Multiple resonance

Through line-shape, saturation, and spin-lock methods, the entire range of rates accessible to NMR is about 10 to 10 s Thus, NMR has become an important method for studying the kinetics of reactions at equilibrium over a very large dynamic range. 

Special effects may be routinely and elegantly created by using sources of radiofrequency energy in addition to the observation frequency (uj = yBi) y = y/2i ). The technique is called multiple irradiation or multiple resonance and requires the presence of a second transmitter coil in the sample probe to provide the new irradiating frequency ( 2 = yBi). When the second frequency is applied, the experiment, which is widely available on modern spectrometers, is termed double resonance or double irradiation. Less often, a third frequency (U3 = yBf) also is provided, to create a triple-resonance experiment. We already have seen several examples of multiple-irradiation experiments, including the removal of 

Experiments in which both the irradiated and the observed nuclei are protons are called homonuclear double-resonance experiments and are represented by the notation The irradiated nucleus is denoted by braces. When the observed and irradiated nuclei are different nuclides, as in proton-decoupled spectra, the experiment is a heteronuclear double-resonance experiment and is denoted, for example, C H.  

NMR spectroscopy as a routine tool. The double-irradiation field B2 was traditionally centered at about 8 5 of the H range. To cover all the H frequencies, B2 was modulated with white noise, so the technique often was called noise decoupling. 

Of course, the temptation will be to run a spectrum for every conceivable nucleus in every sample, which can be wasteful of expensive instrument time. The message we wish to give is that many different nuclei can now be routinely observed, and it is worth remembering that, in some circumstances, running a spectrum of one of the more unusual nuclei may save a lot of time and trouble. The important point is to be able to work out in advance which experiment(s) will solve the structural problem at hand. 

Multiple resonance experiments involve the use of more than one frequency to irradiate the sample. The most often used variant is spin decoupling. In these experiments, a nucleus A is observed while a nucleus X is 

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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. 

Freed J 1979 Theory of multiple resonance and ESR saturation In liquids and related media Multiple Electron Resonance Spectroscopy ed M M Dorlo and J H Freed (New York Plenum) ch 3, pp 73-142... 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

Multiple resonance was observed at T = 723 K and rs = 0.01 s. The enhancement, exceeds 1 at a cycle period between 0.2 and 0.3 s and also at greater than 1000 s, although quasi steady state is also attained at about that period. Resonance also occurs at two different cycle periods at ts = 0.02 s, T is much smaller. As the space-time increases above 0.25 s, the rate enhancement becomes very small and the multiple resonance phenomenon seems to disappear. 

The proton decoupled carbon 13 NMR spectra for three poly( cyclohexylmethyl-co-isopropylmethyl) copolymers are shown in Figure 4. The backbone methyl group is observed as occurring between -4 and -1 ppm and consists of multiple resonances which are due to polymer microstructure. Multiple resonances are also observed for the methyl and tertiary carbon of the isopropyl group and for the methine carbon of the cyclohexyl group. Microstruc-tural assignments for these resonances remain to be made. It has also been found that increasing the bulky character of the substituent yielded broader resonance peaks in the carbon-13 NMR spectra. 

Phosphorescence microwave multiple resonance studies are likely to grow in importance in the next ten years as more systems are studied. 

As suggested by the original resonance theory of Pauling and Wheland,51 such delocalization effects appear to represent some type of average of multiple resonance structures. A general goal of resonance theory is to represent each property (P)true of the true delocalized system in resonance-averaged form... 

Although such textbook diagrams are called Lewis structures, they are not the electron-dot diagrams that G. N. Lewis originally wrote for such species. Lewis s depiction of S042-, for example, is reproduced in Fig. 3.90. This shows a normal-valent S2+ ion with shared-pair bonds to four O- ions, which is fully consistent with the octet rule, with no intrinsic need for multiple resonance structures to account for the observed Td symmetry. According to Lewis s original concept, each ion is... 

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 ENDOR techniques, of course, are not confined to studies of transition metal complexes. A fast growing interest on electron nuclear double and multiple resonance experiments is also noticed in other fields of natural sciences, such as radical, radiation and polymer chemistry, solid state physics, biophysics and mineralogy. 

M. A. El-Sayed, Optical pumping of the lowest triplet state and multiple resonance optical techniques in zero field, J. Chem. Phys. 54, 680-691 (1971). 

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 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... 

El-Sayed, M. A. Phosphorescence-microwave multiple resonance spectroscopy. In MTP International Review of Science, Physical Chemistry Series One, Vol. 3. 

Phosphorescence and Delayed Fluorescence from Solutions (Parker). . . Phosphorescence-Microwave Multiple Resonance Spectroscopy... 

R.D. Kendrick, C.S. Yannoni, High-Power H-1-F-19 Excitation in a Multiple-Resonance Single-Coil Circuit, J. Magn. Reson. 75 (1987) 506-508. 

Uwada T, Asahi T, Masuhara H, Ibano D, Fujishiro M, Tominaga T (2007) Multiple resonance modes in localized surface plasmon of single hexagonal/triangular gold nanoplates. Chem Lett 36(2) 318-319... 

Amides. Although similar to esters in terms of being a functional derivative of a carboxylic acid, amides, unlike esters, are relatively metabolically stable. In general, amides are stable to acid- and base-catalyzed hydrolysis. This stability is related to the overlapping electron clouds within the amide functionality and the corresponding multiple resonance forms. Amidases are enzymes that can catalyze the hydrolysis of amides. Nevertheless, amides are much more stable than esters. 

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. 

R. W. Field Each acetylene polyad contains zero-order states that are easily accessible via plausible direct or multiple-resonance A XAU — X Franck-Condon pumping schemes. Each Vib 16,000... 

When selective layers are deposited, the whole structure must be treated as a multiple resonator in which the reflection and/or refraction of the acoustic energy occurs at each interface. For example, when a polymer film is deposited on top of the gold electrode of the QCM, it is the polymer-Au interface with which we are concerned. When the mass loading of multiple structures becomes too high, the effect of the impedance mismatches becomes significant and the crystal ceases to oscillate. Even approximate treatment of the multiple resonator is difficult because densities, as well as thicknesses and shear moduli, of the individual layers must be known. 

Further support for a long range interaction in IETS came from calculations by Kirtley and Soven (22) showing that multiple resonance scattering of the initial and final electronic wavefunctions, which would be expected for a short range interaction, lead to large second harmonic peaks, much larger than are observed experimentally. 

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