The basis set dependency of Al and Si isotropic chemical shieldings in Al3+. 6(H2O), [Al(OH)(4)](1-). 2(H2O), and tetramethylsilane have been calculated using the CIAO formalism. The Si chemical shielding changes substantially with the addition of extra d-functions; however, this influence is smaller than the effect of using a 311 split valence shell representation. Similarly, the addition of a second set of d-functions to Al lowers the chemical shielding; however, the addition of extra d-functions does not affect the chemical shielding as much if the triply-split valence shell representation is used. The 6-31G* calculation predicts accurate relative chemical shifts for the tetrahedral Al molecule [Al(OH)(4)](1-). 2(H2O) nearest to the experimental value of 79.9 ppm. Calculations were also performed on large (similar to 20 heavy atoms) aluminosilicate molecules to test peak assignments in the experimental NMR spectra of anhydrous and hydrous aluminosilicate glasses.