Interaction energy between methane

The interaction energy between methane and water can then be expressed as... 

Molecular orbital theories (ab initio methods (23)) were chosen and validated in this study to characterize the interaction energies between methane and water, while electron density functional theories (24) were tested, but found to be inadequate (see below). Four different ab initio methods were used in the validation MP2 (25,26), MP4(SDTQ) (27), QCISD(T) (28) and CCSD(T) (29). Three different DFT methods, BLYP (30Jl), B3LYP (32) and BPW91 (33), were used and the results compared with the ab initio methods. In addition, for each of the above methods, the effect of the size of different basis sets was investigated specifically, 6-31++G(2d,2p), cc-pVDZ, cc-pVTZ and cc-pVQZ were used. 6-31+-i-G(2d,2p) was chosen, because it was reported to yield reasonable results compared with that at near the basis set limit on this system (77). The others were chosen in order to observe the effect of systematically increasing the size of the basis set. Gaussian 94 (22) was used for all the above calculations. 

TABLE 2 Arithmetic Average Distance and Interaction Energy" between a Methane Molecule and Touching nearest Neighbors Water Molecules (Type A Water Molecules) in the Ousters CH4" (H20) ... 

TABLE 5 The Average Distance and Interaction Energy between a Water Molecule and nearest Methane Molecules in the Clusters H20-"(CH4) ... 

The Dilute Mixture of Water in Methane. When one molecule of water is surrounded by methane molecules, the molecule of water behaves like a regular nonpolar molecule (see Figure 2, where one of the typical minimized clusters 1 (water) 10 (methane) is presented). The average intermolecular distance and interaction energy between a water molecule and the nearest neighbors methane molecules in the clusters H20 "(CH4)io are listed in Table 5. 

In this paper, the Mpller—Plesset perturbation theory was applied to clusters formed by one molecule of methane and several molecules of water, or one molecule of water and several molecules of methane. The goal was to determine the inter-molecular distances and interaction energies between a water molecule and a methane molecule in the clusters CH4 (H20) and H20 (CH4) and to compare the obtained results with available experimental data. 

In the same figure we also show the distance dependence of the effective interaction energy between the two spheres. The results have been obtained by eomputer simulations where the spheres are methane molecules. Note the pronounced minimum between the two spheres at contact and then the maximum at intermediate distances. The interaction energy falls off to zero as the two spheres move away. In some cases, one finds a second minimum at a distance beyond the maximum [10]. Such a minimum at a larger separation is referred to as a solvent separated pair and arises due to the structuring around the hydrophobic spheres. 

The arguments behind the d band model are quite general and should apply to the interactions in the transition state as well as in the initial and final (adsorbed) states of the process. We therefore expect correlations between the d band center and transition state energies to be the same as for chemisorption energies. This is illustrated in the bottom panel of Figure 4.10. Figure 4.16 shows in detail how the activation energy for methane on different Ni surfaces scales with the center of the d bands projected onto the appropriate metal states to which the transition state couples. 

Kass argued that 2r is stabilized by an interaction between the radical orbital on Cx and ct(C2-C3) orbital. This allows the radical to delocalize, especially onto C3. As listed in Scheme 3.2, the spin densities at Cj and C3 are quite similar, 0.59 and 0.34, respectively. A further manifestation of this delocalization is the short Cl -C3 distance (1.493 A) in 2r compared to that in 2 (1.512 A). This orbital interaction is negligible in the anion 2cb because it is a filled-filled interaction. The charge density is much more localized onto Cj for 2a than is the spin density for 2r. Consequently, 2r is more stable than expected, leading 2 to have a smaller BDE than anticipated. 2 thus has the acidity of an acetylene but the bond energy of methane. ... 

In Figure 6-8(a), the energy of the HOMO of B is well below that of the LUMO of HA. Because the lowest molecular orbital is only slightly lower than the HA orbital, and the middle orbital is higher than the B orbital, little or no reaction occurs. In aqueous solution, interactions between water and molecules with almost no acid-base character, such as CH4, fit this group. Little or no interaction occurs between the hydrogens of the methane molecule arid the lone pairs of surrounding water molecules. 

If we neglect the difference between electrostatic and dispersion interaction energies, then, in accordance with the concept of volume filling of micropores described previously, the equation of adsorption of methane on zeolite L will be expressed by Ref. 3 as... 

The interaction energies were calculated between a central methane molecule and all the water molecules located not further than 4.1 A from the central methane molecule (type A water molecules) as arithmetic averages. The values listed for the distances are also arithmetic averages. 

Figure 3. The dependence of the interaction energy (a) and average distance (b) between a methane molecule and water molecules of type A in the clusters CH4 (H20) on the number of water molecules in the cluster n.

Ab initio quantum mechanical methods were recently applied to the analysis of large clusters formed of one solute molecule and several molecules of solvent for water/methane mixtures. It was shown that they can provide information regarding the interaction energies and intermolecular distances between the molecules of methane and water. The obtained results were compared to the available experimental and molecular simulations regarding condensed mixtures, and agreement was found. A similar methodology of calculations will be used in the present paper as well. 

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