Theoretical study of the NMR chemical shift of Xe in supercritical condition

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the ¹²⁹Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe _n clusters (n = 2 - 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe _n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of ¹²⁹Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.