Spin dynamic

In principle it is not possible to develop an accurate model without an explicit treatment of spin dynamics. Because the reaction rate of a radical pair is partly dependent on its spin state, the recombination kinetics in a spur may depend strongly on the spin correlation of the radicals it contains. In photochemistry it is customary to distinguish between G-pairs (which are initially spin correlated) and F-pairs (which are not), but in a spur all the spins are entangled and this distinction is less meaningful, but nonetheless, this nomenclature will be used in this work, wherever appropriate. One important exception is the radiolysis of water, where the very fast relaxation on the hydroxyl radical destroys any spin effects, such that there is no difference in the reactivity between G-pairs and those whose spins are uncorrelated (F-Pairs). 

In most models of radiation chemistry, spin dynamics are often neglected by assuming reactions to be diffusion controlled, with the microscopic parameters extracted from the experimental rate constant [3-5]. This is not completely satisfactory since the experimental rate constant consists of mostly F-pair recombinations [6], whereas in spurs the spins are correlated which means that the singlet character 

Agarwal, Simulation Studies of Recombination Kinetics and Spin Dynamics in Radiation Chemistry, Springer Theses, DOI 10.1007/978-3-319-06272-3 3, Springer International Publishing Switzerland 2014 

As the preceding examples demonstrate, magnetic field effects can be useful in identifying the nature of charge-transfer intermediates in photoelectron transfer. In particular, with a better understanding of the relationships between AEhf and J, and between J and the separation distance, we can predict that magnetic-field experiments, similar to those pioneered by Weller, will assist in differentiating exciplexes and CIP s from SSIP s. 

---

D. P. Landau, M. Krech. Spin dynamics simulations of ferro- and antiferromagnetic model systems comparison with theory and experiment. J Phys Condens Matter 77 R175-R213, 1999. 

M. D. Hiirlimann, D. D. Griffin 2000, (Spin dynamics of Carr-Purcel-Mei-bohm-Gill-like sequences in grossly inhomogeneous B0 and Bj fields and applications to NMR well logging), J. Magn. Reson. 143, 120-135. 

This chapter reviews all aspects of the 2D NMR of relaxation and diffusion. Firstly, numerous pulse sequences for the 2D NMR and the associated spin dynamics will be discussed. One of the key aspects is the FLI algorithm and its fundamental principle will be described. Applications of the technique will then be... 

However, some aspects of the spin dynamics are better described using functions other than Fourier series. For example, the magnetization decay in a CPMG [28] experiment follows an exponential form,... 

We have shown in this chapter that the major electronic features that determine the spin dynamics of SIMs based on lanthanides can be directly correlated with the local coordination environment around the 4f metal ions. By using an effective point-charge model that accounts for covalent effects, we have shown that the splitting of the ground state,/, of the lanthanide into Mj sublevels, caused by the influence of the CF created by the surrounding ligands, is consistent with... 

In contrast to the spin-1/2 —> spin-1/2 polarization case, the transfer of polarization between spin-1/2 and quadrupolar nuclei presents a considerable challenge due to the very complex spin dynamics involved in the CP process and the spinlocking of quadrupolar nuclei under MAS. The overall sensitivity is rarely enhanced with respect to the direct polarization method, even if T[ is much shorter than Tf. The usefulness of the CP experiment relies mainly on its ability to probe the interactions between the neighboring nuclei in ID or 2D schemes under MAS or isotropic resolution. The theoretical and practical aspects of spin-locking and CP transfer between spin-1/2 and the SQ or MQ coherences of the quadrupolar nuclei (SQ-CP or MQ-CP) have been thoroughly studied and reviewed [20, 221-227]. Some of the challenges involved in such experiments are summarized below. 

The spin dynamics of solids whose primary or sole nuclear interactions (ignoring the omnipresent Zeeman and isotropic chemical shift terms) are dipolar interactions among a very large number of nuclei present interpretive and theoretical challenges... 

Then, there are model Hamiltonians. Effectively a model Hamiltonian includes only some effects, in order to focus on those effects. It is generally simpler than the true full Coulomb Hamiltonian, but is made that way to focus on a particular aspect, be it magnetization, Coulomb interaction, diffusion, phase transitions, etc. A good example is the set of model Hamiltonians used to describe the IETS experiment and (more generally) vibronic and vibrational effects in transport junctions. Special models are also used to deal with chirality in molecular transport junctions [42, 43], as well as optical excitation, Raman excitation [44], spin dynamics, and other aspects that go well beyond the simple transport phenomena associated with these systems. 

Since long it is well known that two-body forces are not enough to explain some nuclear properties, and TBF have to be introduced. Typical examples are the binding energy of light nuclei, the spin dynamics of nucleon-deuteron scattering, and the saturation point of nuclear matter. Phenomenological and microscopic TBF have been widely used to describe the above mentioned properties. 

D. Electron spin dynamics in the equilibrium ensemble Spin-dynamics models Outer-sphere relaxation... 

We call the second category of theoretical tools for dealing with rapidly rotating systems the spin-dynamics methods . The models within this category will he reviewed in Section VI. 

Fig. 13. Predicted magnetic field dependence of the electron spin lattice relaxation time. Solid line pseudorotation model dashed line spin dynamics calculation. Reproduced with permission from Odelius, M. Ribbing, C. Kowalewski, J. J. Chem. Phys. 1996,104, 3181-3188. Copyright 1996 American Institute of Physics.

The spin-dynamics method was applied to the intramolecular PRE in the case of aqueous and methyl protons in the Ni(II)(acac)2(H20)2 complex (acac = 2,4-pentanedione) (131,132). The two kinds of protons are characterized by a different angle between the principal axis of the static ZFS and the dipole-dipole axis. The ratio, p, of the proton relaxation rates in the axial (the DD principal axis coinciding with the ZFS principal axis) and the equatorial (the DD principal axis perpendicular to the ZFS principal axis) positions takes on the value of unity in the Zeeman limit and up to four in the ZFS limit. A similar spin-dynamics analysis of the NMRD data for a Mn(II) complex has also been reported (133). 

In all the approaches mentioned below, it is assumed that the correlation function can be factorized into a product of correlation functions for the three degrees of freedom rotational motion, translational diffusion and electron spin dynamics. 

Abernathy and Sharp (130,145) treated the intermediate regime, when the reorientation of the paramagnetic species is in-between the slow- and fast-rotations limits. They applied the spin-dynamics method, described in Section VI, to the case of outer-sphere relaxation and interpreted NMRD profiles for non-aqueous solvents in the presence of complexes of Ni(II) (S = 1) and Mn(III) (S = 2). 

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

---