| The shielding of Ar in the presence of neutral fragments of zeolites NaA, KA, and CaA are calculated using the gauge including atomic orbital (GIAO) method and Boys-Bernardi counterpoise correction at various positions of Ar relative to fragments. The ab initio isotropic {dollar}sp{lcub}39{rcub}{dollar}Ar shielding values are fitted to a sum of pairwise additive functions to elicit effective individual Xe-O and Xe-cation intermolecular shielding functions, such as {dollar}rmsigma(sp{lcub}39{rcub}Ar, Ar{dollar}-{dollar}rm Osb{lcub}zeol{rcub})=asb6rsp{lcub}-6{rcub}+asb8rsp{lcub}-8{rcub}+asb{lcub}10{rcub}rsp{lcub}-10{rcub}+a sb{lcub}12{rcub}rsp{lcub}-12{rcub},{dollar} where r is the distance between the Ar and the O atom in the zeolite fragment. These are scaled to Xe intermolecular shielding functions using electronic properties only and used in the grand canonical Monte Carlo (GCMC) simulations to calculate average {dollar}sp{lcub}129{rcub}{dollar}Xe chemical shifts.; GCMC simulations are carried out for Xe atoms in various zeolites NaA, KA, AgA, and {dollar}rm Casb{lcub}x{rcub}Nasb{lcub}(12-2x){rcub}A,{dollar} where x = 0-5 and for the mixtures of Xe-Ar and Xe-Kr in NaA. These are the systems showing the separate {dollar}sp{lcub}129{rcub}{dollar}Xe NMR peaks for Xe, clusters inside the alpha cages of the zeolite. The simulations give not only the average chemical shifts but also the distributions of cages having different numbers of Xe atoms, and coadsorbates in the case of mixtures. The GCMC simulations for Xe in these A-type zeolites provide quantitative understanding of {dollar}sp{lcub}129{rcub}{dollar}Xe chemical shifts using the same shielding functions throughout without any changes from system to system. Thus, these simulations provide a paradigm for understanding of average Xe chemical shifts in other microporous materials in which Xe is in fast exchange among many cavities and channels. |
