Theoretical prediction of local distortion in an $ErO6$ cluster: Stabilization of a $C4v$ structure by a rack and pinion effect

As a possible atomic coordination of erbium dopants surrounded by oxygen, a molecular orbital calculation of an $ErO6$ cluster can predict a $C4v$ pseudo-octahedral structure with Er distortion of ∼0.1 Å from the octahedral center. It was found that bond alternation by a “rack and pinion effect” can minimize the electron transfer from $O2−$ to $Er3+$ at this distortion range, resulting in stable ionic bonding; the rotation of an O $2p$ orbital due to Er $5d$ translation, similar to rack and pinion motion, forms a new O $2p–Er$ $5d$ bond, while a dipole moment induced by symmetrical degradation makes an O $2p–Er$ $6s$ bond unstable.