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In the earlier work we used the numerical DFT program DMol. The local exchange correlation functional of von Barth and Hedin was used, although this functional should give results very close to those given by the SVWN functional used in the current study. The basis set (DNP+) used in the earlier work was also by necessity different, although it is comparable to DZVP2 in size. The most important difference is that in the earlier study only the inner three or four atoms of the acid site (≡Si-O-Al≡ or ≡Si-OH-Al≡) were allowed to optimize, whereas all other atoms were fixed in crystal positions. This limited relaxation led to an artificially greater estimate of the acidity, which is remedied in the current work.
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