Xe 129 chemical shift by the perturbational relativistic method: Xenon fluorides

Abstract

(129)Xe nuclear shielding tensor is calculated at the leading-order, one-electron Breit-Pauli perturbation theory (BPPT) level for the xenon fluorides XeF(+), XeF(2), XeF(3) (+), and XeF(4) that cover the large nuclear magnetic resonance chemical shift range of this nucleus. BPPT is found to improve the shift range and relative shifts as compared to the nonrelativistic (NR) theory. While the full BPPT expansion consists of 16 relativistic terms, 5 of them are responsible for the entire chemical shift and shielding anisotropy. The remaining terms are practically isotropic, corelike contributions that are significant for the absolute shielding constant but cancel for the relative chemical shifts. The five principal terms are due to the spin-orbit-modified wave function allowing the Fermi contact and spin-dipole hyperfine interactions to be coupled to the orbital Zeeman interaction, as well as three distinct scalar relativistic modifications of the NR paramagnetic shielding: wave function change due to mass-velocity and Darwin interactions and the relativistic modification of the orbital hyperfine interaction. A very good agreement with the experimental shifts is obtained for XeF(2) and the particularly challenging XeF(+) species when both the NR and the five main relativistic terms are calculated at electron-correlated ab initio levels of theory. The performance of density-functional theory (DFT) with different pure and hybrid exchange-correlation functionals (with increasing exact exchange admixture) is tested against the ab initio data for each individual contribution. It is shown that DFT has difficulties in the description of paramagnetic shielding, already and especially in the NR contribution, which causes a large discrepancy of DFT results with experiment for xenon fluorides. In contrast, the DFT errors for the relativistic terms cancel out to the extent that a fairly good approximation of the total relativistic shift and anisotropy contributions may be obtained. A combination of high-level ab initio NR calculation with hybrid DFT estimates of the five main BPPT terms is proposed for reasonable estimates of xenon chemical shift in molecules. For the difficult cases such as the present XeF(+) and XeF(3) (+) cations, correlated ab initio calculations are unavoidable throughout. None of the other currently available relativistic methods, either at the fully relativistic or a variationally stable quasirelativistic levels of theory, surpasses the quality of the present approach for Xe shifts in these systems.