  The interaction between a Rydberg electron and a neutral atom situated inside
its extended orbit is described via contact interactions for each atom-electron
scattering channel. In ultracold environments, these interactions lead to
ultra-long-range molecular states with binding energies typically ranging from
$10$-$10^4$MHz. These energies are comparable to the relativistic and hyperfine
structure of the separate atomic components. Studies of molecular formation
aiming to reproduce observations with spectroscopic accuracy must therefore
include the hyperfine splitting of the neutral atom and the spin-orbit
splittings of both the Rydberg atom and the electron-atom interaction.
Adiabatic potential energy curves that fully include these additional effects
are presented for Rb$_2$ and Cs$_2$. The influence of spin degrees of freedom
on the potential energy curves and molecular multipole moments probed in recent
experimental work is elucidated and contrasted with other recent theoretical
effort in this direction.
