Systems magnetic resonance spin-Hamiltonian parameters

There are many experimental techniques for the determination of the Spin-Hamiltonian parameters g, Ux, J. D, E. Often applied are Electron Paramagnetic or Spin Resonance (EPR, ESR), Electron Nuclear Double Resonance (ENDOR) or Triple Resonance, Electron-Electron Double Resonance (ELDOR), Nuclear Magnetic Resonance (NMR), occasionally utilizing effects of Chemically Induced Dynamic Nuclear Polarization (CIDNP), Optical Detections of Magnetic Resonance (ODMR) or Microwave Optical Double Resonance (MODR), Laser Magnetic Resonance (LMR), Atomic Beam Spectroscopy, and Muon Spin Rotation (/iSR). The extraction of data from the spectra varies with the methods, the system studied and the physical state of the sample (gas, liquid, unordered or ordered solid). For these procedures the reader is referred to the monographs (D). Further, effective magnetic moments of free radicals are often obtained from static... 

Electron Spin Echo Envelope Modulation (ESEEM) and pulse Electron Nuclear Double Resonance (ENDOR) experiments are considered to be two cornerstones of pulse EPR spectroscopy. These techniques are typically used to obtain the static spin Hamiltonian parameters of powders, frozen solutions, and single crystals. The development of new methods based on these two effects is mainly driven by the need for higher resolution, and therefore, a more accurate estimation of the magnetic parameters. In this chapter, we describe the inner workings of ESEEM and pulse ENDOR experiments as well as the latest developments aimed at resolution and sensitivity enhancement. The advantages and limitations of these techniques are demonstrated through examples found in the literature, with an emphasis on systems of biological relevance. 

One of our main motivations for pursuing the development of a density functional response theory for open-shell systems has been to calculate spln-Hamiltonian parameters which are fundamental to experimental magnetic resonance spectroscopy. It is only within the context of a state with well-defined spin we can speak of effective spin Hamiltonians. The relationship between microscopic and effective Hamiltonians rely on the Wigner-Eckart theorem for tensor operators of a specific rank and states which transform according to their irreducible representations [45]. 

In all single-crystal studies, the variation in resonance frequency or magnetic field is studied as a function of the orientation of the crystal in the magnetic field. A spin Hamiltonian of appropriate form is then solved and the parameters adjusted to fit the calculated variation with the experimental data. Most errors in doing this occur because approximate solutions of spin Hamiltonians are used for systems for which the approximations are not justified. Second-order effects are often very important in analyzing single-crystal ESR and ENDOR measurements. 

The evolution of the density matrix is governed by Eq. (2.10) in which the Hamiltonian for the spin system must be specified. It is noted here that the relaxation effects arising from dissipative interactions between the spin system and the lattice have not been included in the equation. The nuclear spin Hamiltonian contains only nuclear spin operators and a few phenomenological parameters that originate from averaging the full Hamiltonian for a molecular system over the lattice coordinates. These magnetic resonance parameters can, at least in principle, be deduced by quantum chemical calculations [2.3]. The terms that will be needed for discussion in this monograph will be summarized here. 

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