Na+ Complexes with Crown Ethers: Calculation of 23Na NMR Shieldings and Quadrupole Coupling Constants

Abstract

Na+ forms complexes and compounds with both organic ring systems, such as crown ethers, and inorganic ring systems, such as the aluminosilicate “six ring” in the mineral sodalite Na6(SiAlO4)6. 23Na NMR shieldings and quadrupole coupling constants have been calculated at the Hartree−Fock level, using the 6-31G* basis sets for (12−crown−4)2Na+, 15-crown-5Na+, and 18-crown-6Na+ complexes (and with additional H2O for the 15-crown-5 and 18-crown-6 ligands). Geometries have been optimized using the Hartree−Fock method and valence-electron only polarized double-ζ bases, sometimes using starting geometries from crystallographic data. For the 15-crown-5 and 18-crown-6 hydrated compounds, the calculated shieldings agree well with a recent experimental study (Wong, A.; Wu, G. J. Phys. Chem. A 2000, 104, 11844), although the calculated quadrupole coupling constants are sometimes too large. For the (12−crown−4)2Na+ cation, several structures with different symmetry and bond distances are considered, but none matches both the NMR shift and the quadrupole coupling constant observed for solid (12−crown−4)2NaClO4. Our results indicate that the 23Na NMR shift, compared to Na(OH2)6+ (our model for aqueous Na+), can be accurately calculated at the Hartree−Fock level with small basis sets such as 6-31G*, once the geometry is accurately known. The main problem is to obtain a sufficiently accurate geometry for the large (and sometimes flexible) ring molecules which bond weakly to the Na+ in the complex. The absolute deshieldings (referred to free gas-phase Na+) obtained from calculations on these crown-ether complexes can be approximated well using a simple additivity model based on Na+ interactions with isolated (CH3)2O molecules. The Na deshielding in the (CH3)2ONa+ complex is calculated to show a strong but simple exponential distance dependence. The calculated absolute deshieldings in the complexes are also strongly correlated with the bond strength sum received by the Na+. A Si3O3O18H12Na-2 model for sodalite gives a 23Na NMR shift of about −8 ppm and a quadrupole coupling constant of 4.4 MHz, similar to the Na NMR results for 18-crown-6Na+.