Resonance condition systems

With help of the four-level diagram of the =I= system (see figure BL15.8 two conniion ways for recording ELDOR spectra will be illnstrated. In freqnency-swept ELDOR the magnetic field is set at a value that satisfies the resonance condition for one of the two EPR transitions, e.g. 4<- 2, at the fixed observe klystron frequency, The pump klystron is then turned on and its frequency, is swept. When the pump... 

From this equaiion one can determine the required value of neutral circuit impedance for a particular level of ground fault current. The external impedance will be Z, less the ground impedance. In HT systems one c in also delermine the likely value of a ground inductor coil to achieve a near-resonance condition, to eliminate the arcing grounds, on the one hand, and facilitate a strike-free extinction of an arc hy the interrupting device, on the other. 

A capacitor bank will represent reducing impedance to currents of increasing frequency. Such reducing impedance, if matched with a similarly increasing inductance impedance of a transformer or a supply system, can cause a resonant condition. In plants where equipment produces harmonic current, a full survey of the installation is recommended prior to installation of the capacitors. 

Before we develop the resonance conditions for systems with hyperhne and with zero-held interactions, we return to the electronic Zeeman term S B as an example interaction to discuss a hitherto ignored complexity that is key to the usefulness of EPR spectroscopy in (bio)chemistry, namely anisotropy the fact that all interactions... 

Let us rewrite the resonance condition of an S = 1/2 system subject to the Zeeman interaction only as... 

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

In this chapter we continue our journey into the quantum mechanics of paramagnetic molecules, while increasing our focus on aspects of relevance to biological systems. For each and every system of whatever complexity and symmetry (or the lack of it) we can, in principle, write out the appropriate spin Hamiltonian and the associated (simple or compounded) spin wavefunctions. Subsequently, we can always deduce the full energy matrix, and we can numerically diagonalize this matrix to obtain the stable energy levels of the system (and therefore all the resonance conditions), and also the coefficients of the new basis set (linear combinations of the original spin wavefunctions), which in turn can be used to calculate the transition probability, and thus the EPR amplitude of all transitions. 

If one then defines the resonance condition, Br (alternately written as Bo or as Br when referring to the laboratory field associated with a particular EPR instrument system), as the magnetic field at which the energy of the transition comes into resonance with the field, one finds equation 3.16 or, more usefully, equation 3.17 ... 

The probability of finding the system in the state vRjn> has an oscillatory time dependence. For off-resonance conditions, the system presents a line width at half maximum equal to 4 ll/fi. This matrix element can be expanded in a multipolar expansion, the first term being the electric dipole approximation [45, 152, 154],... 

The reactant R2 can also be considered to be a solvent molecule. The global kinetics become pseudo first order in Rl. For a SNl mechanism, the bond breaking in R1 can be solvent assisted in the sense that the ionic fluctuation state is stabilized by solvent polarization effects and the probability of having an interconversion via heterolytic decomposition is facilitated by the solvent. This is actually found when external and/or reaction field effects are introduced in the quantum chemical calculation of the energy of such species [2]. The kinetics, however, may depend on the process moving the system from the contact ionic-pair to a solvent-separated ionic pair, but the interconversion step takes place inside the contact ion-pair following the quantum mechanical mechanism described in section 4.1. Solvation then should ensure quantum resonance conditions. 

Polarization-transfer experiments which are based on a resonance condition, i.e. where a variable quantity in the experiment is matched to a parameter of the investigated spin system, can be carried out as a transient experiment or as an adiabatic experiment Figure 11.5 illustrates the differences between these two types of experiments. In a transient or sudden" experiment, the density operator is prepared in a state orthogonal to the effective polarization-transfer Hamiltonian (Fig. 11.5a). When the polarization-transfer Hamiltonian is switched on, the density operator starts precessing around the effective Hamiltonian, and usually maximum polarization transfer is reached after a 180° rotation. Since often the size of the effective Hamiltonian at the matching condition depends on... 

What is the mechanism by which this energy transfer occurs 86) Figure 9 shows that should happen. We start with the system S (excited)-)- A (ground state) and end up with the system S (ground state) -f A (excited). This is only possible, if one of the levels of A lies at the same height as the luminescent level of S (resonance condition). Further we need an interaction between S and A. 

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