Proton tunneling in benzoic acid crystals at intermediate temperatures: Nuclear magnetic resonance and neutron scattering studies

The dynamics of proton transfer along the hydrogen bonds of dimers of benzoic acid has been characterized in single crystals and powders at temperatures between 10 K and 110 K by quasi-elastic neutron scattering (QENS) and by proton spin-lattice relaxation using field-cycling NMR spectroscopy. These measurements define the geometry of the proton transfer, the energy difference between the two tautomers of benzoic acid corresponding to the two proton positions, as well as the proton correlation time. The proton jump vector agrees well with expectations from recent crystallographic data. The energy difference between tautomers of ${\mathrm{A/k}}_B\text{=86.5±1.5\hspace{0.17em}}\mathrm{K}$ is in contradiction with the lower value of ${\mathrm{A/k}}_B\text{=50\hspace{0.17em}}\mathrm{K}$ derived from older ${}^{\mathrm{13}}\mathrm{C}$ NMR and infrared absorption measurements. NMR and QENS measurements provide mutually consistent values of the proton correlation time, ${\tau }_c,$ and an accurate characterization of the dynamics at temperatures where the onset of thermally activated processes is observed. Tunneling in an excited vibrational level, as well as multiphonon transitions between the lowest tunneling levels, are expected to contribute to these dynamics and are discussed. The inverse correlation time for the proton dynamics over the entire temperature range between 0 K and ambient temperature is well represented by the expression: ${\text{1/τ}}_c{\text{={1.72×10}}^8\hspace{0.17em}\coth {\text{(43/T)+10}}^{10}\hspace{0.17em}\exp \text{(−180/T)}$ ${\text{+6.3×10}}^{11}\hspace{0.17em}\exp \text{(−600/T)}\hspace{0.17em}}{\mathrm{s}}^{\mathrm{-1}}.$