A new vibrational level of the H$_2^+$ molecular ion
  A new state of the H$_2^+$ molecular ion with binding energy of 1.09$\times10^{-9}$ a.u. below the first dissociation limit is predicted, using highly accurate numerical nonrelativistic quantum calculations. It is the first L=0 excited state, antisymmetric with respect to the exchange of the two protons. It manifests itself as a huge p-H scattering length of $a=750\pm 5$ Bohr radii. 
Jaume Carbonell, Rimantas Lazauskas, Dominique Delande, Laurent   Hilico, Senem K{\i}l{\i}\c{c}