Barriers and Splittings

All theoretical studies on benzoic acid dimer underlined the need for a multidimensional potential surface. These studies have investigated the temperature dependence of the transfer process They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al. [26] have calculated the temperature dependence of the spin-lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be 

3 kcal moH. The same assisted proton transfer was found in calculations of the synchronous proton transfer in benzoic acid crystal by Antoniou and Schwarz [27]. It was shown, that for benzoic acid dimer a coupling to the low frequency intramolecular modes will lower the effectively required activation energy. 

In all these calculations it was found that although the activation energy seems to be rather low, which might support the occurrence of classical over barrier reactions, the actual process is, however, a pure quantum mechanical tunneling process. 

The benzoic acid dimer has been extensively studied in various condensed phase environments where it experiences an asymmetric local environment. By doping the crystal the inherent asymmetry in the crystal was reduced. However, in general, the crystal structure and the dopant can influence the observed tunneling matrix element. 

From these experiments the tunneling matrix element of (dye-doped) benzoic acid was determined and was found to be relatively independent of the dopant used [28, 29]. The measured values lie between 8.4 GHz (0.28 cm ) [28] and 6.56 GHz (0.22 cm-i) [29]. 

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