  The internal electric field of a Rydberg atom electron can bind a polar
molecule to form a giant ultralong-range stable polyatomic molecule. Such
molecules not only share their properties with Rydberg atoms, they possess huge
permanent electric dipole moments and in addition allow for coherent control of
the polar molecule orientation. In this work, we include additional Rydberg
manifolds which couple to the nearly degenerate set of Rydberg states employed
in [S. T. Rittenhouse and H. R. Sadeghpour, Phys. Rev. Lett. 104, 243002
(2010)]. The coupling of a set of $(n+3)s$ Rydberg states with the $n(l>2)$
nearly degenerate Rydberg manifolds in alkali metal atoms leads to pronounced
avoided crossings in the Born-Oppenheimer potentials. Ultimately, these avoided
crossings enable the formation of the giant polyatomic Rydberg molecules with
standard two-photon laser photoassociation techniques.
