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| - Toward Calculations of the 129Xe Chemical Shift in Xe@C60 at Experimental Conditions: Relativity, Correlation, and Dynamics
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| - We calculate the 129Xe chemical shift in endohedral Xe@C60 with systematic inclusion of the contributingphysical effects to model the real experimental conditions. These are relativistic effects, electron correlation,the temperature-dependent dynamics, and solvent effects. The ultimate task is to obtain the right result forthe right reason and to develop a physically justified methodological model for calculations and simulationsof endohedral Xe fullerenes and other confined Xe systems. We use the smaller Xe···C6H6 model to calibratedensity functional theory approaches against accurate correlated wave function methods. Relativistic effectsas well as the coupling of relativity and electron correlation are evaluated using the leading-order Breit−Pauli perturbation theory. The dynamic effects are treated in two ways. In the first approximation, quantumdynamics of the Xe atom in a rigid cage takes advantage of the centrosymmetric potential for Xe within thethermally accessible distance range from the center of the cage. This reduces the problem of obtaining thesolution of a diatomic rovibrational problem. In the second approach, first-principles classical moleculardynamics on the density functional potential energy hypersurface is used to produce the dynamical trajectoryfor the whole system, including the dynamic cage. Snapshots from the trajectory are used for calculations ofthe dynamic contribution to the absorption 129Xe chemical shift. The calculated nonrelativistic Xe shift isfound to be highly sensitive to the optimized molecular structure and to the choice of the exchange−correlationfunctional. Relativistic and dynamic effects are significant and represent each about 10% of the nonrelativisticstatic shift at the minimum structure. While the role of the Xe dynamics inside of the rigid cage is negligible,the cage dynamics turns out to be responsible for most of the dynamical correction to the 129Xe shift. Solventeffects evaluated with a polarized continuum model are found to be very small.
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