Characterization of the dynamics in the protonic conductor CsH₂PO₄ by ¹⁷O solid-state NMR spectroscopy and first-principles calculations: Correlating phosphate and protonic motion

¹⁷O NMR spectroscopy combined with first-principles calculations was employed to understand the local structure and dynamics of the phosphate ions and protons in the paraelectric phase of the proton conductor CsH₂PO₄. For the room-temperature structure, the results confirm that one proton (H1) is localized in an asymmetric H-bond (between O1 donor and O2 acceptor oxygen atoms), whereas the H2 proton undergoes rapid exchange between two sites in a hydrogen bond with a symmetric double potential well at a rate ≥10⁷ Hz. Variable-temperature ¹⁷O NMR spectra recorded from 22 to 214 °C were interpreted by considering different models for the rotation of the phosphate anions. At least two distinct rate constants for rotations about four pseudo C₃ axes of the phosphate ion were required in order to achieve good agreement with the experimental data. An activation energy of 0.21 ± 0.06 eV was observed for rotation about the P-O1 axis, with a higher activation energy of 0.50 ± 0.07 eV being obtained for rotation about the P-O2, P-O3^d, and P-O3^a axes, with the superscripts denoting, respectively, dynamic donor and acceptor oxygen atoms of the H-bond. The higher activation energy of the second process is most likely associated with the cost of breaking an O1-H1 bond. The activation energy of this process is slightly lower than that obtained from the ¹H exchange process (0.70 ± 0.07 eV) (Kim, G.; Blanc, F.; Hu, Y.-Y.; Grey, C. P. J. Phys. Chem. C 2013, 117, 6504-6515) associated with the translational motion of the protons. The relationship between proton jumps and phosphate rotation was analyzed in detail by considering uncorrelated motion, motion of individual PO₄ ions and the four connected/H-bonded protons, and concerted motions of adjacent phosphate units, mediated by proton hops. We conclude that, while phosphate rotations aid proton motion, not all phosphate rotations result in proton jumps.