Experimental spectrum

We have alluded to the comrection between the molecular PES and the spectroscopic Hamiltonian. These are two very different representations of the molecular Hamiltonian, yet both are supposed to describe the same molecular dynamics. Furthemrore, the PES often is obtained via ab initio quairtum mechanical calculations while the spectroscopic Hamiltonian is most often obtained by an empirical fit to an experimental spectrum. Is there a direct link between these two seemingly very different ways of apprehending the molecular Hamiltonian and dynamics And if so, how consistent are these two distinct ways of viewing the molecule ... 

Furthermore, the prediction of and NMR spectra is of great importance in systems for automatic structure elucidation. In many such systems, aU isomers with a given molecular formula are automatically produced by a structure generator, and are then ranked according to the similarity of the spectrum predicted for each isomer to the experimental spectrum. 

The identification of chemical compounds by IR spectroscopy is usually done by comparing an experimental spectrum of the compound with a reference spectrum. However, the number of known chemical structures (ca. 17 000 000) greatly exceeds the number of IR spectra the largest database of spectra, Specinfo [76], contains 600 000 spectra. 

Figure 7 Experimental and theoretical inelastic neutron scattering spectrum from staphylococcal nuclease at 25 K. The experimental spectrum was obtained on the TFXA spectrometer at Oxford. The calculated spectrum was obtained from a normal mode analysis of the isolated molecule. (From Ref. 28.)...

One of the major advantages of SEXAFS over other surface structutal techniques is that, provided that single scattering applies (see below), one can go direcdy from the experimental spectrum, via Fourier transformation, to a value for bond length. The Fourier transform gives a real space distribudon with peaks in at dis-... 

When an element is present on the surface of a sample in several different oxidation states, the peak characteristic of that element will usually consist of a number of components spaced close together. In such cases, it is desirable to separate the peak into its components so that the various oxidation states can be identified. Curve-fitting techniques can be used to synthesize a spectrum and to determine the number of components under a peak, their positions, and their relative intensities. Each component can be characterized by a number of parameters, including position, shape (Gaussian, Lorentzian, or a combination), height, and width. The various components can be summed up and the synthesized spectrum compared to the experimental spectrum to determine the quality of the fit. Obviously, the synthesized spectrum should closely reproduce the experimental spectrum. Mathematically, the quality of the fit will improve as the number of components in a peak is increased. Therefore, it is important to include in a curve fit only those components whose existence can be supported by additional information. 

Short-lived molecules may often be identified by their infrared spectra measured at extremely low temperatures. In most cases, the experimental spectrum will be incomplete, although a few characteristic lines or bands are often sufficient to decide among alternative structures. 

Assign the vibrational frequencies in the experimental spectrum using the data from the structure you selected. 

Figures 8 and 9 shows a part of the bending region at low temperature containing the components of Vg (150-160 cm ) and Vs (190-200 cm ). The Vg vibration, IR active in the free molecule, has weak components in the Raman spectrum. According to theoretically calculated Raman intensities, which almost perfectly fit the experimental spectrum, the big component has a very low scattering cross-section [87] and is accidentally degenerate with the b2g component at ca. 188 cm. The IR active components of Vg cause strong absorptions in the IR spectrum even if the crystalline sample used for transmission studies is as thin as 400 pm [107, 109].

Fig. 12b). Since practically the same spectral shape is obtained at Q-band (35 GHz) (Fig. 12c), the commonly used criterion stating that the shape of an interaction spectrum is frequency-dependent fails to apply in this case. Actually, outer lines arising from the exchange interaction are visible on the spectrum calculated at Q-band (Fig. 12c), but these lines would be hardly detectable in an experimental spectrum, because of their weak intensity and to the small signal-to-noise ratio inherent in Q-band experiments. In these circumstances, spectra recorded at higher frequency would be needed to allow detection and study of the spin-spin interactions. 

A general purpose program has been developed for the analysis of NMR spectra of polymers. A database contains the peak assignments, stereosequence names for homopolymers or monomer sequence names for copolymers, and intensities are analyzed automatically in terms of Bernoullian or Markov statistical propagation models. A calculated spectrum is compared with the experimental spectrum until optimized probabilities, for addition of the next polymer unit, that are associated with the statistical model are produced. 

Simulated spectra can be created by another option in the main menu of the program. Probabilities (P1-P4) are prompted from the user, depending on the model, if vaiues other than those stored with the data base are desired and a single linewidth is entered. Equation 1 and 2 are then used to simulate a spectrum which can be saved, compared to the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or plotted. 

