The observation of coherent tunnelling in ${\mathrm{Cu}}^{2+}$- and ${\mathrm{Ag}}^{2+}$-doped MgO and $\mathrm{Ca}\mathrm{O}:{\mathrm{Cu}}^{2+}$ was a crucial discovery in the realm of the Jahn-Teller (JT) effect. The main reasons favoring this dynamic behavior are now clarified through ab initio calculations on ${\mathrm{Cu}}^{2+}$- and ${\mathrm{Ag}}^{2+}$-doped cubic oxides. Small JT distortions and an unexpected low anharmonicity of the $e_g$ JT mode are behind energy barriers smaller than $25{\mathrm{cm}}^{-1}$ derived through CASPT2 calculations for ${\mathrm{Cu}}^{2+}$- and ${\mathrm{Ag}}^{2+}$-doped MgO and $\mathrm{Ca}\mathrm{O}:{\mathrm{Cu}}^{2+}$. The low anharmonicity is shown to come from a strong vibrational coupling of $M{\mathrm{O}}_6^{10-}\text{units}$ $(M=\mathrm{Cu},\mathrm{Ag})$ to the host lattice. The average distance between the $d^9$ impurity and ligands is found to vary significantly on passing from MgO to SrO following to a good extent the lattice parameter.

• Received 28 July 2005

DOI:https://doi.org/10.1103/PhysRevB.72.155107