129Xe NMR chemical shift in Xe@C60 calculated at experimental conditions: essential role of the relativity, dynamics, and explicit solvent

The isotropic (129)Xe nuclear magnetic resonance (NMR) chemical shift (CS) in Xe@C60 dissolved in liquid benzene was calculated by piecewise approximation to faithfully simulate the experimental conditions and to evaluate the role of different physical factors influencing the (129)Xe NMR CS. The (129)Xe shielding constant was obtained by averaging the (129)Xe nuclear magnetic shieldings calculated for snapshots obtained from the molecular dynamics trajectory of the Xe@C60 system embedded in a periodic box of benzene molecules. Relativistic corrections were added at the Breit-Pauli perturbation theory (BPPT) level, included the solvent, and were dynamically averaged. It is demonstrated that the contribution of internal dynamics of the Xe@C60 system represents about 8% of the total nonrelativistic NMR CS, whereas the effects of dynamical solvent add another 8%. The dynamically averaged relativistic effects contribute by 9% to the total calculated (129)Xe NMR CS. The final theoretical value of 172.7 ppm corresponds well to the experimental (129)Xe CS of 179.2 ppm and lies within the estimated errors of the model. The presented computational protocol serves as a prototype for calculations of (129)Xe NMR parameters in different Xe atom guest-host systems.