Quantum Chemical Investigation of Hyperfine Coupling Constants on First Coordination Sphere Water Molecule of Gadolinium(III) Aqua Complexes

Hyperfine interactions (HFI) on the nuclei of the first coordination sphere water molecules in a model [Gd(H<sub>2</sub>O)<sub>8</sub>]<sup>3+</sup> aqua complex and in the magnetic resonance imaging contrast agent [Gd(DOTA)(H<sub>2</sub>O)]<sup>-</sup> were studied theoretically. Density functional theory (DFT) calculations combined with classical molecular dynamics (MD) simulations have been used in order to take into account dynamic effects in aqueous solution. DFT relativistic calculations show a strong spin-polarization of the first coordination sphere water molecules. This spin-polarization leads to a positive <sup>17</sup>O isotropic hyperfine coupling constant (<i>A</i><sub>iso</sub>(<sup>17</sup>O) = 0.58 ± 0.11 MHz) and to a significant increase of the effective distance (〈<i>r</i><sub>eff</sub>(Gd−O)〉 = 2.72 ± 0.06 Å) of dipolar interaction compared to the mean internuclear distance (〈<i>r</i>(Gd−O)〉 = 2.56 ± 0.06 Å) obtained from the MD trajectory of [Gd(DOTA)(H<sub>2</sub>O)]<sup>-</sup> in aqueous solution. The point-dipole model for anisotropic hyperfine interaction overestimates therefore the longitudinal relaxation rate of the <sup>17</sup>O nucleus by ∼45%. The <sup>1</sup>H isotropic hyperfine coupling constant of the bound water molecule is predicted to be very small (<i>A</i><sub>iso</sub>(<sup>1</sup>H) = 0.03 ± 0.02 MHz), and the point-dipole approximation for first coordination sphere water protons holds. The calculated hyperfine parameters are in good agreement with available experimental data.