Waals Interactions between Nonidentical Atoms

The foregoing discussion involving van der Waals forces has been mainly limited to interactions between pairs of atoms in which the two atoms were identical (two hydrogen atoms, two neon atoms, etc.). We now need to consider the other important case, which is the van der Waals interactions between two atoms when they are not identical. (It is always assumed that van der Waals interactions in molecular mechanics can be adequately described by two-body interactions only. No three-body or higher interactions are used, and up until now at least, this has always been an adequate approximation.) We need especially to consider the interaction between carbon and hydrogen but also between any two different kinds of atoms present in a molecule. Because of the forms used for van der Waals curves, the early assumption was made that the van der Waals interaction between nonidentical atoms could be formulated in a simple way, as follows. For the van der Waals distances, if the two atoms are the same, we simply sum the two van der Waals radii to obtain the van der Waals distance. If the two atoms are not the same, we can similarly sum the van der Waals radii of those two atoms to get the van der Waals distance. This assumption is almost always made, and is a reasonable hrst approximation. 

This is the equation used in MM4. If either a or b (or both) is hydrogen, its position is measured from the offset corresponding to the electron density (discussed earlier). We continue to use this well depth approximation for interactions of all first-row and second-row atoms with one another, and it seems to work adequately. There is, however. 

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