Orientational disorder of the molecular carbonate anions in BaCO3, which occurs naturally as the mineral witherite, has been studied using a combination of neutron total scattering analysed by the Reverse Monte Carlo method and molecular dynamics simulations. The primary focus is on the phase transition to the cubic phase, which assumes a rocksalt structure (Strukturbericht type B1) with highly disordered orientations consistent with the mismatch between the site (m3m) and molecular (3/m) symmetries. Both experiment and simulation show a high degree of disorder, with the C-O bond orientation distribution never exceeding 25% variation from that of a completely uniform distribution, although there are differences between the two methods regarding the nature of these variations. Molecular dynamics simulations are also reported for the analogous phase transitions in the very important mineral calcite, CaCO3. The combination of the simulations and comparison with BaCO3 shows that the properties of calcite at all temperatures within its stability field are affected mostly by the onset of orientational disorder associated with the high-temperature cubic phase, even though this lies outside the stability field of calcite. This is a new understanding of calcite, which previously had been interpreted purely in terms of the phase transition to an intermediate partially-disordered phase. Finally, we also found that witherite itself appears to support the development of orientational disorder on heating, with the simulations showing a sequence of phase transitions that explain the much larger thermal expansion of one axis