, another "magical" set of box-length ratios is discovered with $L_y/L_z\!=\!0.57804765578$ and $L_x/L_z\!=\!0.33413909235$, where the self-diffusion coefficient in $x$-direction becomes system size independent, such that $D_0\!=\!D_x$.Comment: 7 pages, 4 figures. Corrected typos and errors and added an additional new equation (now eq 7). arXiv admin note: text overlap with arXiv:2307.0159

OrthoBoXY: A Simple Way to Compute True Self-Diffusion Coefficients from MD Simulations with Periodic Boundary Conditions Without Prior Knowledge of the Viscosity

Recently, an analytical expression for the system size dependence and direction-dependence of self-diffusion coefficients for neat liquids due to hydrodynamic interactions has been derived for molecular dynamics (MD) simulations using orthorhombic unit cells. Based on this description, we show that for systems with a ``magic'' box length ratio of $L_z/L_x\!=\!L_z/L_y\!=\!2.7933596497$ the computed self-diffusion coefficients $D_x$ and $D_y$ in $x$- and $y$-direction become system-size independent and represent the true self-diffusion coefficient $D_0\!=\!(D_x+D_y)/2$. Moreover, by using this particular box geometry, the viscosity can be determined with a reasonable degree of accuracy from the difference of components of the diffusion coefficients in $x$-,$y$- and $z$-direction using the simple expression $\eta\!=\!k_\mathrm{B}T\cdot 8.1711245653/[3\pi L_z(D_{x}+D_{y}-2D_z)]$. MD simulations of TIP4P/2005 water for various system-sizes using both orthorhombic and cubic box geometries are used to test the approach.Comment: 5 pages, 1 figure, 2 table

Hydrogen bonding in a mixture of protic ionic liquids: A molecular dynamics simulation study

We report results of molecular dynamics (MD) simulations characterising the hydrogen bonding in mixtures of two different protic ionic liquids sharing the same cation: triethylammonium-methylsulfonate (TEAMS) and triethylammonium-triflate (TEATF). The triethylammonium-cation acts as a hydrogen-bond donor, being able to donate a single hydrogen-bond. Both, the methylsulfonate- and the triflate-anions can act as hydrogen-bond acceptors, which can accept multiple hydrogen bonds via their respective SO3-groups. In addition, replacing a methyl-group in the methylsulfonate by a trifluoromethyl-group in the triflate significantly weakens the strength of a hydrogen bond from an adjacent triethylammonium cation to the oxygen-site in the SO3-group of the anion. Our MD simulations show that these subtle differences in hydrogen bond strength significantly affect the formation of differently-sized hydrogen-bonded aggregates in these mixtures as a function of the mixture-composition. Moreover, the reported hydrogen-bonded cluster sizes can be predicted and explained by a simple combinatorial lattice model, based on the approximate coordination number of the ions, and using statistical weights that mostly account for the fact that each anion can only accept three hydrogen bonds