Spin Hamiltonian quadrupole coupling

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

The quadrupole coupling term in the spin Hamiltonian can be written as ... 

In this section analytical expressions for ENDOR transition frequencies and intensities will be given, which allow an adequate description of ENDOR spectra of transition metal complexes. The formalism is based on operator transforms of the spin Hamiltonian under the most general symmetry conditions. The transparent first and second order formulae are expressed as compact quadratic and bilinear forms of simple equations. Second order contributions, and in particular cross-terms between hf interactions of different nuclei, will be discussed for spin systems possessing different symmetries. Finally, methods to determine relative and absolute signs of hf and quadrupole coupling constants will be summarized. 

The resolution of the molecular beam experiments is high enough to observe even rather small nuclear hyperfine interactions such as the spin-spin and spin-rotation interactions as well as the larger quadrupole coupling interactions. The largest terms in the Hamiltonian for the hyperfine splittings are given below 66) ... 

In this section, we attempt to review the solid-state Co NMR data published up to the end of 1998. The data on chemical shift tensors and quadrupole coupling constants are summarized in Tables 1-4. Data obtained by nuclear quadrupole resonance (NQR) are included wherever appropriate. Readers interested in the spin-spin coupling between spin-1 /2 and Co nuclei are referred to an article by Wasylishen and colleagues and the references cited therein. The NMR conventions employed in this review are defined in the next section. This is followed by a discussion of the techniques that have been applied to solid-state Co NMR studies with emphasis on what has been applied to Co systems. A detailed discussion on the techniques and Hamiltonians for quadrupolar nuclei is referred to the comprehensive review by Freude and Haase. 

A more general spin Hamiltonian of the form (3.9) is applied when zero-field splittings (S > V2), anisotropic hyperfine interactions (/ 0), and nuclear quadrupole couplings (/ > 1) occur. 

The first three terms are usually the ones of relevance for the ESR analysis, where D and A are the zero-field (or fine structure) and hyperfine coupling tensors. They are represented by 3-3 symmetric matrices and specified by three principal values and three principal directions as for the -tensor. The remaining nuclear Zeeman and quadrupole (/ > Vi) terms do not affect the ESR spectra, unless they are of comparable magnitude to the hyperfine coupling, but must be taken into account in the analysis of ENDOR and ESEEM spectra. The spin Hamiltonian formalism introduced by M.H.L. Pryce and A. Abragam [79] is used explicitly or implicitly in the ESR literature as a convenient way to summarise resonance parameters. 

In the presence of quadrupole interactions the spin hamiltonian may be written as a sum of the nuclear Zeeman interaction and the quadrupole coupling term... 

The simulated spectra in Figure 18 represent a series of replicate ESEEM experiments performed on a system containing a single Cu- N interaction with a Fermi contact interaction energy of 26 MHz and quadrupole coupling (e Qqzz) of 3.5 MHz. It is immediately evident from these simulations that the behavior observed at the X-band is reproduced at the W-band provided that the spin-Hamiltonian model that is used to describe experiments at the X-band is not affected in the extremely high magnetic fields of the W-band i.e., no introduction of nonlinear effects). The W-band ESEEM spectra of the Type I copper center of azu-... 

The information obtained from the spin Hamiltonian, the 3x3 matrices g, D, A, and P, is very sensitive to the geometric and electronic structure of the paramagnetic center. The electron Zeeman interaction reveals information about the electronic states the zero-field splitting describes the coupling between electrons for systems where S > Vi the hyperfine interactions contain information about the spin density distribution [8] and can be used to evaluate the distance and orientation between the unpaired electron and the nucleus the nuclear Zeeman interaction identifies the nucleus the nuclear quadrupole interaction is sensitive to the electric field gradient at the site of the nucleus and thus provides information on the local electron density. 

---