Subject interaction energy

The equations we have written until now in this section impose no restrictions on the species they describe or on the origin of the interaction energy. Volume and entropy effects associated with reaction (8.A) will be less if x is not too large. Aside from this consideration, any of the intermolecular forces listed above could be responsible for the specific value of x- The relationships for ASj in the last section are based on a specific model and are subject to whatever limitations that imposes. There is nothing in the formalism for AH that we have developed until now that is obviously inapplicable to certain specific systems. In the next section we shall introduce another approximation... 

Here is the energy gain or loss when a site reconstructs. The lateral interaction energies and V2s between nearest (a) and next nearest (b) (and further) neighbors are most likely attractive to favor the growth of domains that are either reconstructed or unreconstructed. If V2s were repulsive then a c(2 x 2) pattern of alternately reconstructed and unreconstructed cells would be favored. A gas phase particle can adsorb either on the unreconstructed ui = 0 or 1) or the reconstructed surface (r, = 0 or 1) subject to the constraints... 

Suppose now that the system is subjected to an oscillating electromagnetic field with a representative Fourier component of the electric field F0( >] cos cot. The predominant term in the interaction energy V is usually the electric dipole term Ei , e.g. for an electron in an atom... 

More sensitive to the level of theory is the vibrational component of the interaction energy. In the first place, the harmonic frequencies typically require rather high levels of theory for accurate evaluation. It has become part of conventional wisdom, for example, that these frequencies are routinely overestimated by 10% or so at the Hartree-Fock level, even with excellent basis sets. A second consideration arises from the weak nature of the H-bond-ing interaction itself. Whereas the harmonic approximation may be quite reasonable for the individual monomers, the high-amplitude intermolecular modes are subject to significant anharmonic effects. On the other hand, some of the errors made in the computation of vibrational frequencies in the separate monomers are likely to be canceled by errors of like magnitude in the complex. Errors of up to 1 kcal/mol might be expected in the combination of zero-point vibrational and thermal population energies under normal circumstances. The most effective means to reduce this error would be a more detailed analysis of the vibration-rotational motion of the complex that includes anharmonicity. 

Marcus presented a thorough discussion related to this subject, where the different experimental techniques useful to characterize hydration numbers are carefully evaluated. He concluded that for a given ion-water interaction energy, geometric limitations define coordination numbers, while d5mamic hydration numbers are determined by the mean residence time of the water... 

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