  The processes of ionization and energy transfer in a quantum system composed
of two distant H atoms with an initial internuclear separation of 100 atomic
units (5.29 nm) have been studied by the numerical solution of the
time-dependent Schr\"odinger equation beyond the Born-Oppenheimer
approximation. Thereby it has been assumed that only one of the two H atoms was
excited by temporally and spatially shaped laser pulses at various laser
carrier frequencies. The quantum dynamics of the extended H-H system, which was
taken to be initially either in an unentangled or an entangled ground state,
has been explored within a linear three-dimensional model, including two z
coordinates of the electrons and the internuclear distance R. An efficient
energy transfer from the laser-excited H atom (atom A) to the other H atom
(atom B) and the ionization of the latter have been found. It has been shown
that the physical mechanisms of the energy transfer as well as of the
ionization of atom B are the Coulomb attraction of the laser driven electron of
atom A by the proton of atom B and a short-range Coulomb repulsion of the two
electrons when their wave functions strongly overlap in the domain of atom B.
