First-Principles Calculation of the ¹⁷O NMR Parameters in Ca Oxide and Ca Aluminosilicates:  the Partially Covalent Nature of the Ca−O Bond, a Challenge for Density Functional Theory

Abstract

We apply density functional theory (DFT) to the calculation of the (17)O NMR parameters in Ca and Mg oxides and aluminosilicates. We study the accuracy of the Perdew, Burke, and Ernzerhof (PBE) generalized-gradient approximation to DFT in the description of these systems and the origin of the experimentally observed large dependence of the (17)O chemical shift on the alkaline earth ion. We find that (i) the partially covalent nature of the Ca-O bond has a huge impact on the O chemical shifts. The Ca-O covalence alone explains why in Ca oxides and aluminosilicates the (17)O chemical shifts are much more deshielded than those of the corresponding Mg compounds. (ii) The Ca-O covalence is overestimated by the PBE functional. Thus PBE-DFT is not able to reproduce the measured (17)O NMR parameters in Ca oxide and Ca aluminosilicates. (iii) It is possible to correct for the PBE-DFT deficiency in a simple and transferable way and to predict very accurate (17)O NMR parameters. Such accuracy allows us to assign the (17)O NMR spectra of two important model systems: the grossite aluminate (CaAl(4)O(7)) and the wollastonite (CaSiO(3)) silicate.

NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations

“…This value is significantly smaller than for CaO (3.2 eV). 60 This difference can be explained as (i) we used USPP whereas Profeta et al The effect of the shift applied on the 3d orbitals is clearly observed in the conduction band: the energy of the band having mostly a Ca(3d) character is increased and becomes closer to the one obtained using hybrid functional. The band gap stays unchanged (mainly imposed by the position of Ca(4s) states in the conduction band) and is calculated to 6.3 eV using PBE functional.…”

“…In a second step, the correlation between the calculated 19 F σ iso values for 25 twelve binary crystalline compounds and experimental 19 F δ iso values is investigated. A critical problem that was already observed for Ca in oxides 60 is evidenced in fluorides: PBE-DFT (Perdew, Burke and Ernzerhof -Density Functional Theory) method 61 is deficient in describing 3d and 4f localized empty orbitals when considering NMR shielding calculations. To circumvent this problem the Ca, Sc, and La pseudopotentials have been adapted using the methodology described in [60] and a reference calibration curve is proposed.…”

“…A critical problem that was already observed for Ca in oxides 60 is evidenced in fluorides: PBE-DFT (Perdew, Burke and Ernzerhof -Density Functional Theory) method 61 is deficient in describing 3d and 4f localized empty orbitals when considering NMR shielding calculations. To circumvent this problem the Ca, Sc, and La pseudopotentials have been adapted using the methodology described in [60] and a reference calibration curve is proposed. We then show that the correlation established for the studied compounds fit nicely with the 30 calculations on others inorganic fluorides reported in [56] and [26].…”

“…115 In our case, the very large deviation observed for LaF 3 (Figure 3(a)) shows that the La 3+ ion (4f 0 ) has a similar symptomatic behaviour as Ca 2+ and Sc 3+ ions. Therefore, we have applied the Profeta et al 60 procedure to shift 4f orbitals. LaF 3 having three fluorine sites, the 4f-shift was determined by simultaneously minimizing for the three sites the 10 differences between the experimental 19 F δ iso and the δ iso values deduced from the calculated 19 F σ iso using equation (1).…”

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

“…Indeed, it is known that the empty Ca 3d-states are too close to the valence band maximum in density functional theory (DFT), resulting in a deviation of the O shift. 39 The fit of Eq. (36) relates the calculated shieldings to chemical shifts from experiment.…”