Nature of second hydration shell in Mn⁺²-aquoion system: Influence on proton relaxivity in nuclear magnetic resonance

Using the unrestricted Hartree-Fock procedure, we have studied the numbers and locations of water molecules in the second hydration shells of the Mn ⁺²-aquoion system. Two arrangements for the second hydration shell were considered, one involving 8 water molecules located along the body diagonals of a cube with Mn⁺² ion at the body center and the other with 12 water molecules located in the directions of the lines joining the Mn⁺² ion and the midpoints of the sides of the cube. Both these arrangements of the second hydration shells were considered in the presence of the octahedral arrangement of six water molecules in the first hydration shell. The total energies of the composite clusters were minimized with respect to the metal-oxygen distance for the second shell of water molecules to determine the equilibrium geometries in the two cases. From a consideration of the hydration energies, the eight-molecule configuration was found to be the more likely one for the second hydration shell, the metal-oxygen distance for the second shell being 3.75 Å as compared to 2.19 Å for the first. A physical reason associated with steric effects within the second shell water molecules and between the first and second shell molecules is suggested for the greater stability of the 8-member hydration shell as compared to the 12-member one. Using the calculated geometry, the contribution to the proton relaxivity in aqueous solution from the second hydration shell was determined to be 9.9% of that from the first hydration shell in the dipolar interaction regime, in magnetic fields of 0.25 T (corresponding to proton resonance frequency of about 10 MHz) and above and progressively smaller in importance as one went to lower fields corresponding to the contact interaction regime.