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Loosely bound van der Waals dimers of lanthanide atoms, as might be obtained in ultracold atom experiments, are investigated. These molecules are known to exhibit a degree of quantum chaos, due to the strong anisotropic mixing of their angular spin and rotation degrees of freedom. Within a model of these molecules, we identify different realms of this anisotropic mixing, depending on whether the spin, the rotation, or both, are significantly mixed by the anisotropy. These realms are in turn generally correlated with the resulting magnetic moments of the states.

Ultracold collisions of LiO molecules in the $^{2}\Pi_{3/2}$ ground state are considered, under the influence of either an external magnetic or electric field. Inelastic collisions are shown to be suppressed in the presence of modest laboratory strength magnetic and electric fields. The rate of elastic collisions that rethermalize the thermal distribution, and the corresponding low rate of heating state-changing collisions, suggest that quantum degeneracy or even molecular Bose-Einstein condensation of LiO gas may be attainable, provided that the initial temperatures in the milliKelvin range are achievable.

Ultracold collisions of the polyatomic species CaOH are considered, in internal states where the collisions should be dominated by long-range dipole-dipole interactions. The computed rate constants suggest that evaporative cooling can be quite efficient for these species, provided they start at temperatures achievable by laser cooling. The rate constants are shown to become more favorable for evaporative cooling as the electric field increases. Moreover, long-range dimer states (CaOH)$^*_2$ are predicated to occur, having lifetimes on the order of microseconds., Comment: 18 pages, 8 figures

Cold collisions of $^{14}$N$^{16}$O molecules in the $^{2}\Pi_{1/2}$ ground state, subject to electric and magnetic fields, are investigated. It is found that elastic collision rates significantly exceed state-changing inelastic rates only at temperatures above 0.5 K at laboratory strength fields. It is found, however, that in very large fields $> 10^{4}$ V/cm, inelastic rates can be somewhat suppressed. Magnetic fields have negligible influence on scattering for this nearly non-magnetic state.