Symmetric double-well hydrogen bond

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 ... 

Quantum effects and strong interactions with vibrating surrounding atoms complicate the detailed study of proton transfer in the hydrogen bond AH B. Owing to the small mass, quantum tunneling of the proton plays an important role at a symmetric double-well potential. 

Figure 3.1 Typical potential energy curves for strong, low-barrier hydrogen bonds. The homoconjugated HjOj (a) exhibits a (relaxed) symmetric, double-well potential as a function ofthe difference of the bridging...

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. 

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. 

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. 

It was from these data that the potential function for the proton was modelled as the superposition of a double well (+ 0.8 A) with a barrier of 150-200 cm and a very narrow central well with a dissociation threshold of 1200-1400 cm, see Fig. 9.16. The energy gain upon hydrogen bond formation is a maximum when the proton is localised in the narrow central well in the totally symmetric structure. 

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... 

The second isotope effect, 87 , requires the proton and deuteron to be accurately located. The distance between the equilibrium positions of the potential energy well of double minima, symmetrical hydrogen bonds, which Ichikawa calls 7 h/h defined as q — 2i o . This distance can... 

Other structural analyses of crystals in which the bifluoride is present are listed in Table 7. One compound, p-toluidinium fluoride [C7H,oN ][HF2 ], is worthy of further comment. The first X-ray diffraction study reported a symmetrical anion (Denne and MacKay, 1971), but a later analysis showed that the proton was not centred between the two fluorines and 7 f h values were 102.5 and 123.5 pm (Williams and Schneemeyer, 1973). This can be explained not by a double minimum potential energy well but by asymmetry due to other forces, such as secondary hydrogen bonding between one end of the bifluoride anion and the N—H group of the cation. An alternative explanation attributes the asymmetry of the bifluoride hydrogen bond to an unsymmetrical crystal field caused by the cation (Ostlund and Bellenger, 1975). 

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