  By treating idealized zeolite frameworks as periodic mechanical trusses, we
show that the number of flexible folding mechanisms in zeolite frameworks is
strongly peaked at the minimum density end of their flexibility window. 25 of
the 197 known zeolite frameworks exhibit an extensive flexibility, where the
number of unique mechanisms increases linearly with the volume when long
wavelength mechanisms are included. Extensively flexible frameworks therefore
have a maximum in configurational entropy, as large crystals, at their lowest
density. Most real zeolites do not exhibit extensive flexibility, suggesting
that surface and edge mechanisms are important, likely during the nucleation
and growth stage. The prevalence of flexibility in real zeolites suggests that,
in addition to low framework energy, it is an important criterion when
searching large databases of hypothetical zeolites for potentially useful
realizable structures.
