\textbf{Dynamics of H}$_{\mathrm{\mathbf{i}}}^{\mathrm{\mathbf{+}}}$\textbf{ in Indium Oxide}*

Studies of IR absorption[1] under uniaxial stress[2] and diffusion[3] of H$_{\mathrm{i}}^{\mathrm{+}}$ as well as the dynamics of positively charged muonium[4] in In$_{\mathrm{2}}$O$_{\mathrm{3}}$ provide an experimental framework to understand these processes in detail. While the bixbyite structure[5] of In$_{\mathrm{2}}$O$_{\mathrm{3}}$ has overall cubic symmetry, its remarkable internal asymmetries lead to a number of candidate locations for H$_{\mathrm{i}}^{\mathrm{+}}$. Furthermore, the unique topology of In$_{\mathrm{2}}$O$_{\mathrm{3}}$ leads to constraints on possible H diffusion paths. We have used the CRYSTAL06 code[6] with a hybridized DFT Hamiltonian to determine equilibrium positions and vibrational frequencies for possible sites for H$_{\mathrm{i}}^{\mathrm{+}}$ and have analyzed candidate diffusion paths and processes for H$_{\mathrm{i}}^{\mathrm{+}}$ and Mu$^{\mathrm{+}}$.[1] W. Yin \textit{et al.}, Phys. Rev. B \textbf{91}, 075208 (2015). [2] P Weiser \textit{et al.}, this meeting. [3] Ying Qin \textit{et al.}, this meeting. [4] B. B. Baker \textit{et al.}, AIP Conf. Proc. \textbf{1583}, 323 (2014). [5] M. Marezio, Acta Crystallogr. \textbf{20}, 723 (1966). [6] R. Dovesi \textit{et al.}, \textit{Crystal06 User's Manual }(University of Torino, Torino, 2006).