The vibrational modes of double six-member ring (D6R) clusters with general composition (Mn+)(x/n) H12Si12-xAlxO18 (where x = 0, 2; M = H+, Li+, Na+, K+, Ca2+) are studied by DFT with the B3LYP method. The point group symmetry of the fragments with Si,Al substitution descends from C-2h with AlO(SiO)(3)Al linkages, via C-2v, with AlO(SiO)(2)Al linkages in one T6O6 ring of a D6R, to C-s, where the Al atoms are closely spaced in an AlOSiOAl sequence. The C-2h symmetry fragments represent centrosymmetric structures with maximum separation of Al atoms. The lower symmetry fragments C-2v, and C-s describe the band broadening, which arises from specific Si,Al distributions. The ring-opening vibrations, defined as in-phase radial displacement of tetrahedral and oxygen atoms parallel to the ring plane, are correlated to the framework vibrations of the zeolite structures, which contain D6R as secondary building units. The oxygen atom displacements are part of the ring-opening vibrations in the 200-600 cm(-1) frequency range. The vibration assigned to the D6R in zeolites, based on previous empirical studies, is calculated at 570-600 cm(-1) for cluster models with Si/Al = 5 ratio and Al atoms at different positions. Both the shape and frequency of this vibration are sensitive to the specific Si,AI ordering and also to the type and position of the extraframework cations.