Unconventional Chemical Bonding of Lanthanide-OH Molecules

We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. We focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restricted-active-space self-consistent field method combined with spin-orbit coupling as well as a relativistic coupled-cluster method. In addition, electric dipole and magnetic moments are computed with the self-consistent field method. Analysis of the results from both methods shows that the dominant molecular configuration of the ground state is one where an electron from the partially filled and submerged 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most 6s$^2$ lone electron pair of the lanthanide atom intact in sharp contrast to the bonding in alkaline-earth monohydroxides and YbOH, where an electron from the outer-most s shell moves to the hydroxyl group. For linear molecules the projection of the total electron angular momentum on the symmetry axis is a conserved quantity with quantum number $Ω$ and we study the polynomial $Ω$ dependence of the energies of the ground states as well as their electric and magnetic moments. We find that the lowest energy states have $|Ω|=15/2$ and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these $Ω$ states is approximately $hc\times 1\,000$~cm$^{-1}$. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units. The magnetic moments are closely related to that of the corresponding atomic Ln$^+$ ion in an excited electronic state. We also realize that the total electron angular momentum is to good approximation conserved and has a quantum number of 15/2 for both triatomic molecules.