J. Phys. Chem. B 1998, 102, 8943-8944
Reply to the Comment on “Molecular Thermodynamics of Hydrophobic Hydration” N. A. M. Besseling* and J. Lyklema Laboratory for Physical Chemistry and Colloid Science, Wageningen Agricultural UniVersity, Dreijenplein 6, 6703 EK Wageningen, The Netherlands ReceiVed: April 1, 1998; In Final Form: August 17, 1998 Grigera et al. concluded from their simulations that a hydrophobic surface induces an increase of the degree of hydrogen bonding in water. This does not agree with our theoretical results.1,2 However, we will show that Grigera’s results are not convincing evidence that our model for hydrophobic hydration1,2 and other results obtained with the same model for water3,4 should be dismissed. Whereas our study provides a comprehensive and consistent account of structural and thermodynamic aspects, Grigera et al.’s paper only gives results on a few aspects of water structure. Only the aVerage degree of hydrogen bonding5 in a simulated box of water molecules is computed. No information is given on where in the system increased hydrogen bonding occurs, near the surface or throughout the whole system, although we know that the system is inhomogeneous and anisotropic. No results on the of thermodynamic functions (e.g., entropy and enthalpy of hydration) are provided. There are several uncertainties pertaining to the interpretation of Grigera’s finding of increased hydrogen bonding. First of all we should pay attention to the differences in the models for the hydrophobic surface, as was already suggested by Grigera et al. in their comment. Because we wanted to make a comparison with the “hydration” of vacancies, the hydrophobic surface in our study is just a repulsive wall that does not have any attractive interaction with the water molecules.1,2 In the simulations by Grigera et al., the hydrophobic surface consists of a sheet of “Lennard-Jones argon atoms” arranged as the oxygen centers of water molecules in ice. The two aspectss (i) the attractive interactions with water and (ii) the fact that the surface is commensurate with icesmight well be responsible for the increase of hydrogen bonding as found by Grigera et al. It would be interesting to find out whether the water layer(s) adjoining the surface do have ice-like ordering and whether this is also the case with a surface that is not commensurate with ice. We think it cannot be excluded that Grigera et al.’s findings are quite specific for their particular model surface and should not be generalized to hydrophobic surfaces, let alone to small hydrophobic solutes. Moreover, there is the issue of what is counted as a hydrogen bond. For real water and for any continuum model (as opposed to a discrete lattice model), the criterion is somewhat arbitrary. The criterion used by Grigera et al.5 does have its peculiarities: e.g., a configuration O-H-H-O with two protons (more or less) on a straight line between the oxygens is counted as a hydrogen bond. It would be interesting to find out whether the trends would be the same with other criteria. * Corresponding author. fax ++31 317 483777 or 484141; e-mail
[email protected].
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Finally, there are in our opinion some uncertainties in the pressure control in Grigera et al.’s simulations. This is important in this context because inaccuracies in the pressure lead to densities that are different from what they are supposed to be. Obviously, this will have its consequences for the fluid structure and the degree of hydrogen bonding. In Figure 2b of Grigera et al.’s paper,6 where density profiles of water molecules are plotted for supposedly the same pressure, the density “far” from the wall for the hydrophobic surface appears to be about 10% higher than for the hydrophilic surface. This suggests that the pressure was higher in the case of hydrophobic surface than with the hydrophilic surface. Unfortunately, the density obtained in the simulations of water without any surface is not given. Calculation of the pressure in molecular dynamics simulations is known to be difficult. The results are subject to fluctuations that are much larger than for e.g. the temperature. As a consequence, pressure control in a constant-pressure simulation will also suffer from inaccuracies. An example from the literature might give an impression of what might happen:7 In a number of simulations of water aiming for the same pressure, the resulting pressures ranged from -55 to +28 bar. In addition to these random errors in the pressure, we fear there is also a systematic flaw in the “pressure bath” in Grigera et al.’s simulations. In GROMOS84, the pressure p in a volume V containing N atoms is calculated using the virial expression
p)
(∑
2 1
N
3V 2 i)1
miVi2 +
1
N
)
∑rij‚Fij
2 i
