We investigate the energetics of reactions involving pairs of alkali-metal dimers. Atom exchange reactions to form homonuclear dimers are energetically allowed for some but not all of the heteronuclear dimers. We carry out high-level electronic structure calculations on the potential energy surfaces of all the heteronuclear alkali-metal trimers and show that trimer formation reactions are always energetically forbidden for low-lying singlet states of the dimers. The results have important implications for the stability of quantum gases of alkali-metal dimers.

We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system $\mathrm{Rb}+\mathrm{Sr}$. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.

We investigate the energy levels of heteronuclear alkali-metal dimers in levels correlating with the lowest rotational level of the ground electronic state, which are important in efforts to produce ground-state ultracold molecules. We use density-functional theory to calculate nuclear quadrupole and magnetic coupling constants for KRb and RbCs and explore the hyperfine structure in the presence of electric and magnetic fields. For nonrotating states, the zero-field splittings are dominated by the electron-mediated part of the nuclear spin-spin coupling. They are a few kilohertz for KRb isotopologs and a few tens of kilohertz for RbCs isotopologs.