A systematic attempt to estimate the quantitative validity of the charge‐dipole model of cation hydration is made by giving the model a quantum‐theoretical structure. It is shown, in the first order of approximation, that physically reasonable results may be obtained for the proton affinity of H2O and the Gibbs potential and entropy of hydrate water. The calculated proton affinity, for example, is different by about 20% from the average of the observed values. It is concluded that because of the structural simplicity of the charge‐dipole model a truly quantitative theory of cation hydration may be developed by perturbation‐theoretic techniques and the incisive choice of parameters to define the multipole field of the water molecule.
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The monomer population in liquid water at room temperature does not appear to be a limiting factor. See
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6.
It should be pointed out that the coefficient of η in the bracketed term in Eq. (9) depends to some extent upon the method of discarding terms in when reducing Eq. (6). The general form of this coefficient (for which we thank the referee) is , where s is a real number satisfying For values of between zero (the one we choose) and there does not appear to be much effect on the lower‐lying values of E. Therefore, since our solution of Eq. (6) turns out to be valid for no harm is done in choosing However, the reader is to be reminded that, even in the present approximation, the values of may differ by a few percent, depending upon the way Eq. (6) is reduced.
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See H. Margenau and G. M. Murphy, The Mathematics of Physics and Chemistry (D. Van Nostrand Co., Inc., Princeton, N.J., 1956), Vol. 1, pp. 128–131.
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The equilibrium value will be smaller than for an oriented dipole. Thus, should be slightly larger than 0.96 Å. The difference, however, is not at all large, as can be seen by minimizing and calculating in terms of
16.
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It may be argued that an unphysical decoupling of the interand intramolecular vibrational modes of the hydrate molecules is implied by considering the and the and separately. Against this argument is the fact that a normal‐coordinate analysis of the planar molecule‐ion using the force constants for water vapor and those derivable from Eq. (2) shows that the intramolecular vibrational modes are shifted in frequency by less than 5% in the most severe case
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G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Co., Inc., Princeton, N.J., 1945).
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© 1967 American Institute of Physics.
1967
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