Electron spin relaxation due to reorientation of a permanent zero field splitting tensor.

Electron spin relaxation of transition metal ions with spin S> or =1 results primarily from thermal modulation of the zero field splitting (zfs) tensor. This occurs both by distortion of the zfs tensor due to intermolecular collisions and, for complexes with less than cubic symmetry, by reorientational modulation of the permanent zfs tensor. The reorientational mechanism is much less well characterized in previous work than the distortional mechanism although it is an important determinant of nuclear magnetic resonance (NMR) paramagnetic relaxation enhancement phenomena (i.e., the enhancement of NMR relaxation rates produced by paramagnetic ions in solution or NMR-PRE). The classical density matrix theory of spin relaxation does not provide an appropriate description of the reorientational mechanism at low Zeeman field strengths because the zero-order spin wave functions are stochastic functions of time. Using spin dynamics simulation techniques, the time correlation functions of the spin operators have been computed and used to determine decay times for the reorientational relaxation mechanism for S=1. In the zfs limit of laboratory field strengths (H(Zeem)<<H(zfs) (composite function)), when the zfs tensor is cylindrical, the spin decay is exponential, the spin relaxation time, tau(S) (composite function) approximately 0.53tau(R)((1)), where tau(R)((1)) is the reorientational correlation time of a molecule-fixed vector. The value of tau(S) (composite function) is independent of the magnitude of the cylindrical zfs parameter (D), but it depends strongly on low symmetry zfs terms (the E/D ratio). Other spin dynamics (SD) simulations examined spin decay in the intermediate regime of field strengths where H(Zeem) approximately H(zfs) (composite function), and in the vicinity of the Zeeman limit. The results demonstrate that the reorientational electron spin relaxation mechanism is often significant when H(zfs) (composite function)> or =H(Zeem), and that its neglect can lead to serious errors in the interpretation of NMR-PRE data.