Tetrahedral distortion and energetic packing penalty in "zeolite" frameworks: linked phenomena?

We report a computational study on the distortion of SiO4 tetrahedra in zeolite frameworks. For all previously observed frameworks, the tetrahedral mismatch was found to span a narrow range (1.0 x 10(-3) to 2.5 x 10(-2) angstroms2) of values, in contrast to the hypothetical frameworks, which were calculated to have a much wider range of mismatch values. The energy of the frameworks was not found to be a function of the tetrahedral distortion for the previously observed and moderately distorted (tetrahedral mismatch <2.5 x 10(-2) angstroms2) hypothetical frameworks. In contrast, the energy of the bulk of the hypothetical frameworks was shown to be a strong function of the tetrahedral distortion. The fact that the framework energies of some hypothetical frameworks lie much higher than both those of the observed frameworks and the values we would expect from our previously developed topological method (the so-called energetic packing penalty) is explained in terms of the tetrahedral distortion contribution to the framework energy which is negligible for the observed frameworks. Finally, it is hypothesized that the absence of tetrahedral distortion is pivotal for a framework to be experimentally realized, in which case a large fraction of hypothetical frameworks are unrealizable and will forever remain in the realms of the abstract.