  We present the first theoretical treatment of the formation of highly excited
neutral H atoms (H$^{*}$) for strongly driven H$_{2}$. This process, with one
electron ionizing and one captured in a Rydberg state, was recently reported in
an experimental study in Phys. Rev. Lett {\bf 102} 113002 (2009). We show that
two mechanisms underlie this process: a non-sequential one resembling
non-sequential double ionization, and a sequential one resembling double
ionization through enhanced ionization. We also predict a new feature,
asymmetric energy sharing between H$^{*}$ and H$^{+}$ with increasing
intensity. This feature is a striking demonstration of the influence the
electron has on the nuclear motion.
