Paramagnetic enhanced proton spin-lattice relaxation in the Ni²⁺ hexa-aquo complex: A theoretical and molecular dynamics simulation study of the Bloembergen-Morgan decomposition approach

A reinterpretation of the experimental NMR proton spin-lattice dispersion curve of the Ni²⁺(H₂O)₆ complex is presented within a general slow-motion theory. The extended pseudo rotation (PR) model developed allows for cross-correlation effects between the nuclear spin-electron spin dipole-dipole and zero field splitting (ZFS) interaction. It is shown that the decomposition approach, treating the electron spin relaxation and the reorientational dynamic of the dipole-dipole correlation function as independent processes is not generally valid. For the Ni-hexa-aquo complex the transient ZFS interaction and the reorientational correlation time change by about 20 per cent due to the correlation effects. Molecular dynamics (MD) simulation of a divalent ion in water provided the timescale of the dynamics present in the PR and the Smoluchowsky models. The structure and dynamics of the octahedral complex is described. The transient ZFS interaction generated by the low frequency vibration modes n(M ↔ OH₂) is characterized by a correlation time τ_v = 0·2 ps and the timescale of the orientational motion of the PR model is in the range τ_v = 1-10 ps. The fast E- and A-symmetric vibrations cause partial averaging of the ZFS interaction. The timescale of the ligand orientational modes, wag, twist and rock modes are comparable with the electron spin dynamics. The reinterpretation of the NMRD curve suggests that the dynamics described by the single exponential reorientational correlation time, τ_R reflects the wag, twist and rock modes rather than the overall reorientation of the whole metal-aquo complex. The simulations also suggest that the relatively short proton-metal ion distance obtained from the interpretation of the NMRD curve reflects neglect of outer sphere contributions rather than oversimplification of electron spin dynamics.