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ION–SOLVENT INTERACTIONS 211

Thus,

and

One can now use the binomial expansion, i.e.,

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and drop off all terms higher than the third. Thus,

and, omitting all terms with powers r greater than 3, one has

Further,

Subtracting Eq. (A2.3.16) from Eq. (A2.3.15), one has

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It is at this stage that the treatment of ion–quadrupole interactions diverges from that of ion–dipole
interactions (cf. Appendix 2.2). In the latter, the binomial expansion was terminated after the second term.