Spectrum decomposition

The Mossbauer parameters are derived from the peak parameters (base line parameters, peak position, peak width, and peak area/height) via the fitting process by computer evaluation of spectra in the case of the so-called model-dependent evaluation. In this case, an exact a priori knowledge about the spectrum decomposition (peak-shape function, number, and type of subspectra corresponding to the interactions assumed for each microenvironment in the model) is inevitably necessary. (Incorrectly chosen number of peaks renders the analysis itself incorrect.)... 

Figure 7.2.8. Spectrum decomposition of water band in the wavenumber region from 11,000 cm to 9000 cm . The terms Sq, Si, S2, S3, and S4 are different species of water differing in the number of hydrogen bonds (61).

Abstract A formal derivation of the nuclear-ensemble method for absorption and emission spectrum simulations is presented. It includes discussions of the main approximations employed in the method and derivations of new features aiming at further developments. Additionally, a method for spectrum decomposition is proposed and implemented. The method is designed to provide absolute contributions of different classes of states (localized, diffuse, charge-transfer, delocalized) to each spectral band. The methods for spectrum simulation and decomposition are applied to the investigation of UV absorption of benzene, furan, and 2-phenylfuran, and of fluorescence of 2-phenylfuran. 

The method for spectrum decomposition proposed above is certainly not unique, and other criteria and threshold values could be invoked. Besides that, it depends on the approximate validity of a few hypotheses. First, we assume the adequacy of CIS wavefunctions to describe the electronic density. Second, we also assume that the usage of time-dependent DPT amplitudes together with Kohn-Sham orbitals results in an acceptable representation of the CIS wavefunction. Third, we assume that the density partition among the units is uniquely defined, even though the molecular orbitals (Kohn-Sham or Hartree-Fock) are not unique and the MuUiken partition employed is somewhat arbitrary. Due to all these factors, we should take the decomposition as a qualitative analysis of the several contributions to each band, rather than an exact numerical analysis. 

Figure 4— bottom—shows the decomposition of the spectrum of 2-phenylfuran in terms of the several classes of states. The spectrum-decomposition method explained in Sect. 3 was applied for each of the Np x Nf = 19,550 lines composing the spectrum. The threshold values are tp = 0.9, fcT — 0-6, fr - 0.8, and to — 0.35. These values... 

Fig. 4 Top simulated (TD-CAM-B3LYP/aug-cc-pVDZ) and experimental absorption cross section of 2-phenytfuran. Experimental data in hexanes from Ref. [16]. Bottom Spectrum decomposition. CT contributions are negligible and are not shown...

The nuclear-ensemble approach is especially well tailored to investigate how different properties contribute to each band in the spectrum. In particular, we have proposed and implemented a method for spectrum decomposition in terms of the contributions from different classes of states (localized, delocalized, diffuse and charge-transfer). 

Using the nuclear-ensemble approach, we have simulated the absorption spectra of benzene, fiiran and 2-phenylfuran in gas phase. Based on these simulations, experimental vertical excitations were estimated. For the three molecules, the main bands were assigned and the spectrum-decomposition method was applied to 2-phenylfuran. 

Fig. 23 shows Si 2p peak. Table 1 below shows the spin-orbital splitting values of this peak (components ratio in the doublet is 2 1), as well as values of full width at half-height of Gauss and Lorentz functions used in experimental spectra decomposition, energy shifts for surface component of silicon, and its compounds in relation to its bulk component. The values shown in the table 3 were taken from (Olmstead et al., 1986). The shift value for Si-Ba bond was determined in the course of spectrum decomposition, and slightly differed from similar energy shift for Si-Ca bond. 

Figure Bl.7.5. (a) MIKE spectrum of the iinimoleciilar decomposition of 1-butene ions (m/z 56). This spectrum was obtained in the second field-free region of a reverse geometry magnetic sector mass...

In contrast to IR and NMR spectroscopy, the principle of mass spectrometry (MS) is based on decomposition and reactions of organic molecules on theii way from the ion source to the detector. Consequently, structure-MS correlation is basically a matter of relating reactions to the signals in a mass spectrum. The chemical structure information contained in mass spectra is difficult to extract because of the complicated relationships between MS data and chemical structures. The aim of spectra evaluation can be either the identification of a compound or the interpretation of spectral data in order to elucidate the chemical structure [78-80],... 

Davies and Warren" found that when 1,4-dimethylnaphthalene was treated with nitric acid in acetic anhydride, and the mixture was quenched after 34 hr, a pale yellow solid with an ultraviolet spectrum similar to that of a-nitro-naphthalene was produced. However, if the mixture was allowed to stand for 5 days, the product was i-methyl-4 nitromethylnaphthalene, in agreement with earlier findings. Davies and Warren suggested that the intermediate was 1,4-dimethyl-5 nitronaphthalene, which underwent acid catalysed rearrangement to the final product. Robinson pointed out that this is improbable, and suggested an alternative structure (iv) for the intermediate, together with a scheme for its formation from an adduct (ill) (analogous to l above) and its subsequent decomposition to the observed product. 

The reasonable stable products are characterized by an ir-absorption near 1615 cm". The 4-protons resonate near 6.2 ppm in the H NMR spectrum (23). NMR spectra exhibit a carbonyl atom signal near 173 ppm, whereas C-4 resonates near 8 108 these positions are characteristic of other mesoionic ring carbon atoms (24). In the mass spectra, decomposition with loss of CO, rupture of the 1,5 and 2.3 bonds with elimination of R NC2R 0 and cleavage of the 1,2 and 3,4 bonds with elimination of C2R 0S is observed (11)... 

The importance of linked scanning of metastable ions or of ions formed by induced decomposition is discussed in this chapter and in Chapter 34. Briefly, linked scanning provides information on which ions give which others in a normal mass spectrum. With this sort of information, it becomes possible to examine a complex mixture of substances without prior separation of its components. It is possible to look highly specifically for trace components in mixtures under circumstances in which other techniques could not succeed. Finally, it is possible to gain information on the molecular structures of unknown compounds, as in peptide and protein sequencing (see Chapter 40). 

Pyridinium iodide, l-ethyl-4-methoxycarbonyl-UV spectrum, 2, 127 Pyridinium iodide, 1-methyl-decomposition, 2, 300 Pyridinium iodide, 6-pterinylmethyl-synthesis, 3, 312... 

Figure 16-1. Decomposition of a time signai into a sum of osciiiatory functions from which a spectrum can be obtained.

On thermal decomposition of alstonine at 300-330°, the bases produced distilled at l20-170°/0-15 mm., and on fractionation as picrates gave three products Base D, C4,HigN2, picrate, m.p. 254-6°. Base E, C18H20N2, or CjgHgaNj, picrate m.p. 193-5-195°, not identical with Sharp s alstyrine, and base F, Cj3Hi2N2, m.p. 79-81°, pierate, m.p. 261-262-5°, hydrochloride, m.p. about 275° (dec.), methiodide, m.p. 283-4° (dec.). Base F has an ultraviolet absorption spectrum very similar to that of 2-ethyl- -carboline, but it is not that substance nor is it 1 2-dimethyl-/3-carboline, 2 3-dimethyl-j3-carboline, 1-ethyl- -carboline or 3-ethyl- -wocarboline. Base F was also produced when alstonine was distilled with zinc dust. 

Fig. 3.2 NMR spectrum for the products of the decomposition of BuN=Se=N Bu in toluene at 20°C after 2 days [Reproduced with permission from Inorg. Chem., 39, 5341 (2000)]...

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