Multiple resonant frequencies

The corresponding quantum mechanical expression of s op in Equation (4.19) is similar except for the quantity Nj, which is replaced by Nfj. However, the physical meaning of some terms are quite different coj represents the frequency corresponding to a transition between two electronic states of the atom separated by an energy Ticoj, and fj is a dimensionless quantity (called the oscillator strength and formally defined in the next chapter, in Section 5.3) related to the quantum probability for this transition, satisfying Jfj fj = l- At this point, it is important to mention that the multiple resonant frequencies coj could be related to multiple valence band to conduction band singularities (transitions), or to transitions due to optical centers. This model does not differentiate between these possible processes it only relates the multiple resonances to different resonance frequencies. 

The semiquinone biradical produced in the photocycle of bacterial photosynthetic reaction centres was trapped at 77 K and examined at 9.6, 35, and 94 GHz.16 Simulations of spectra at the multiple resonant frequencies using the simulated annealing method revealed the spatial and electronic structure of the biradical. The value of r was found to be 17.2 + 0.2 A, which is in good agreement with the value of 17.4 0.2 A obtained in an X-ray crystal structure. This study shows the power of high-frequency EPR combined with data obtained at lower frequencies. 

FIGURE 15.43 An example of the isolated molecular ion cluster for a heptabromodiphe-nylether congener. Multiple resonant frequencies in the ion trap can be used to achieve dissociation of the entire cluster. The approach is highly sensitive and selective. 

In the previous chapters experiments have been discussed in which one frequency is applied to excite and detect an EPR transition. In multiple resonance experiments two or more radiation fields are used to induce different transitions simultaneously [19, 20, 21, 22 and 23], These experiments represent elaborations of standard CW and pulsed EPR spectroscopy, and are often carried out to complement conventional EPR studies, or to refine the infonnation which can in principle be obtained from them. 

The electronic structure of dichorodiphenylplumbane was calculated by the SCF-MS (self-consistent field multiple scattering) molecular orbital method and compared to that of dichlorodiphenylstannane. The results suggest that one has to look for 35C1 NQR (nuclear quadrupole resonance) frequencies of dichorodiphenylplumbane in the 5-6 MHz region1613. 

Two methods of further enhancing detection sensitivity rely on the use of multiple resonators or multiple fiber modes. The first will just be mentioned briefly, because although it is absorption based it uses a frequency shift. When two microresonators have resonances that are coincident in frequency, and the second resonator is brought near to the first resonator, which is in contact with the coupling fiber, the... 

The development of simple, multiple-frequency solvent suppression techniques has greatly improved the quality of data that can be obtained using LC-NMR. One of the most useful methods for multiple resonance solvent suppression in LC-NMR is... 

Acquisition scheme for the multiple selective heteronuclear inverse detected ID COSY experiment. Four experiments have to be performed with 3 carbon resonances selected for selective perturbation. The frequencies are set either on-resonance (/i, fi, /j) or off-resonance to the selected resonance frequencies. 

Note that if j = 1, (9.12) is formally identical with the classical expression (9.7) the classical multiple oscillator model, which will be discussed in Section 9.2, is even more closely analogous to (9.12). However, the interpretations of the terms in the quantum and classical expressions are quite different. Classically, o30 is the resonance frequency of the simple harmonic oscillator quantum mechanically 03 is the energy difference (divided by h) between the initial or ground state / and excited state j. Classically, y is a damping factor such as that caused by drag on an object moving in a viscous fluid quantum mechanically, y/... 

In general, the resonant frequencies can be used to determine molecular structures. H resonances are fairly specific for the types of carbon they are attached to, and to a lesser extent to the adjacent carbons. These resonances may be split into multiples, as hydrogen nuclei can couple to other nearby hydrogen nuclei. The magnitude of the splittings, and the multiplicity, can be used to better determine the chemical structure in the vicinity of a given hydrogen. When all of the... 

To mimic the PG electrode surface for QCM measurements of layers adsorbed on the gold-quartz resonators, we first chemisorb a mixed monolayer of mercaptopropionic acid/mercaptopropanol. This layer is represented by the first point in Fig. 2, labeled MPA. The second layer is PDDA. Quartz crystal microbalance frequency decreasing in a roughly linear fashion and at regular intervals for the multiple adsorption steps demonstrates repeatable adsorption for the two DNA/en-zyme films. Relative precision of layer formation on multiple resonators within 15% can be achieved. Film thicknesses and component weights in Table 1 were obtained by analyzing the QCM data with Eqs. 1 and 2. 

Facilities for a variety of multiple-resonance experiments, including broad-band, homo- or hetero-nuclear decoupling, are now generally built into the spectrometer, instead of being provided by auxiliary audio-oscillators. Oscilloscopes for optimization of magnetic-field homogeneity, precalibrated recorder-charts, and frequency counters for accurate calibration of charts and frequencies for multiple... 

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