Ab initio studies of the nuclear magnetic resonance chemical shifts of a rare gas atom in a zeolite

Abstract

The intermolecular chemical shift of a rare gas atom inside a zeolite cavity is calculated by ab initio analytical derivative theory using gauge-including atomic orbitals (GIAO) at the Ar atom and the atoms of selected neutral clusters each of which is a 4-, 6-, or 8-ring fragment of the zeolite cage. The Si, Al, O atoms and the charge-balancing counterions (Na+, K+, Ca2+) of the clusters (from 24 to 52 atoms) are at coordinates taken from the refined single crystal x-ray structure of the NaA, KA, and CaA zeolites. Terminating OH groups place the H atom at an appropriate O–H distance along the bond to the next Si or Al atom in the crystal. The chemical shift of the Ar atom located at various positions relative to the cluster is calculated using Boys–Bernardi counterpoise correction at each position. The dependence of the rare gas atom chemical shift on the Al/Si ratio of the clusters is investigated. The resulting shielding values are fitted to a pairwise additive form to elicit effective individual Ar–O, Ar–Na, Ar–K, Ar–Ca intermolecular shielding functions of the form σ(39Ar, Ar...Ozeol)= a6r−6+a8r−8+a10r−10+a12r −12, where r is the distance between the Ar and the O atom. A similar form is used for the counterions. The dependence of the Ar shielding on the Al/Si ratio is established (the greater the Al content, the higher the Ar chemical shift), which is in agreement with the few experimental cases where the dependence of the 129Xe chemical shift on the Al/Si ratio of the zeolite has been observed.