The electronic structure and relative stability of [H8Si8-xAlxO12](x-) structural fragments with Si and Al atoms located at tetrahedral sites and connected by bridging oxygen atoms so as to form a tetragonal prism, together with oxygen-coordinated charge-compensating cations, are studied by the B3LYP/G-31G(d) method. Clusters with Al/Si ratios in the 0-1 range and different orderings of the extraframework cations and Si and Al at tetrahedral sites are proper models for the double four-member rings, which an secondary building units of the LTA structure. The stability of the structure fragments is higher when the framework＇s negative charges are at maximum distance, in agreement with Dempsey＇s rule. The HOMO orbitals of H8Si8O12, the anionic clusters [H8Si8-xAlxO12](x-), and the proton-balanced ones are mainly O 2p nonbonding AO. In fragments with Al/Si > 0 and Na+ at extraframework cation positions, the oxygen nonbonding nature of the HOMO orbital decreases and certain electron density is shifted to the Al centers. The LUMO orbitals of NaxH8Si8-xAlxO12 clusters consist of the charge-balancing cations＇ AO.