Relaxation mechanisms hydrogen bonds

Figure 2. The two relaxational mechanisms in hydrogen bonding. F, fast mode S, slow mode B, bending mode TB, thermal bath.

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

The total Hamiltonian H should include all the vibrational modes involved in the hydrogen bond dynamics, as well as the various couplings taking place between these modes. At last, H would include the relaxation mechanisms. 

In recent years, evidence has been found that both mechanisms of proton transfer can occur for certain intramolecularly hydrogen-bonded acids. Also, new kinetic behaviour has been obtained which allows a much more detailed examination of the reaction steps in (22). Kinetic data for the second ionization of substituted phenylazoresorcinols in the presence of hydroxide ions (25) were some of the first to be obtained for an intramolecularly hydrogen-bonded acid. The reciprocal relaxation time (t ) for the approach to equilibrium in a temperature-jump experiment was measured at different hydroxide-ion concentrations. A linear dependence of x on [OH] was obtained of the form of (26) (Eigen and Kruse, 1963 Inskeep et al., 1968 Rose and Stuehr, 1971). However, careful measurements at lower hydroxide-ion concentrations (Perlmutter-Hayman and Shinar, 1975 Perl-mutter-Hayman et al., 1976 Yoshida and Fujimoto, 1977) revealed that the... 

The 13C nuclei in formic and acetic acids relax faster and show larger nuclear Over-hauser enhancements than the 13C nuclei of the methyl esters (Table 3.18) [183], Hence a methyl ester is more mobile than its parent carboxylic acid, which is dimerized via hydrogen bonding. It may also be seen that a pure DD mechanism operates in formic acid, owing to the directly bonded proton (tjc = 2.0), whereas spin rotation also contributes to 13C relaxation in methyl formate (tjc = 1.55). 

Thus, specific interactions directly determine the spectroscopic features due to hydrogen bonding of the water molecules, while unspecific interactions arise in all or many polar liquids and are not directly related to the H-bonds. Now it became clear that the basis of four different processes (terms) used in Ref. [17] and mentioned above could rationally be explained on a molecular basis. One may say that specific interactions are more or less cooperative in their nature. They reveal some features of a solid state, while unspecific interactions could be understood in terms of a liquid state of matter, if we consider chaotic gas-like motions of a single polar molecule, namely, rotational motions of a dipole in a dense surroundings of other molecules. The modem aspect of the spectroscopic studies leads us to a conclusion that both gas-like and solid-state-like effects are the characteristic features of water. In this section we will first distinguish between the following two mechanisms of dielectric relaxation ... 

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