A theoretical spin relaxation and molecular dynamics simulation study of the Gd(H₂O)₉³⁺ complex

A theoretical analysis of the paramagnetically enhanced water proton spin–lattice relaxation of a hydrated Gd³⁺ ion is combined with Molecular Dynamics (MD) simulations. The electron–proton dipole–dipole correlation function, C^DD_p(τ), as well as the pseudo-rotation (PR) model of the transient zero-field splitting (ZFS) are evaluated with the help of the data from MD simulations. The fast local water motion in the first hydration shell, i.e. the wagging and rocking motions, is found not to change the mono exponential character of the dipole correlation function C^DD_p(τ), but is important in the time dependence of the transient ZFS interaction.

The dynamics of the transient ZFS interaction is modeled as the water-induced electric field gradient tensor at the site of the metal ion. This approach follows the ideas of the pseudo-rotation model, describing the fluctuating zero-field interaction as a constant amplitude in the principal frame but reorienting according to a rotational diffusion equation of motion. The MD results indicate that the pseudo-rotation model gives a multi-exponential correlation function which oscillates at short times and is described by three exponential terms. The time scale is shorter than previously assumed but contain an intermediate time constant (1–2 ps). The electron spin resonance (ESR) spectral width at half height at frequencies of X-band, Q-band, 75 MHz, 150 MHz and 225 MHz can be reproduced at 320 K without any contributions from 4th or 6th rank ZFS interactions. Consequently, there are two mutually inconsistent dynamic models of the ZFS interaction which can describe the water proton T₁-NMRD (nuclear magnetic resonance dispersion) profile and the field dependent ESR spectra of the hydrated Gd(III) complex equally well.