Multi-resonance

Panels of multi-resonator material are made from perforated plate sandwiched with solid plate and an intermediate absorber layer between them. These panels can be built up in enclosures, taking care to seal all junctions adequately. Typically, these enclosures are made to surround small machines (e.g. compressors). They may be fitted together with spring catches to allow for dismantling for maintenance purposes. 

In practice, the NBO program labels an electron pair as a lone pair (LP) on center B whenever cb 2 > 0.95, i.e., when more than 95% of the electron density is concentrated on B, with only a weak (<5%) delocalization tail on A. Although this numerical threshold produces an apparent discontinuity in program output for the best single NBO Lewis structure, the multi-resonance NRT description depicts smooth variations of bond order from uF(lon) = 1 (pure ionic one-center) to bu 10n) = 0 (covalent two-center). This properly reflects the fact that the ionic-covalent transition is physically a smooth, continuous variation of electron-density distribution, rather than abrupt hopping from one distinct bond type to another. 

The Sn2 reactions are good examples to highlight the different merits of VB and MO theories in quantum chemistry [65]. In the VB method, the atomic features are preserved and the focus is the two-electron-two-center bonds, and each molecule is formed with bonds (plus the lone and core pairs). Whereas one resonance structure is not enough to describe a molecule, multi-resonance structures are adopted. In fact, the resonance theory can also be applied to illustrate the reactions in an intuitive way. For example, for the chloride-exchange reaction... 

The orbital <[>res is a resonant orbital, in which a hot electron is attached to form a temporary anion. We assume that desorption is triggered by single orbital resonance to ([>res through an extension to multi-resonant levels is straightforward. The term n) is the occupation of the electron in the ground state, and is required to keep the Pauli principle. The coefficient r eN is the reactive eN coupling factor and assumed to be... 

Equation (4.2.11) describes the response to three delta pulses separated by ti =oi — 02 >0, t2 = 02 — 03 > 0, and t3 = 03 > 0. Writing the multi-pulse response as a function of the pulse separations is the custom in multi-dimensional Fourier NMR [Eml ]. Figure 4.2.3 illustrates the two time conventions used for the nonlinear impulse response and in multi-dimensional NMR spectroscopy for n = 3. Fourier transformation of 3 over the pulse separations r, produces the multi-dimensional correlation spectra of pulsed Fourier NMR. Foinier transformation over the time delays <7, produces the nonlinear transfer junctions known from system theory or the nonlinear susceptibilities of optical spectroscopy. The nonlinear susceptibilities and the multi-dimensional impulse-response functions can also be measured with multi-resonance CW excitation, and with stochastic excitation piul]. 

Abstract Multi-resonance involves ENDOR, TRIPLE and ELDOR in continuous-wave (CW) and pulsed modes. ENDOR is mainly used to increase the spectral resolution of weak hyperfine couplings (hfc). TRIPLE provides a method to determine the signs of the hfc. The ELDOR method uses two microwave (MW) frequencies to obtain distances between specific spin-labeled sites in pulsed experiments, PELDOR or DEER. The electron-spin-echo (ESE) technique involves radiation with two or more MW pulses. The electron-spin-echo-envelope-modulation (ESEEM) method is particularly used to resolve weak anisotropic hfc in disordered solids. HYSCORE (Hyperfine Sublevel Correlation Spectroscopy) is the most common two-dimensional ESEEM method to measure weak hfc after Fourier transformation of the echo decay signal. The ESEEM and HYSCORE methods are not applicable to liquid samples, in which case the FID (free induction decay) method finds some use. Pulsed ESR is also used to measure magnetic relaxation in a more direct way than with CW ESR. 

Multi-resonance and pulsed ESR techniques can provide better spectral resolution than conventional ESR. Multi-resonance involves ENDOR, TRIPLE and ELDOR. In an ENDOR experiment a radiofrequency (RF) field is applied in addition to the microwave (MW) employed in standard continuous wave (CW) ESR. ENDOR is mainly used to increase the spectral resolution, so that overlapping or unresolved hyperfine structure in the ESR spectra can be detected. In the classical work by Feher [1] the radiofrequency was continuously swept. CW X-band spectrometers with an ENDOR attachment have been commercially available for a long time. Accessories for other frequency bands and for pulsed ESR have been developed more recently. In a TRIPLE experiment two RE fields are applied [2, 3]. A theoretical application has been to determine the relative signs of two hyperfine couplings. In an ELDOR experiment two MW frequencies are applied. Early applications using... 

The use of multi resonance techniques such as ENDOR together with general / special TRIPLE resonance techniques has now become much more common as the techniques move more into more general use, certainly towards the end of the review period. The use of such techniques has enabled very small hyperfine coupling constants (smaller than the linewidth) to be measirred which would normally be inaceessible to... 

However, most sensors used currently in AE applications for concrete are manufactured in a more traditional way, showing either a resonant behavior or several particular resonances. These sensors, which are called multi-resonance transducers, have a higher sensitivity than sensors with a backward mass used outside of their resonance fiequency. Such sensors should not, however, be considered as (true) broadband and it is essential to know their frequency response function. Otherwise, signal characteristics from the source are not distinguishable from artifacts introduced by incorrect knowledge of the frequency response. A calibration of the sensors frequency response, as well as understanding of the direction sensitivity, is important for many applications of AET. 

However, all four designs have practical advantages, and certainly in our own laboratory we believe in a flexible multi-resonator, multi-frequency approach to spectrometer design. 

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