Theoretical and physical aspects of nuclear shielding

Cynthia J. Jameson and Angel C. De Dios

DOI: 10.1039/9781849734851-00038

1.1 General theory

Several recent relativistic studies involve the shielding in molecules containing Cl, Br, and I, with special attention to the investigation of heavy atom effect on itself, the heavy atom effects on vicinal heavy atoms, and the heavy atom effects on light atoms. The importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL2 (L=Cl, Br, I, CH3) compounds has been investigated using three different relativistic methods: the fully relativistic four-component approach and the two- component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). The calculations were performed at the level of HF and DFT theories. DFT calculations employed three different functionals (GGA/BP86 and the hybrid functionals B3LYP and PBE0). It is found that LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH3)2 within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ~2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr2 and HgI2 when ZORA results are compared with four-component calculations with noncollinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ~500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. The largest possible basis set, QZ4P, also contains the largest number of high-exponent functions, important for the calculation of shielding constants and especially the spin-orbit term. The effect of using a Gaussian charge distribution model for the nuclear Coulomb potential as opposed to a point charge model was also investigated. A Gaussian nucleus model for the Coulomb potential reduces the Hg absolute shielding values by ~100–500 ppm and the Hg chemical shifts by 1–143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible. Although ZORA underestimates Hg absolute shielding values by ~2100 ppm, the differences between Hg chemical shift values obtained using ZORA and four-component approaches (without spin-density contribution to the XC kernel) are less than 60 ppm and are similar for all three. This is in a good agreement with the conclusion made by Autschbach that ZORA is a reliable tool for the investigation of chemical shifts as a "valence" property due to very accurate hyperfine integrals for the valence shells of heavy atoms in contrast to inner-most core shells which are important for absolute shielding values.

The four-component calculations using the relativistic polarization propagator formalism and also the two-component LR-ESC method were employed by Melo et al. to investigate Sn and Pb shielding in SnH2XY and PbH2XY with X,Y being F, Cl, Br, and I. At the same time they also examined the halogen nuclear shieldings in these molecules. The two-component results are about 20% smaller than the benchmark 4-component results. The non-relativistic behavior of σ(Sn) is that the nucleus becomes less shielded with heavier substituents. The relativistic results in SnH2X2 exhibit the same decreasing behavior of σ(Sn) in going from F to Cl, but this is followed by an increase in going from Cl to Br to I. Most of the relativistic correction terms are not sensitive to the chemical environment; only three of the correction terms vary with substitution, of which the spin-orbit – Fermi contact term is the most variable. Electron correlation effects on σ(Sn) in these molecules are significant in the non- relativistic treatment, but are not significant for the relativistic results. The results are in qualitative agreement with earlier results by Nakatsuji et al. and by Bagno et al.

Halogen substituent effects on La shielding in LaX3 molecules have been investigated using two-component DFT based on the zeroth-order regular approximation. A detailed analysis of the inverse halogen dependence of σ(La) was carried out via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. As with σ(Pb) in PbH2XY, both the relativistic effects of the heavy atom on itself and the relativistic effects of heavy atoms on the vicinal heavy atom are significant, the latter increasing in going from Cl to Br to I. Analysis shows that the cancellation of spin-orbit contributions of opposite sign from La itself and from the halogen leads to the trend which is the so-called inverse halogen dependence, the σ(La) in LaX3 decreasing in going from F to I. In decomposing the shielding contributions to σ(La) in LaX3 molecules, the diamagnetic component is almost identical across the series, the paramagnetic and spin-orbit contributions reinforce one another in going from Cl to I, with the paramagnetic term being the dominant contribution. This is in contrast to the σ(C) in CH3X, for example, where the so-called normal halogen dependence arises from the spin orbit effect from the halogen, a heavy atom effect on the shielding of a light atom, increasing in going from Cl to I, so that σ(C) in the series of CH3X molecules increases in this order. The calculated values are in agreement with the earlier calculations by Ooms et al. The calculated values for the gas phase molecules give too large a σ(La) shielding difference between the Cl and I compounds in comparison with the solid state observations, but this is expected. Ooms et al....