Nuclear magnetic dipole moment of ${}^{209}\mathrm{Bi}$ from NMR experiments

We report the ${}^{209}\mathrm{Bi}$ magnetic moment derived from NMR experiments and first-principles calculated shielding constants of ${\mathrm{Bi}}^{3+}$ ions in aqueous solutions of $\mathrm{Bi}{\left({\mathrm{NO}}_3\right)}_3$ and $\mathrm{Bi}{\left({\mathrm{ClO}}_4\right)}_3$ salts. Our values represent an independent confirmation of the ${}^{209}\mathrm{Bi}$ magnetic moment recently determined by Skripnikov et al. [L. V. Skripnikov et al., Phys. Rev. Lett. 120, 093001 (2018)], which is of utmost importance for the interpretation of ${\mathrm{Bi}}^{82+}$ ion hyperfine splitting experiments. The accuracy limit of the ${}^{209}\mathrm{Bi}$ magnetic moment set by the present computational chemistry methods is discussed.

Figure 1

Concentration dependence of $\nu {(}^{209}\mathrm{Bi})/\nu {(}^1\mathrm{H}\mathrm{in}\mathrm{TMS})$ resonance frequency ratio for $\mathrm{Bi}{\left({\mathrm{NO}}_3\right)}_3$ and $\mathrm{Bi}{\left({\mathrm{ClO}}_4\right)}_3$ in aqueous solutions, respectively. ${}^1\mathrm{H}$ NMR frequency was measured for pure liquid TMS.

Figure 2

Stick representation of the structure of aqueous complexes with nitrate and perchlorate anions (symmetry point group in brackets): (a) ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6{\mathrm{NO}}_3\right)}^{2+} \left[C_1\right]$, (b) ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_7{\mathrm{ClO}}_4\right)}^{2+} \left[C_1\right]$, (c) ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5{\mathrm{NO}}_3\right)}^{2+} \left[C_{2v}\right]$, (d) ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5{\mathrm{ClO}}_4\right)}^{2+} \left[C_{2v}\right]$. Color code: hydrogen white, nitrogen blue, oxygen red, chlorine green, bismuth yellow.

Figure 3

Nonrelativistic Hartree-Fock NMR shielding of bismuth vs energy of ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_7{\mathrm{ClO}}_4\right)}^{2+}$ and ${\left(\mathrm{Bi}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6{\mathrm{NO}}_3\right)}^{2+}$ complexes calculated for various local minimum structures optimized at the DFT level. For both data sets, the energy is plotted relative to the structure with the lowest energy (see Appendix pp2 for details).

Figure 4

Magnetic dipole moment of ${}^{209}\mathrm{Bi}$ from different sources. “Skripnikov [2018]” represents Ref. [5]. “${\mathrm{BiF}}_6^{-}$ This work” is based on the experiment of Ref. [5] and our shielding calculations. The “NMR [1953]” value is from Refs. [1, 46].