The total attractive interaction
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص636-637
2025-12-16
40
The total attractive interaction
We shall consider molecules that are unable to participate in hydrogen bond formation. The total attractive interaction energy between rotating molecules is then the sum of the three van der Waals contributions discussed above. (Only the dispersion interaction contributes if both molecules are nonpolar.) In a fluid phase, all three contributions to the potential energy vary as the inverse sixth power of the separation of the molecules, so we may write V=−
where C6 is a coefficient that depends on the identity of the molecules. Although attractive interactions between molecules are often expressed as in eqn 18.27, we must remember that this equation has only limited validity. First, we have taken into account only dipolar interactions of various kinds, for they have the longest range and are dominant if the average separation of the molecules is large. However, in a complete treatment we should also consider quadrupolar and higher-order multi pole interactions, particularly if the molecules do not have permanent electric dipole moments. Secondly, the expressions have been derived by assuming that the molecules can rotate reasonably freely. That is not the case in most solids, and in rigid media the dipole–dipole interaction is proportional to 1/r3 because the Boltzmann averaging procedure is irrelevant when the molecules are trapped into a fixed orientation. A different kind of limitation is that eqn 18.27 relates to the interactions of pairs of molecules. There is no reason to suppose that the energy of interaction of three (or more) molecules is the sum of the pairwise interaction energies alone. The total dispersion energy of three closed-shell atoms, for instance, is given approximately by the Axilrod–Teller formula:
Where , C′= a (3 cos θA cos θB cos θC + 1) , The parameter a is approximately equal to 3–4α′C6; the angles θ are the internal angles of the triangle formed by the three atoms (14). The term in C′ (which represents the 14 non-additivity of the pairwise interactions) is negative for a linear arrangement of atoms (so that arrangement is stabilized) and positive for an equilateral triangular cluster. It is found that the three-body term contributes about 10 per cent of the total interaction energy in liquid argon.
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