  The clustering and drift properties of barium ions in xenon gas are explored
theoretically, using density functional theory and computational ion mobility
theory, with the goal of better understanding barium ion transport for
neutrinoless double beta decay. We derive the equilibrium conformations,
energies and entropies of molecular ions in the Ba$^{+}$-Xe and Ba$^{++}$-Xe
systems, which yield a predictive model of cluster formation in high pressure
gas. We calculate ion-neutral interaction potential curves for these species
and use them to predict effective molecular ion mobilities. Our calculation
consistently reproduces experimental data on effective mobility and molecular
ion formation for the Ba$^+$ system, and predicts strong cluster formation in
the Ba$^{++}$ system, dominated by stable [BaXe$_6$]$^{++}$,[BaXe$_7$]$^{++}$,
[BaXe$_8$]$^{++}$ and [BaXe$_9$]$^{++}$ complexes in the range of interest.
Some implications for barium tagging in gas-phase neutrinoless double beta
decay experiments are discussed, and the first predictions of
pressure-dependent mobility of the doubly charged Ba$^{++}$ species are
presented.
