Double harmonic approximation, hydrogen

Take a mean value of 80 (i.e., 0.83 eV). Numerical calculations show that T] < 0.2 V is the condition up to which 9.38 yields the experimental version of Tafel s law (of course, the value depends on the Fs chosen and the allowed T, for the applicability of 9.38 will be roughly halved at the lower limit and doubled at the higher one. In any case, this harmonic approximation, which is involved in the Weiss—Marcus theory, cannot be applied to the experimental current-potential data, which in reality extend over 0.2 V and even 1.0 V (for hydrogen and oxygen evolution). 

The thermodynamic treatment discussed so far employed the harmonic approximation. Its use for weak intermolecular interactions is, however, not entirely justified. With strong vdW molecules (of course, except strong hydrogen-bonded complexes, vide supra) we can hope that the anharmonicity (in connection with thermodynamic treatment) does not play a crucial role. There exists another complication concerning complexes possessing a double-minimum on energy hyper-surface. If the minima are separated by low energy barrier the harmonic approximation is not adequate . The role of anharmonicity is essential with true vdW molecules. Unfortunately, except for the H O... HF and (HjO), complexes no complete experimental thermodynamic characteristics are available for the for-... 

The weak hydrogen bond, case 1, is a double minimum - high barrier in which the proton s motion is approximately harmonic and the deuteron s more so. Their motions are centred around the same point so that their shielding is roughly the same and thus there is no change in 6 on going from one to the other. The vast majority of hydrogen bonds are of this weak variety. 

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