Derivatives of spectra

Derivatives of spectra (dT/dA or dA/dA, and their wavenumber equivalents in FTIR) have been known and used in spectroscopy for a long time. Both first derivatives and second derivatives (d2T/dA2 or d2A/dA2) are in common use in modern spectroscopy, particularly in NIR spectroscopy. We also note that they also enjoy widespread use in some nonoptical spectroscopic techniques, such as NMR and ESR spectroscopies. The mathematics and behavior of the derivative is independent of the particular spectroscopic technique to which it is applied, however. But since our own backgrounds are in optical spectroscopy, where pertinent we will discuss it in terms of the spectroscopy we are familiar with. 

Figure 5.3 Urine cytology, (a-c) Photomicrographs of glycogen-containing, glycogen-free squamous cells, and a urothelial cell, respectively (d) Vector-normalized IR spectra of cells shown in (a-c) (e) Second derivatives of spectra shown in (d).

Figure 7. The second derivative of spectra consisting of two component bands separated by a, D = AA ,/ b, D = V2 Xift and c, D = Va nt,...

Figure 6.21 FT-IR imaging absorbance maps obtained on the basis of the second derivative of spectra for esters of fatty acids at 1734cm" (a), amides at 1656cm" (b), unidentified pattern 1 (UNP1 potentially cellulose) at 1106cm (c), UNP2 (potentially...

The usual mean-square deviation is of restricted value as long as the fit is not very close. So, a double-peak structure approximated by a single simple peak may yield about the same mean-square deviation as the approximation by a shifted double peak as qualitatively visuahzed in Figure 3.2.1.32a. Therefore, more appropriate measures use the derivatives of spectra, in which zeros describe the location of maxima (and minima). Probably, the most frequently applied measure is the Pendry R-factor [46], Rp, on which we concentrate. Instead of comparing the intensities, it uses their logarithmic derivatives, L = (dI/dE)/I(E), or a related function, Y(E), which avoids singularities when erroneously low measured intensity values enter the denominator of I. The Pendry R-factor is the mean-square deviation of the... 

Mantini A R, Marzocchi M P and Smulevich G 1989 Raman excitation profiles and second-derivative absorption spectra of beta-carotene J. Chem. Phys. 91 85-91... 

However, in the case of derivatives of the type 2-(phenylamino)-4-oxo-5-phenylselenazoline (Scheme 65), the tautomeric equilibrium is displaced towards the imino form (69, 70) This was also shown by the ultraviolet spectra. 

Out-of-Plane Vibrations, yCH and yCD. In accordance with all the proposed assignments (201-203), the bands at 797 and 716 cm correspond to yCH vibrators, which is confirmed by the C-type structure observed for these frequencies in the vapor-phase spectrum of thiazoie (Fig. 1-9). On the contrary, the assignments proposed for the third yCH mode are contradictory. According to Chouteau et al. (201), this vibration is located at 723 cm whereas Sbrana et al. (202) prefer the band at S49cm and Davidovics et al. (203) the peak at 877 cm This last assignment is the most compatible with the whole set of spectra for the thiazole derivatives (203) and is confirmed by the normal vibration mode calculations (205) (Table 1-25). The order of decreasing yCH frequencies, established by the study of isotopic and substituted thiazole derivatives, is (203) yC(4)H > 70(2)13 > yC(5)H. Both the 2- and 4-positions, which seem equivalent for the vCH modes, are quite different for the yCH out-of-plane vibrations, a fact related to the influence observed for the... 

The ultraviolet spectra of these compounds are similar to those of trans stilbene or of 2- and 4-stilbazole. The effect on the ultraviolet spectrum of various substituents have been found to parallel in many respects the efiects produced by the corresponding group in derivatives of aromatic hydrocarbons (142). 

Mass Spectroscopy. A coUection of 125,000 spectra is maintained at Cornell University and is avaUable from John WUey Sons, Inc. (New York) on CD-ROM or magnetic tape. The spectra can be evaluated using a quaHty index algorithm (63,76). Software for use with the magnetic tape version to match unknowns is distributed by Cornell (77). The coUection contains aU avaUable spectral information, including isotopicaUy labeled derivatives, partial spectra, and multiple spectra of a single compound. 

J3 4 = 3.45-4.35 J2-4 = 1.25-1.7 and J2-5 = 3.2-3.65 Hz. The technique can be used quantitatively by comparison with standard spectra of materials of known purity. C-nmr spectroscopy of thiophene and thiophene derivatives is also a valuable technique that shows well-defined patterns of spectra. C chemical shifts for thiophene, from tetramethylsilane (TMS), are 127.6, C 125.9, C 125.9, and C 127.6 ppm. 

The NMR spectra of some derivatives of the benzo fused pyrido[3,4-f ]quinoxaline (1-deazaflavin) (391) system have been recorded (74JCS(P1)1965). 

Although the conventional mass spectra of the five C- nitro derivatives of indazole are nearly identical, the corresponding metastable peak shapes associated with the loss of NO-can be used to differentiate the five isomers (790MS114). The protonation and ethylation occurring in a methane chemical ionization source have been studied for a variety of aromatic amines, including indazoles (80OMS144). As in solution (Section 4.04.2.1.3), the N-2 atom is the more basic and the more nucleophilic (Scheme 5). 

Once the 3D strucmre of a molecule and all the parameters required for the atomic and molecular connectivities are known, the energy of the system can be calculated via Eqs. (l)-(3). First derivatives of the energy with respect to position allow for determination of the forces acting on the atoms, information that is used in the energy minimization (see Chapter 4) or MD simulations (see Chapter 3). Second derivatives of the energy with respect to position can be used to calculate force constants acting on atoms, allowing the determination of vibrational spectra via nonnal mode analysis (see Chapter 8). 

The use of RBS concurrendy with ERS is necessary for the complete derivation of a hydrogen profile, and it offers some simplifications of analysis. For example, for thin-layer spectra that have been normalized for a common ion fluence Qand solid angle SI, the total yields Y (the areas under the spectral peaks) may be compared in order to derive the layer composition. For... 

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