Symmetric single-well hydrogen bond

Figure 17. (a) One-dimensional potential curve and squared ground state wave function (schematically) of a symmetric single-well hydrogen bond ALB, L = H, D. (b) Chemical shifts S(ALB) (schematically) of B and L as a function of qi. The average chemical shift of D is larger than for H because of the maximum of S(ALB) and the narrower wave function of D compared with H. By contrast, as 5(ALB) is a linear function of qi, 5(AHB) = 5(ADB), reprinted from Ref [78] by permission granted by Wiley-VCh. 

The dominant intermolecular interaction in vater is hydrogen bonding. The introduction of an excess proton (i.e. the formation of a protonic defect) leads to the contraction of hydrogen bonds in the vicinity of such a defect. This corresponds to the vell-kno vn structure forming properties of excess protons in water (see for example Ref. [26]). Thus the isolated dimer H5O2+ finds its energetic minimum at an O / O separation of only 240 pm [27, 28[ with an almost symmetrical single well potential for the excess proton in the center of the complex. 

The single particle auto-correlation time tc in Eq. 9 can, of course, exhibit also a non-critical temperature dependence. Consider a set of independent hydrogen bonds with symmetric double well potentials and a barrier a between the wells. In this case the motion is thermally activated and tc shows an Arrhenius behaviour ... 

Fig. 2 (a) Two inde[>endent single-well potential curves for the vibrating OH groups, (b) The double-well potential curve for the hydrogen-bonded OH group (-OH 0= vs. =0- HO-). The solid curve indicates a symmetric combination of the two individual proton wave-functions and the broken curve is for an antisymmetric combination. The tunnelling splitting (Ao) is also shown. 

In all Type A crystals, the hydrogen bond has a symmetrical potential-energy curve. In many acid salts, with open structures, the O- -H- -O distance in the double-anion, R COgHO C R, is close to 2.44 A. In a smaller number of chelated, but otherwise similar, structures, the 0- H - 0 distance is somewhat shorter and there are stereochemical reasons for this. For the latter cases, the hydrogen bond probably is genuinely symmetrical, with a single-well potential. Some, at least, of the open Type A structures may also contain symmetrical 0---H---0 bonds. 

Structural data from in situ high pressure ND studies are analyzed in [163], they show that the O-H and H- - -O distances follow the same correlations as have been established at ambient conditions on different compounds. Another pressure effect is the evolution of the double-welled, hydrogen bond potential into a single-well potential. According to ab initio calculations, the bulk modulus must have a discontinuity at this point and this can be an indication for hydrogen bond symmetrization it means that the hydrogen bond symmetrization is a second-order phase transition. 

Mobile protons could be transferred in two types of motions (1) Protons could rattle back and forth between symmetric minima of the effective substrate potential energy. The minima are located at hydrogen bond distance from either of the two neighboring SGs. The double well potential, experienced by the intermittent proton, depends on the equilibrium separation of SGs and on their fluctuations. Similar to what happens in the formation of a Zundel ion in water, the double well potential may transform into a single well potential upon close approach of neighboring SGs. Spontaneous symmetry-breaking, associated with these proton motions, leads to the... 

Introduction of a second adsorbed ammonia molecule in the neighboring position generates a weak potential barrier in this rotation (broken line in Fig. 7b), which decreases with increase of the distance between the two adsorbed species. The most influenced intramolecular vibration after the adsorption is the umbrella, connected with molecular inversion of the three N-H bonds in gas-phase ammonia. Stronger attraction of the nitrogen atom to the siuface and repulsion of the hydrogens converts the symmetric double-well inversion potential of the gas molecule into a distorted single well (Fig. 8). This change in the potential ciuve modifies the distances between the vibrational levels for this mode. 

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