Absolute NMR shielding scales in methyl halides obtained from experimental and calculated nuclear spin-rotation constants

The nonrelativistic “Ramsey-Flygare relationship” is the most used procedure to obtain semiexperimental nuclear magnetic resonance (NMR) absolute shieldings by a correspondence between NMR shieldings ($\mathit{\sigma }$) and nuclear spin-rotation constants ($\mathit{M}$). One of its generalizations to the relativistic framework is known as the M-V model, which was proposed few year ago by some of the authors of the present work and right now is only applied to linear molecules. This model includes terms that do not have nonrelativistic counterparts and also include the paramagnetic contribution to the NMR shielding of nuclei in free atoms. All this ensures that its results fit quite well with those of four-component (4c) calculations. The first application of the M-V model to nonlinear molecules, like methyl halides or ${\mathrm{CH}}_{3}X$ molecules ($X=\mathrm{F}$, Cl, Br, and I), is given here. The analysis of each electronic mechanism of $\mathit{\sigma }$ shows that most of their electron correlation effects are strongly related with the same effects in $\mathit{M}$. By including experimental data of $M$ in the M-V model most of the correlation effects are accurately taken into account for the absolute values of $\mathit{\sigma }$. Calculations of ${\mathit{M}}_Y$ and ${\mathit{\sigma }}_Y$ ($Y=\mathrm{H}$, C, and $X$) were carried out within the linear response formalism at the random-phase level of approach and density functional theory in both 4c and nonrelativistic frameworks. The best fits between calculations of $\mathit{M}$ and experimental data are obtained from calculations at 4c-PBE0 level of theory in all cases, but not for $M_{\parallel ,\mathrm{Cl}}$, which suggests that a revision of the available experimental data may be necessary. There is an additional advantage of using the M-V model: one can indirectly calculate shieldings of open-shell free atoms, which cannot be obtained at the moment by applying 4c methods.

Figure 1

(a) Perpendicular ($e\text{−}e$) and (b) parallel ($e\text{−}e$) tensor contributions (in ppm) to ${\mathit{\sigma }}_X^{\left(e\text{−}e\right)}, {\mathit{M}}_X^{\left(e\text{−}e\right)}, {\mathit{\sigma }}_X^{\mathrm{FA}\left(e\text{−}e\right)}$, and ${\mathit{\nu }}_X^{S\left(e\text{−}e\right)}-{\mathit{\nu }}_X^{\mathrm{FA},S\left(e\text{−}e\right)}$ for the $X$ nuclei in ${\mathrm{CH}}_{3}X$ molecules ($X$ = F, Cl, Br, and I). Calculations were performed at the relativistic RPA level of approach. Values of ${\mathit{\sigma }}_X^{\mathrm{NR}\text{−}\mathrm{para}}$ are also displayed.

Figure 2

4c RPA values of the spans of NMR shielding, SR tensors, and results using the M-V model (i.e., perpendicular minus parallel contributions to ${\mathit{\sigma }}_X, {\mathit{M}}_X$, and ${\mathit{\sigma }}_X^{\mathrm{M}\text{−}\mathrm{V}}$) in ${\mathrm{CH}}_{3}X$ molecules ($X$ = F, Cl, Br, and I). All values are given in ppm.

Figure 3

Relativistic RPA values of the perpendicular and parallel contributions to ${\mathit{\sigma }}_C^{\left(e\text{−}e\right)}$ and ${\mathit{M}}_C^{\left(e\text{−}e\right)}$ in ${\mathrm{CH}}_{3}X$ molecules ($X$ = F, Cl, Br, and I), together with their NR limits. Values are given in ppm.