The question as to how zeolites are able to hold tightly bound ions is
answered. We show that zeolite frameworks can support whole bands of
rigid unit modes (floppy modes) in k space and hence show that localiz
ed rigid unit modes can form within such frameworks that do not distor
t the constituent tetrahedra to any significant degree. It is these lo
cal modes that enable cations at certain sites to pull the framework-w
ith virtually zero cost in elastic energy-in such a way that oxygen-ca
tion bonding distances become exactly optimal for the cation concerned
.