Spectra of first and higher order

CH group [two vicinal H), a quartet for the OCH2 group (three vicinal H) and a singlet for the  

First-order spectra (multiplets) are observed when the coupling constant is small compared with the frequency difference of chemical shifts between the coupling nuclei This is referred to as an An (n spin system, where nucleus A has the smaller and nucleus X has the considerably larger chemical shift. An AX system (Fig. 1.4) consists of an. d doublet and an X doublet with the common coupling constant. The chemical shifts are measured from the centres of each doublet to the reference resonance. 

An AB system (Fig. 1.6) consists, for example, of an doublet and a B doublet with the common coupling constant Jab, where the external signal of both doublets is attenuated and the internal signal is enhanced. This is referred to as an AB effect, a roofing symmetric to the centre of the AB system roofing is frequently observed in proton NMR spectra, even in practically first order spectra (Fig. 1.2, ethyl quartet and triplet). The chemical shifts Va and Vb are displaced from the centres of the two doublets, approaching the fi equencies of the more intense inner signals. 

The //NMR spectrum of ethyl dichloroacetate (Fig. 1.2), as an example, displays a triplet for the CHs group two vicinal H), a quartet for the OCH2 group (three vicinal H) and a singlet for the C//CI2 fragment (no vicinal H for coupling). 

Speetra of greater eomplexity may oeeur for systems where the eoupling eonstant is of similar magnitude to the ehemieal shift differenee between the eoupled nuelei. Sueh a ease is referred to as an A ,B system, where nueleus A has the smaller and nueleus B the larger ehemieal shift. 

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For the case of oblique incidence, first- and higher-order diffractions are permitted. The polarization becomes elliptical in this case. Precise measurements of the reflection spectrum for the obhque incidence of this hght were given in [19]. First- and second-order reflection spectra were calculated and observed. The analytical solution of Maxwell s equations by the dynamical theory of diffraction [20] is in good agreement with experimental data [19]. The exact solution of Maxwell s equations has not been yet developed, because the theory is very complicated. 

While Hartree-Fock type calculations of F and CsfCan be carried out for any arbitrary state of ionization of an actinide ion, the relative importance of the ligand (or crystal) field must also be established in order to develop a correlation to experimentally observed transition energies. Ab initio models of the ligand field are characteristically very crude. The spectra of penta- and higher-valent actinides are strong-crystal-field cases and the development of correction terms for the first-order crystal field model may well be essential to any detailed analysis. 

The quadrupolar effects of order higher than two (7) are usually assumed to be negligible, especially at high magnetic fields. However, once the first- and second-order effects are removed, the measurement of third-order contributions becomes realistic. It can be easily shown that, similar to the first-order case, the CT and all symmetric MQ transitions (q = 0) are free of the third-order contribution, which thus can be safely ignored in DAS, DOR, and MQMAS experiments [161,162]. This is not the case for transitions between non-symmetric spin states, such as the STs. Indeed, numerical simulations of the third-order effect have explained the spectral features that have been observed in 27A1 STMAS spectra of andalusite mineral [161]. 

Derivative spectroscopy provides a means for presenting spectral data in a potentially more useful form than the zero th order, normal data. The technique has been used for many years in many branches of analytical spectroscopy. Derivative spectra are usually obtained by differentiating the recorded signal with respect to wavelength as thf spectrum is scanned. Whereas early applications mainly relied on hard-wired units for electronic differentiation, modem derivative spectroscopy is normally accomplished computationally using mathematical functions. First-, second-, and higher-order derivatives can easily be generated. 

Interpretation of NMR spectra can be very difficult if we consider all the multiplicities that are possible from the interactions of all the nuclei. If we confine ourselves to spectra in which the chemical shift between interacting groups is large compared with the value of /, the splitting patterns and the spectra are easier to interpret. This is called utilizing first order spectra. The more complicated systems resulting in second order and higher order spectra will not be dealt with in this text. The term second order spectrum must not be confused with 2D NMR spectra, which will be discussed later in the chapter. 

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