  We analyze the pressure-induced metal-insulator transition in a
two-dimensional vertical stack of $H_2$ molecules in x-y plane, and show that
it represents a striking example of the Mott-Hubbard-type transition. Our
combined exact diagonalization approach, formulated and solved in the second
quantization formalism, includes also simultaneous ab initio readjustment of
the single-particle wave functions, contained in the model microscopic
parameters. The system is studied as a function of applied side force
(generalized pressure), both in the $H_2$-molecular and $H$-quasiatomic states.
Extended Hubbard model is taken at the start, together with longer-range
electron-electron interactions incorporated into the scheme. The stacked
molecular plane transforms discontinuously into a (quasi)atomic state under the
applied force via a two-step transition: the first between molecular insulating
phases and the second from the molecular to the quasiatomic metallic phase. No
quasiatomic insulating phase occurs. All the transitions are accompanied by an
abrupt changes of the bond length and the intermolecular distance (lattice
parameter), as well as by discontinuous changes of the principal electronic
properties, which are characteristic of the Mott-Hubbard transition here
associated with the jumps of the predetermined equilibrium lattice parameter
and the effective bond length. The phase transition can be interpreted in terms
of the solid hydrogen metallization under pressure exerted by e.g., the
substrate covered with a monomolecular $H_2$ film of the vertically stacked
molecules. Both the Mott and Hubbard criteria at the insulator to metal
transition are discussed.
