Electron-spin interactions

Bayburt and Sharp 143) formulated a low-field theory (i.e. a theory for the case of ZFS dominating over the electron spin interaction) for the outer-sphere relaxation, treating also the electron spin relaxation in the simplified manner expressed by Eq. (52). That model predicted only a weak dependence of the PRE on the magnitude of the static ZFS and its application to the cases of high static ZFS is problematic. 

A special focus will be on phenomenological Hamiltonians involving electronic spin interactions. For this it is necessary to define atomic surrogate spin operators—so-called local spin operators—that may be directly related to the effective spins in... 

The notation of Sect. Ill for adiabatic wave functions is being used.) Assuming that the electronic spin interaction matrix element varies only... 

Fig. 8. BPR spectra of [3Fe-xS] clusters in oxidized hydrogenases, showing th influences of weak Ni-Fe-S electron-spin interactions, (a) Desulfovibrio desulfurican (strain Norway 4) hydrogenase, showing the spectrum of an isolated [3Fe-xS] cluster (b Chromatium vinosum hydrogenase the outer lines (Signal 2) correspond to interactio with Ni(lH) (c) Paracoccus denitrificans hydrogenase (d) Alcaligenes eutrophu membrane-bound hydrogenase. Spectra were recorded at approximately 20 K. Sample were provided by K. K. Rao, J. Serra, and K. Schneider.

The first term on the right-hand side arises from external electric fields. The second (B) term arises from external magnetic inductions interacting with electronic orbital motion. The SL term arises from electron spin-orbital motion interactions. The Z term arises from the Zeeman interaction between electron spin and the external electric field. H s arises from electron spin-electron spin interactions and includes all hyperfine terms arising from nuclear spins. 

Historically, the first experimental evidence of the JT effect was observed by ESR by the splitting of the Lande factor (0-tensor) in 1952 on magnetically diluted Cu2+ salts. Indeed this factor is very sensitive to even small deviation from the cubic symmetry, as will be the case for a static JTD. However, in many cases, such effects could be hidden for C60-based materials by broad linewidths arising from strong electron-spin interactions. It is essential to work with well-separated Cgo ions for this effect to be detectable. 

The eigenfunctions of Hare written as W, and the eigenvalues as E. Although H contains no electron spin interactions, the F do depend upon both the spatial and spin co-ordinates of the electrons ... 

Electron spin-electron spin interaction. The transition betwen a and P spin states takes place by the interaction between the A spins and the surrounding off-resonant spins (called B spins). The most important process in this type of the relaxation is cross relaxation. In the cross relaxation, the excess energy of the A spin system is resonantly transferred to the surrounding B spins through a flip-flop process. The relaxation rate depends on either the distance betwen the A and B spins or the number of the B spins surrounding an A spin. It is this relaxation mechanism which provides us with a means for studying the local spatial distribution of radical species. 

The transverse relaxation is often called spin-spin relaxation and its relaxation rate is expressed by the inverse of the spin-spin relaxation time T2. However, these seems to be misleading, because the transverse relaxation is induced not only by electron spin-electron spin interaction, and the observed kinetics of the relaxation cannot always be expressed by a single exponential function. 

W = —/A-H /A-(vXE) = /A (pX r)jE/mcr for a spherically symmetric field E = Er/r. Since L = — (p X r) and fi = — Spa, equation 8 follows immediately.] For the transition metals of the iron group, the spin-orbit parameter X is of the order of 100 to 1000 cm 1. Goudsmit (231) has shown that X reverses sign on going from a less than half to a more than half filled shell. The physical origin of this sign reversal lies in the fact that an electron spin interacts more strongly with its own orbital momentum. From Hund s rule it follows that if a shell is less than half filled, the individual electrons have their spins parallel to the net spin if the shell is more than half filled, the individual electrons responsible for a multiplet have their spins antiparallel to the net spin. 

The next step is to add terms representing the potential energy, the electron spin interactions and the nuclear spin interactions. The total Hamiltonian Xj can then be subdivided into electronic and nuclear Hamiltonians,... 

In our subsequent development we shall take the origin of coordinates to be at the centre of mass of the two nuclei, although we could equally well have chosen the molecular centre of mass as origin. Setting aside the translational motion of the molecule, we use equation (2.28) to represent the kinetic energy of the electrons and nuclei. To this we add terms representing the potential energy, electron spin interactions, and nuclear spin interactions. We subdivide the total Hamiltonian Xx into electronic and nuclear Hamiltonians,... 

In addition to these modifications on transforming the electron spin to molecule-fixed quantisation, we must rewrite the electron spin interactions 36(5)) as... 

In a detailed consideration of the full Hamiltonian, De Santis, Lurio, Miller and Freund [44] in paper II show that the required effective Hamiltonian for a given vibrational level v can be written as the sum of a part describing the rotational motion with electron spin interactions, and a part describing the magnetic and electric hyperfine interactions. The first part may be written ... 

With the exception of CN, all molecular identifications of interstellar lines are based on direct laboratory measurements. The location of the CN radio transitions can be predicted from laboratory ultraviolet data (Poletto and Rigutti, 1965) and is found to be in reasonable agreement with the positions given by the interstellar observations. However, the hyperfine structure (electric quadra-pole and nuclear spin-electronic spin interaction) cannot be uniquely assigned therefore an element of caution has to be maintained until more observational evidence — either from interstellar or laboratory measurements — confirms the assignment. (See Note Added in Proofs- 33). 

For proton—proton coupling it has been shown that the spin interaction arises principally from the electron spin—electron spin interaction, not from orbital interaction of electrons. This simplifies the theory somewhat. For some other nuclei, orbital interaction may also come into play. We shall summarize a few of the conclusions applicable to spin—spin coupling without going through the details of the theory. 

B. Electron Spin Interactions A Source of Chemical Information... 

The presence of two spins in a triplet [70, 71] or biradical [72] species results in additional ESR features, viz. fine structure effects as a result of electron spin-electron spin interactions [69], The phenomena observed and results derived therefrom are best discussed for simple examples, viz., the interaction of two equivalent centers in structurally well-characterized molecules. 

The prominence of these quantum dynamical models is also exemplified by the abundance of theoretical pictures based on the spin-boson model—a two (more generally a few) level system coupled to one or many harmonic oscillators. Simple examples are an atom (well characterized at room temperature by its ground and first excited states, that is, a two-level system) interacting with the radiation field (a collection of harmonic modes) or an electron spin interacting with the phonon modes of a surrounding lattice, however this model has found many other applications in a variety of physical and chemical phenomena (and their extensions into the biological world) such as atoms and molecules interacting with the radiation field, polaron formation and dynamics in condensed environments. 

CIDNP is based on the following principle 431,432 Initially, the radical pair is born in a spin-correlated state. To form a product in the singlet ground state, the electronic spin state of the radical pair must be a singlet state. Importantly, the electron spins interact with the nuclear spin states. ISC from a triplet to a singlet radical pair is favoured, when... 

The energy shift due to the electron spin interacting with the magnetic field is named the Zeeman term. 

As the ENDOR spectrum is in effect an NMR spectrum obtained by devious means, when considering the response of a nucleus with spin / one must keep track of all interactions that it and its coupled electron spin undergo. The energy levels of an unpaired electronic spin S in an externally applied magnetic field, and the associated EPR spectra, are described in detail elsewhere in this volume. As described therein, the interaction of an electronic spin in an external magnetic field is characterized by the parameter g. In a molecule, the magnitude of the electron spin interaction depends on the orientation of the molecule with respect to the external magnetic field, and thus g is a tensor quantity. 

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