Methane -water interaction

Szalewicz and co-workers have fit force fields to SAPT data for numerous other particular systems, including the Ne-HCN complex (Murdachaew et al., 2001), the methane-water interaction (Akin-Ojo and Szalewicz, 2005), and the interaction of CO2 with itself (Bukowski et al., 1999), dimethylnitramine, acetonitrile, or methyl alcohol (Bukowski and Szalewicz, 1999). 

Figure 15 Normalized energy autocorrelation function (ACF) of methane-water interaction energies in S-I methane hydrate at various temperatures at a time slice of 1 ps (3-4 ps) (inset) the full 20 ps ACF. Reprinted with permission from N. J. English and J. S. Tse, Phys. Rev. Lett., 103, 015901 (2009). Copyright 2009 American Physical...

Arthur and Haymet s calculation of the hydration free energy of methane illustrates how various simulation pathways are possible in the staged FEP approach. " In their work, X was used to scale the full methane-water interaction potential rather than the size and well-depth parameters separately. Results displayed in Figure 7 show a very different X dependence for the free energy compared to the results of Figure 6, yet the final answer (1.92 0.72 kcal/mol) is still in good agreement with the experimental value. Their calculation was performed only in the more reliable insertion direction. 

Methane-water interactions are of significant interest. Not only is this system an important model of hydrophobic interactions, but methane-water clathrates (also commonly called methane hydrates) are one of the largest energy resources on Earth. These clathrates are nonstoichiometric mixtures of the two molecules, with the water molecules forming a cage (clathrate) around a methane molecule. Even conservative estimates predict that methane clathrates... 

A recent Monte Carlo study of structure of the dilute aqueous solution of methane from this Laboratory involves one methane molecule and 124 water molecules at 25°C at liquid water density. The configurational energy of the system is developed under the assumption of pairwise additivity using potential functions representative of initio quantum mechanical calculations for both the water-water and methane-water interactions. For the water-water interaction we have carried over the MCY-CI potential function used in our previous study of the structure of liquid water reviewed in the preceeding section. For the methane water interaction energy, we have recently reported an analytical potential function representative of quantum mechanical calculations based on SCF calculations and a 6-31G basis set, with correlation effects Included via second order Moller-Plesset (MP) corrections,52 This function was used for the methane-water con-... 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

Methane - Water System. Interaction parameters were generated for the vapor phase and the aqueous liquid phase for the methane -... 

A constant interaction parameter was capable of representing the mole fraction of water in the vapor phase within experimental uncertainty over the temperature range from 100°F to 460°F. As with the methane - water system, the temperature - dependent interaction parameter is also a monotonically increasing function of temperature. However, at each specified temperature, the interaction parameter for this system is numerically greater than that for the methane - water system. Although it is possible for this binary to form a three-phase equilibrium locus, no experimental data on this effect have been reported. 

The Mpller—Plesset perturbation theory will be employed in this paper to investigate the mixture methane/water. We selected this mixture because it is an ideal candidate for investigating the hydrophobic hydration. The mixture methane/water has also importance in understanding the structure and intermolecular interactions of the methane hydrates, though the specifics of these hydrates will not be addressed in this paper. These hydrates constitute a major potential fuel reserve. 

It would be ideal to use for these calculations molecular clusters containing a single molecule of a solute and many (dozens or even hundreds of molecules) of a solvent. Unfortunately, at the present time, the ab initio methods based on the Mpller—Plesset perturbation theory have computational limitations regarding the size of the cluster. " Therefore, we will have to compromise between a dilute solution and a relatively small number of solvent molecules. The largest investigated molecular clusters will contain a single molecule of methane (water) surrounded by 10 molecules of water (methane). To verify whether this cluster (1 10) is sufficiently large to capture the essential physics of the interactions, the same procedure will... 

Figure 13. Interaction energy curve of a methane-water complex oriented as shown in Fig. 12. The curve has been computed at the MP2/aug-cc-pvTZ level and the interaction energy has been corrected by the BSSE.

Table 9. C-H- O interaction energy computed for the methane-water complex using the MP2 method. The BSSE-uncorrected ( ) and BSSE-corrected ( cp) energies are given in kcal/mol. The BSSE is also indicated. The geometry is the optimum MP2/aug-cc-pVTZ geometry...

As already mentioned above, the stability of the C-H- -O in the prototypical methane-water complex originates in the combination of electrostatics and dispersion (see Table 2), the latter terms being similar in strength to the electrostatic term. Thus, the situation is very different to that found in the Ar-Ar van der Waals bond, where the dispersion term (—0.28 kcal) is much stronger than the electrostatic term (—0.04 kcal/mol). As a consequence, the C-H- - -O hydrogen bond in methane water retains some of the directionality of the 0-H- - -O bonds. This fact added to the nondominant character of these interactions in... 

Figure 14. Variation of the MP2 BSSE-uncorrected and BSSE-corrected interaction energies of the methane-water complex with the basis set. Circles indicate results obtained using Pople basis set, while squares indicate results obtained with the aug-cc-pVxZ basis sets. The geometry is the optimum one computed at the MP2/aug-cc-pVTZ level.

Table 12. Value of the BSSE-corrected MP2/aug-cc-pVTZ interaction energy for the indicated systems, computed at their optimum geometry, computed at the MP2/aug-cc-pVTZ (methane-water), or MP2/6-31+G(d) (the other two complexes) levels...

In order to obtain a direct and more accurate pressure determination, various internal pressure calibrants (e.g. quartz and ruby chips) are generally used. Internal calibrants, however, could not be used in the high temperature hydrothermal experiments due to interactions with the chemical system. In such cases, one of the more prevalent phases of the chemical system was calibrated as pressure indicator. For fluid-rich systems (methane-water), the pressures were also determined using the known phase equilibria of the methane hydrate decomposition and using shifts in the ruby fluorescence peak [8]. 

Typically we wouldn t expect a nonpolar molecule, such as methane, to interact with a polar molecule, such as water. So, then, how is this structure formed As we have studied earlier, water molecules interact with one another by strong hydrogen bonding. In the frozen state, these hydrogen-bonded water molecules form an open latticework. The nonpolar methane molecule is simply trapped inside one of the spaces within the lattice. 

Methane molecules interact with the surface by the dispersion mechanism. If doing so, they can adsorb both in nanopores and on oxidized carbon atoms and positions of junction of graphene planes. The maximum value of the A8 parameter for methane is equal to -6 ppm, which is by 3 ppm smaller than for water. On the assumption that graphene plane nanopores affect the chemical shifts for any adsorbed molecules in the same way, it is possible to draw a conclusion that the nanopores contain about two-thirds of all the adsorbed methane molecules. 

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