Model 2D Treatment

The 2D model [28, 33, 35, 56] enables one to get a qualitative agreement with the available structural and spectroscopic regularities established for molecular crystals with a quasi-symmetric 0- -H- -0 fragment. However, a strong dispersion of the experimental points implies that the considered properties do not depend on one variable (R ), but on several other characteristics there are first bending of the O -H -O fragment, the chemical composition of the compound, and the crystal structure. To get a semi-quantitative, and in some cases quantitative, agreement with experiment, one has to increase the dimensionality of the PES, for example see [66-68], and to take into account effects of the crystalline environment, see Section 9.3. 

In some H-bonded systems, for example the hydrogen maleate ion [69], vibrations of the O-H-O fragment are mixed strongly with the other vibrations. This implies that Eq. (9.2) is not applicable to such systems and the F function depends on other vibrational coordinates, in particular, the CO stretch mode. 

In the case of synchronous proton transfer in cyclic H-bonded clusters consisting of a single type of monomer the s and R coordinates can be treated as totally symmetric OH and 0---H---0 stretches [70]. In order to compute anharmonic frequencies of the IR active asymmetric OH stretch the asymmetric coordinate a, see Eq. (9.12b), is to be taken into consideration, for example see Refs. [62, 71]. 

It was mentioned in Section 9.2.3.1 that two different model 2D PESs were used to evaluate the temperature dependence of the nuclear spin-lattice relaxation time in benzoic acid dimer. The problem arising in this connection is how to choose values for the fitting parameters entering the model PESs. In most investigations they are defined from the experiment to be interpreted. Unfortunately the potentials determined this way are as a rule unable to properly describe other experimental regularities and data (spectroscopic, structural) known for the same compounds. Moreover the agreement between theory and experiment disappears if the fitting parameter values are taken, for example, from spectroscopic data [72]. 

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