Heavy atom tunneling, hydrogen bonds

Heavy atom tunneling of entire alkyl groups between the different sides of the hydrogen bonded ring plane is much less likely even for methanol, in contrast to the analogous but fighter water case [108]. These motions correspond to hindered rotation of the monomer and are slowed down considerably in the complex due to the librational constraints. 

Let the chain obey the periodical boundary conditions and let protons be strongly connected with heavy atoms, so that tunnel proton transitions along the hydrogen bond are negligible in comparison with the reorientation motion of A—H groups. This means that only one proton is localized near each heavy atom in the chain that is, equality + /z/ / i = 1 holds, which makes it possible to introduce the following pseudo-spin operators ... 

Thus starting from the simplest pseudo-spin model of proton dynamics in the hydrogen bond, we have studied a possibility of spontaneous tunnel oscillations of the polarization of a short hydrogen-bonded chain. The phenomenon can be affected by two reasons (a) the coherent motion of protons along the hydrogen bonds and (b) the coherent motion of protons around heavy backbone atoms. 

The heavy atom contribution reduces generally the value of kg /kg. For example, if during H-tunneling in an OHO-hydrogen bond over 2a = 0.5 A both oxygen atoms are displaced, each by 2a = 0.05 A, it follows that Am= 0.32, and the total tunneling mass is 1.32 instead of 1. 

Tuckeeman, M. F., Marx, D., Heavy-atom skeleton quantization and proton tunneling in intermediate-barrier hydrogen bonds, Phys. Rev. Lett. 2001, 86, (21), 4946-4949. 

The double hydrogen bond in principle facilitates two mechanisms of double proton transfer stepwise and concerted. Studying the transfer rates within the semi-classical tunneling approximation of the variational transition state theory, Kim found that the two protons are transferred synchronously across the transition state with D2h symmetry [194], The actual proton-tunneling distance is considerably reduced due to the contraction of the hydrogen bonds, i.e., heavy atom motion promotes the proton transfer. On the other hand, the ab initio path-integral Car-Parinello calculations predict that the motion of the two protons in the vicinity of the potential minima is... 

Finally, we note that in all cases besides the heavy atom motions leading to hydrogen bond compression as well as the minor heavy atom motions during proton tunneling no major reorganization of the environment takes place. 

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