Nuclear spin relaxation in paramagnetic complexes of S=1: Electron spin relaxation effects

Abstract

Static zero field splitting effects on the electronic relaxation of paramagnetic metal ion complexes in solution A low-field paramagnetic nuclear spin relaxation theory Electron spin relaxation for an Sϭ1 system and its field dependence in the presence of static zero-field splitting ͑ZFS͒ has been described and incorporated in a model for nuclear spin-lattice relaxation in paramagnetic complexes in solution, proposed earlier by the group in Florence. Slow reorientation is assumed and the electron spin energy level structure ͑at any orientation of the molecule with respect to the laboratory frame͒ is described in terms of the Zeeman interaction and of the static ZFS. The electron spin relaxation is assumed to be caused by a transient ZFS modulated by the deformation of the complex described as a distortional ͑or pseudorotational͒ motion and the Redfield theory is used to derive the electron spin relaxation matrices. In the description of the electron spin relaxation we neglect any contribution from mechanisms involving modulation by reorientation, such as those of the static ZFS and the less important Zeeman interaction, as we limit ourselves to the slow-rotation limit ͑i.e., R ӷ S ͒. This in general covers the behavior of proteins and macromolecules. The decomposition ͑DC͒ approximation is used, which means that the reorientational motion and electron spin dynamics are assumed to be uncorrelated. This is not a serious problem, due to the slow-rotation condition, since reorientational and distortional motions are time-scale separated. The resulting nuclear magnetic relaxation dispersion ͑NMRD͒ profiles obtained using the Florence model are calculated and compared with the calculations of the Swedish approach, which can be considered essentially exact within the given set of assumed interactions and dynamic processes. That theory is not restricted by the Redfield limit and can thus handle electron spin relaxation in the slow-motion regime, which is a consequence of not explicitly defining any electron spin relaxation times. Furthermore, the DC approximation is not invoked, and in addition, the electron spin relaxation is described by reorientationally modulated static ZFS and Zeeman interaction besides the distortionally modulated transient ZFS. The curves computed with the Florence model show a satisfactory agreement with these more accurate calculations of the Swedish approach, in particular for the axially symmetric static ZFS tensor, providing confidence in the adequacy of the electron spin relaxation model under the condition of slow rotation. The comparison is also quite instructive as far as the physical meaning of the electron spin relaxation and of its interplay with the nuclear spin system are concerned.

The synthesis and in vitro testing of a zinc-activated MRI contrast agent

“…The SBM theory in fact neglects the presence of static ZFS. Data were also analyzed by using a slow-rotation program including ZFS (28,29). Even in such a model, the data are consistent with the presence of a regularly coordinated water molecule (dashed lines in Fig.…”

“…Presently available fitting programs cannot properly account for their simultaneous presence in fast-rotating systems. Therefore, we analyzed the data by using either SBM theory (no static ZFS) or slow-rotation programs including ZFS (28,29).…”

Field Dependent Electron and Quadrupole Spin Relaxation: A Unified Treatment

“…In fact, because of the common Hamiltonian formalism, in order to describe the S spin dynamics one does not need to distinguish between the two interactions. Thus, the main Hamiltonian, H 0 (S), represented in the laboratory frame (H (L) 0 (S)), takes the following form [12,14]:…”

“…Depending on the system under interest, various types of motion can be responsible for the fluctuations in the orientation of the molecular frame (the principal axis system of the electric field gradient tensor or the ZFS tensor). The relative orientation of the laboratory and molecular frames can change in time due to rotational motion of the molecule carrying the S spin [11][12][13][14][15]. In solid state systems spins S can move between non-equivalent lattice sites characterized by a different local crystal field due to, for example, exchange motion of the particles (ions, nuclei).…”

“…The above definition of the F T m (t) quantities is based on a very simple motional model assuming that their amplitudes do not undergo any time fluctuations (this model is referred to as "pseudorotational model" [8,9,[11][12][13][14][15][16]). Taking into account that the interactions are affected by damped vibrations in crystal lattices or molecules, such a treatment is an apparent simplification.…”