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

Abstract

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.

Quadrupole-enhanced proton spin relaxation for a slow reorienting spin pair: (I)–(S). A stochastic Liouville approach

“…The latter observation has also been reported for paramagnetic systems (S=1) [45,17,18] and it was also recently analysed in detail [19]. Consider a proton spin ( I=1/2) which is dipole-dipole coupled to a quadrupole spin with spin quantum number S=1 (assuming an axial symmetry η = 0).…”

Lanthanide Complexes of a Picolinate Ligand Derived from 1,4,7‐Triazacyclononane with Potential Application in Magnetic Resonance Imaging and Time‐Resolved Luminescence Imaging

“…[5,18] Though large efforts have been devoted to the understanding of the molecular parameters that govern the relaxivity, the mechanisms and the coordination properties underlying the electronic relaxation of Gd III complexes still remain poorly understood. [19][20][21][22] This prevents the ligand design required to optimise the electronic relaxation, which becomes especially important in the new generation macromolecular complexes with long rotational correlation times.…”

“…It has to be computed either by setting up and inverting the very large matrices of the superoperator Liouville formalism of the general slow-motion theory [19] or by numerical simulation. [20][21][22] Rather than using the questionable SBM formalism at low field, Troughton et al [60] contented themselves with interpreting the experimental relaxivity above 0.2 T. Indeed, in this "high"-field region, it depends practically only on the longitudinal electronic relaxation rate 1/T 1e , which is given by general expressions of the McLachlan type. [61][62][63] In this paper, we propose a simple three-step method for interpreting the relaxivity profile of the water protons for all field values.…”

“…[22,73] Describing the influence of the quantum motion of the electronic spin S on the low-field relaxivity is a difficult task. [2,5,19,20,22,60,68] At least, two major questions are raised by the use of the McLachlan electronic relaxation times T 1e and T 2e . The first question concerns the existence of T 1e and T 2e , which depend on particular time evolutions of the longitudinal and transverse TCFs hS z (t)S z i and hS + (t)S À i of the electronic spin components S a (a = x,y,z).…”

Joint analysis of ESR lineshapes and 1H NMRD profiles of DOTA-Gd derivatives by means of the slow motion theory

“…In this context, one should mention somewhat different implementations of the slow motion theory, SLE-L, (stochastic Liouville equation in Langevin form) presented by Åman and Westlund. 31,32 Predictions of the slow motion theory 30 were recently compared 33 with two other treatments, referred to as the Grenoble, 21,34 and Ann Arbor approaches, [35][36][37] respectively. It was found that the "Swedish slow motion theory" and the Grenoble approach agreed very well with each other, while some discrepancies were observed when compared to the Ann Arbor method, which was explained by a somewhat different description of the electron spin dynamics.…”