First-derivative-shaped bands

The first and second derivatives of an absorbance spectrum A(v) with respect to wavenumber V can provide useful information for spectral analysis. In a first-daivative spectrum, local maxima, local minima, and inflection points in the original spectrum are more easily detected. As the first-derivative spectrum has an effect of baseline correction, bands of first-derivative shape are more clearly observable than the corresponding bands in the original... 

Electron spin relaxation in aqueous solutions of Gd3+ chelates is too rapid to be observed at room temperature by the usual pulsed EPR methods, and must be studied by continuous wave (cw) techniques. Two EPR approaches have been used to study relaxation studies of the line shape of the cw EPR resonance of Gd3+ compounds in aqueous solution, and more direct measurement of Tle making use of Longitudinally Detected EPR (LODEPR) [70]. Currently, LODESR is available only at X-band, and the frequency dependence of relaxation is studied by following the frequency dependence of the cw EPR line shape, and especially of the peak-to-peak line width of the first derivative spectrum (ABpp). 

Temperature information from CARS spectra derives from spectral shapes either of the 2-branches or of the pure rotational CARS spectra of the molecular constituents. In combustion research it is most common to perform thermometry from nitrogen since it is the dominant constituent and present everywhere in large concentration despite the extent of chemical reaction. The 2-branch of nitrogen changes its shape due to the increased contribution of higher rotational levels which become more populated when the temperature increases. Figure 6.1-21 displays a calculated temperature dependence of the N2 CARS spectrum for experimental parameters typically used in CARS thermometry (Hall and Eckbreth, 1984). Note that the wavenumber scale corresponds to the absolute wavenumber value for the 2320 cm 2-branch of N2 when excited with the frequency doubled Nd.YAG laser at 532 nm ( 18796 cm ), i. e. = 18796 -1- 2320 = 21116 cm. The bands lower than about 21100 cm are due to the rotational structure of the first vibrational hot band. 

Fig. 9. Magnetic circular dichroism selection rules. (A) Transitions between Zeeman-split y (or S) = i paramagnetic ground (G) and excited (E) states. Right circularly polarized (RCP) and left circularly polarized (LCP) transitions are indicated. (B) MCD spectra associated with the energy scheme in (A). The dashed bands correspond to individual left and right polarized transitions, whereas the solid line spectra give the dichroism. The C-term spectrum corresponds to a Gaussian band shape, which peaks at the absorption maximum, whereas an A-term reflects its first derivative which crosses zero at the absorption maximum.

The first derivative of any curve goes through zero at the curve s maxima and minima. For a single band (Fig. 10.59a) the characteristic shape of the first derivative is a maximum followed by a minimum. 

The first EMIRS experiment immediately showed the importance of the bands with a bipolar shape. In fact, a bipolar band has a pseudo-derivative shape, the origin of which had been clearly established. It remains to correlate quantitatively the peak-to-peak intensity to the superficial concentration of adsorbed species in other words, the question is how to obtain quantitative information from the peak-to-peak intensity of a bipolar EMIRS band. An attempt has been made assuming a Lorentzian profile for the peak. " The mathematical expression of such a peak is given by ... 

In our previous chapter we derived the expressions for the first and second derivatives of both the Normal and Lorentzian band shapes [1]. For the following discussion, however, we will address only the Normal case, as we will see, the Lorentzian case will parallel it closely. 

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