Calculation of ²⁹Si and ²⁷Al MAS NMR Chemical Shifts in Zeolite-β Using Density Functional Theory:  Correlation with Lattice Structure

²⁹Si and ²⁷Al NMR chemical shifts have been evaluated from the NMR shielding tensors obtained using the SOS-DFPT technique. The ²⁹Si NMR chemical shifts have been calculated for the nine crystallographically distinct Si sites of the zeolite-β lattice. The calculations were carried out on cluster models Si(OSiH₃)₄ and R₃SiOSiR₃ (R = OSiH₃) representing one (1T) and two (2T) sites in the zeolite lattice, respectively. Using the 1T models, the nine signals of the experimental spectrum have been assigned with a relative error of less than 1 ppm, the absolute error being estimated at about 5 ppm. The use of a “fragment-averaging” technique based on the results obtained with the 2T models leads to calculated absolute NMR shifts with an accuracy of ±1 ppm. The ²⁷Al NMR shifts of AlH(OSiH₃)₄ models have also been calculated, after relaxation of the local geometry. It was found that the relative positions of the ²⁷Al chemical shifts are in agreement with the experimental spectrum.