Proton transfer in benzoic acid crystals: A chemical spin–boson problem. Theoretical analysis of nuclear magnetic resonance, neutron scattering, and optical experiments

Abstract

The double proton transfer in benzoic acid crystals can be described by a double-minimum potential. At low temperatures one need consider only the two lowest energy eigenstates, which must be coupled to the crystalline phonons in order to obtain relaxation. Thus the benzoic acid system provides a well-defined chemical example of the spin–boson Hamiltonian. Within this model the tunneling relaxation between localized states occurs by one-phonon emission or absorption. Alternatively, at high temperatures the proton transfer is thermally activated. With this simple picture in mind we analyze NMR T1 relaxation experiments. The temperature-dependent proton transfer rate that emerges from the NMR analysis is in good agreement with inelastic neutron scattering experiments. Optical transitions of a dye probe have also been used to determine proton transfer rates in crystalline benzoic acid. Our model allows us to discuss both doped and pure crystal experiments within a unified framework. Thus, we find that all three different experimental probes yield results that are consistent with our simple theoretical picture. From our results we can determine the proton–phonon coupling constant.