  A ground state atom immersed in the wave function of the valence electron of
a Rydberg atom can generate a long-range Rydberg molecule (LRRM). In this work,
using the multipole expansion of the electrostatic interaction in prolate
spheroidal coordinates, approximate and compact expressions of the
electrostatic potential that determine the chemistry of trilobite and butterfly
LRRM are explored. It is shown that even the spheroidal monopole term can be
used to describe general features of the potential generated by a LRRM at short
distances. It is also shown that even at long separations that allow a
perturbative description of the intermolecular interaction between two LRRM,
the convergence of the multipole spheroidal expansion is faster than that of
its spherical analogue.
