  While the hydrogen molecular ion is the simplest molecule in nature and very
well studied in all of its properties, it remains an interesting system to use
for explorations of fundamental questions. One such question treated in this
study relates to finding an optimal adiabatic representation of the physics,
i.e. the best adiabatic description that minimizes the role of nonadiabatic
effects. As a test case explored here in detail, we consider the ungerade
symmetry of H$_2^+$, which is known to have a huge scattering length of order
750 bohr radii, and an incredibly weakly bound excited state. We show that a
hyperspherical adiabatic description does an excellent job of capturing the
main physics. Our calculation yields a competitive scattering length and shows
that nonadiabatic corrections are small and can even be adequately captured
using the postadiabatic theory of Klar and Fano.
