  Breathing transitions represent recently discovered adsorption-induced
structural transformations between large-pore and narrow-pore conformations in
bistable metal-organic frameworks, such as MIL-53. We present a multiscale
physical mechanism of the dynamics of breathing transitions. We show that due
to interplay between host framework elasticity and guest molecule adsorption,
these transformations on the crystal level occur via layer-by-layer shear. We
construct a simple Hamiltonian that describes the physics of host-host and
host-guest interactions on the level of unit cells and reduces to one effective
dimension due to the long-range elastic cell-cell interactions. We then use
this Hamiltonian in Monte Carlo simulations of adsorption-desorption cycles to
study how the behavior of unit cells is linked to the transition mechanism at
the crystal level through three key physical parameters: the transition energy
barrier, the cell-cell elastic coupling, and the system size.
