Giant molecules composed of polar molecules and atoms in mixed dimensions

Two or three polar molecules, confined to one or two dimensions, can form stable bound states with a single atom living in three dimensions, if the molecule and the atom can interact resonantly such that their mixed dimensional scattering length is large. We call these bound states ``giant molecules'' since it's a molecule composed of smaller molecules and atoms. We study their properties using techniques including exact numerical solution, exact qunatum diffusion Monte Carlo (QMC), Born-Oppenheimer approximation (BOA), and semiclassical approximation. These bound states have a hierarchical structure reminiscent of the celestial systems.