Hydrogen bond, double potential well

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... 

An asymmetric hydrogen bond is common even where a proton coordinates two equivalent anions. The rc-bond repulsive forces between two coordinated anions tend to prohibit a close X-H-X separation, so competition between the two equivalent anions for the shorter X-H bond may set up a double-well potential for the equilibrium proton position between the two coordinated anions. With oxide anions, an O-H-O separation greater than 2.4 A sets up a double-well potential and creates an asymmetric hydrogen bond, which we represent as O-H O. Although displacement toward one anion may be energetically equivalent to a displacement toward the other, one well is made deeper than the other by an amount AH, as a result of the motion of the proton from the centre of the 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 ... 

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. 

First consideration for the motion of the hydrogen atom in double-well potentials were proposed by Kovner and Chuenkov [64] and Hadzi [65], However, the detailed analysis of the separability of the X H stretching vibrations (with energy about 3000 cm1) from the hydrogen bond vibrations (with energy around 100 cm-1) in the linear triatomic X H Y system was carried out by Marechal and Witkowski [66]. 

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. 

It was recently evidenced [55] that also very short OHO hydrogen bonds reveal a low-barrier double-well potential. This was shown in the case of hydrogen bond with the length of 2.393 A in 4-cyano-2,2,6,6-tetramethyl-3,... 

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...

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