Scale all spectra

The intensity of the HREELS peaks, including that of the elastic peak, depends strongly on the adsorbate and the degree of ordering on the surface. Therefore it is common practice to scale all spectra with respect to the elastic peak, as has been done for the spectra in Fig. 8.14. 

Vibrational Spectra Many of the papers quoted below deal with the determination of vibrational spectra. The method of choice is B3-LYP density functional theory. In most cases, MP2 vibrational spectra are less accurate. In order to allow for a comparison between computed frequencies within the harmonic approximation and anharmonic experimental fundamentals, calculated frequencies should be scaled by an empirical factor. This procedure accounts for systematic errors and improves the results considerably. The easiest procedure is to scale all frequencies by the same factor, e.g., 0.963 for B3-LYP/6-31G computed frequencies [95JPC3093]. A more sophisticated but still pragmatic approach is the SQM method [83JA7073], in which the underlying force constants (in internal coordinates) are scaled by different scaling factors. 

Fig. 2.10. Potential step SNLFTIRS spectra from a polished polycrystalline Pt electrode, immersed in 10 2 M CHjOH/O.l M HC104 electrolyte. All spectra (90 scans each, 8 cm 1 resolution) were normalized to the base spectrum collected at 0 mV vs. RHE. Insert part of the curve at 450 mV in expanded scale.

Figure 12 Comparison of Vch artefacts intensity illustrated with ID rows taken from a BIRD-HMBC (A), (D) and (G) a G-BIRD-HMBC (B), (E) and (H) and a double tuned G-BIRD-HMBC (C), (F) and (I) experiments showing the Vch artefacts and nJCH responses of C-6 at 135.6 ppm (A), (B) and (C), C-l at 67.2 ppm (D), (E) and (F) and C-10 at 27 ppm (G), (H) and (I) of the 1,3-butadiynyl (tert-butyl) diphenylsilane molecule dissolved in CDCl3. For the BIRD-HMBC and G-BIRD-HMBC experiments, the delays S were adjusted to aV-value of 190 Hz, as an average value for the extreme range of coupling constants for this molecule (125-260 Hz). For the double tuned G-BIRD-HMBC, the /ch nnax and /ch nnin values were set to 240 and 145 Hz, respectively. The corresponding values for the S and S delays were 3.13 and 2.17 ms, adjusted toj values of 160 and 230 Hz, respectively. For both G-BIRD-HMBC experiments, 192 is BIP 720-100-10 pulses have been used for 13C inversion. The same vertical scale is used for all spectra. Residual /ch signals are denoted with arrows.

For the purpose of comparison all spectra taken from the literature were digitized by means of a Hewlett-Packard Digitizer (model 9864 A) on-line with a small computer (HP, model 9820) and replotted on a common scale (HP, model 9862 A). 

A with respect to the corresponding reference peaks in Fig. 2.19B, C. Note that all spectra are normalized to the same intensity scale and were obtained using 10 pL of the mixture where the protease concentration was 20 pM in each sample. Reprinted from reference [13] with permission from John Wiley Sons. 

Fig. 3. EPR spectra of 100 pairs of Rhodnius salivary glands homogenized in 125 xl of phosphate-buffered saline at pH 7.2 (A) before argon equilibration (B) after equilibration in an argon atmosphere for 4 h (C) after equilibration of (B) with NO for 2 min. (D) difference spectrum, that is B — C. (E) homogenate as in (B) treated with dithionite (DT) to reduce Fe(III) to Fe(II), followed by equilibration with NO for 2 min. (The small signal at g = 2 in A-C is due to copper oxide in the liquid helium which had been condensed at the University of Arizona in a copper-plumbed helium liquiflcation apparatus ) All spectra are plotted on the same scale except (E), which is reduced in amplitude by a factor of 3. Reproduced with permission from Ref 24).

A productive exploitation of the synergy between experiment and theory requires that practitioners familiarize themselves with the scope and limitations of the methods they use, so they can avoid pitfalls due to artifacts that may occur both in experiment and in theory. It is, for example, disturbingly easy to create or annihilate bands by formation of suitably scaled difference spectra. On the other hand, the harmonic approximation that is at the basis of all practicable modeling calculations of vibrational spectra may lead to predictions that have no relation to experiment (as demonstrated above for the case of phenylcarbene). 

Figure 21. C02 stretching during three successive cycles of photolyzing and annealing a single UP crystal. All spectra have the same scale and were measured at the photolysis temperature of 90 K. After the first and third 78-min photolyses (a and f) many extra bands accompany the Species D singlet. After the second 30-min photolysis (d) they do not appear, although the singlet is nearly as large. Reproduced from Ref. 83 with permission from Gordon and Breach Science Publishers S.A.

The half-width of all the absorption bands is approximately 1.5 e.v. When plotted on an energy scale the spectra are seen to be asymmetric on the high-energy side. If the asymmetric portion is deleted, the remaining symmetrically drawn peak has a half-width of about 1 e.v. for all five alcohols. 

FIGURE 51. 29Si CPMAS NMR spectra of Aerosil A-200 with trimethylsiloxane surface coverage and chemical shifts of the peak maxima ( maximum error) as indicated. All spectra are on the same intensity scale. Reproduced by permission of Elsevier Science from Reference 152... 

Fig. 11. Pressure dependence of the IR spectra of H2 adsorbed at 20 K on high-surface-area (230m g ), sintered (dOm g ). and smoke (10m g ) MgO samples, parts (a), (b), and (c), respectively. The upper curve of each series of spectra has been collected after an elapsed time allowing the surface species to reach the equilibrium conditions and corresponds to the maximum H2 coverage (Fjj, = 1010 kPa), while the bottom spectrum has been recorded after prolonged outgassing at 20 K (Ph, <10 Pa). All spectra have been vertically shifted for the sake of clarity. Note that the ordinate scale is progressively expanding when passing from part (a) to part (c), to account for the loss of band intensity with the decrease of the MgO surface area. (Adapted with permission from Gribov et al. (,124).)...

Additional information on electronic structure may be obtained from the x-ray emission spectra of the SiOj polymorphs. As explained in Chapter 2, x-ray emission spectra obey rather strict selection rules, and their intensities can therefore give information on the symmetry (atomic or molecular) of the valence states involved in the transition. In order to draw a correspondence between the various x-ray emission spectra and the photoelectron spectrum, the binding energies of core orbitals must be measured. In Fig. 4.12 (Fischer et al., 1977), the x-ray photoelectron and x-ray emission spectra of a-quartz are aligned on a common energy scale. All three x-ray emission spectra may be readily interpreted within the SiO/ cluster model. Indeed, the Si x-ray emission spectra of silicates are all similar to those of SiOj, no matter what their degree of polymerization. Some differences in detail exist between the spectra of a-quartz and other well-studied silicates, such as olivine, and such differences will be discussed later. 

Fig. 14.16 Raman spectra recorded for (a) PP and PNP samples and (b) P2D60 and NP2D60 samples. The data were recorded at 0.2 mW laser intensity. For comparison, all spectra were in the same scale (Reprinted with permission from Ref. [56]. Copyright American Chemical Society (2007))...

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