Once creation of the PV A database is complete, optimized probabilities may be calculated for the experimental spectrum at hand. Since the iterative procedure is restricted to a 2048 data point region, zoom cursors are displayed and set by the user until this condition is satisfied. In this case, the methylene region was selected and an initial guess for the Bernoullian probability (Pr=0.5) and linewidth (13.0Hz) were given. Optimized values for the probability and linewidth were Pr=0.52 and 12.8Hz, respectively. 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

Figure 4. Experimental laser-induced fluorescence, upper plot, and calculated spectra, lower plot, of the linear He P Cl feature in the ICl B—X, 3-0 region. An P Cl(X,v" = 0) rotational temperature of 0.19 K was measured for the experimental spectrum, and a temperature of 0.20 K was used in the calculations. Adapted from Ref. [51].

Figure 8. TEM and optical absorption of the sample implanted with 5 x 10 Au /cm (a) TEM cross-sectional micrograph (dashed lines represent the free surface and film-substrate interface) (b) nanoparticles size distribution (c) simulated optical spectra (1) Au cluster in a non-absorbing medium with n = 1.6 (2) Au cluster in polyimide (absorbing) (3) Au(core)-C(shell) cluster in a nonabsorbing medium with n = 1.6 (4) the experimental spectrum of Au-implanted polyimide sample, (d) X-ray diffraction patterns as a function of the implantation fiuence.

Cahbration spectra must be measured at defined temperamres (ambient temperature for a-iron) because of the influence of second-order Doppler shift (see Sect. 4.2.1) for the standard absorber. After folding, the experimental spectrum should be simulated with Lorentzian lines to obtain the exact line positions in units of channel numbers which for calibration can be related to the hteramre values of the hyperfine splitting. As shown in Fig. 3.4, the velocity increment per channel, Ostep, is then obtained from the equation Ustep = D,(mm s )/D,(channel numbers). Different... 

The fitted and calculated vibrational frequencies and normal mode composition factors corresponding to the 17 most important NIS bands are presented in Table 5.9. It is evident that the vibrational peaks in the calculated NIS spectrum are typically 0-30 cm lower than to the experimental values. In the calculated NIS spectra, there are two small peaks at 635 and 716 cm (Fig. 5.14b) that are not visible in the experimental spectrum. According to the normal mode calculations these are Fe-N-N and Fe-O-C deformation vibrations. Small admixtures of Fe-N and Fe-O stretching modes account for the calculated nonzero normal mode composition factors. Although the calculated relative intensities are slightly above detection limit dictated by the signal-to-noise ratio, they are determined by values of pea which are very small (0.028 and 0.026 for the peaks at 635 and 716 cm ). They must be considered to be within the uncertainties of the theoretical... 

For the NFS spectrum of [Fe(tpa)(NCS)2] recorded at 108 K, which exhibits a HS to LS ratio of about 1 1, a coherent and an incoherent superposition of the forward scattered radiation from 50% LS and 50% HS isomers was compared, each characterized by its corresponding QB pattern (Fig. 9.16) [42]. The experimental spectrum correlates much better with a purely coherent superposition of LS and HS contributions. However, this observation does not yield the unequivocal conclusion that the superposition is purely coherent, because in the 0.5 mm thick sample the longitudinal coherence predominates since many HS and LS domains lie along the forward scattering pathway. In order to arrive at a more conclusive result, the NFS measurement ought to be performed with a smaller ratio aJD on a much thinner sample. Such an experiment would require a sample with 100% eiuiched Fe and a much higher beam intensity. 

The computed intensities of the predominant 4f — 4f65d1 transitions, represented by the height of the lines, are well matching the resolution details of the complex experimental spectrum.22 Note that unless there is a global scaling, because of the arbitrary units in experimental data, no fit is implied in the representation of computed results. 

Figure 1-3 shows a comparison of the calculated and experimental spectra. There are two high-energy transitions predicted by theory, around 190 and 240 nm. The first one is clearly visible in the experimental spectrum at the same wavelength, and roughly the same broadening. The second one was predicted to have intensity of 0.01 relative to the first peak, and is probably masked by the broad 200 nm band. Both are n - n transitions localized in the C=C bond in the ring and are likely to be present in most molecules found in the aromatic acid pathways, which hinders... 

Figure 1-3. Comparison between experimental and theoretically derived spectra for prephenate anion in solution. The vertical lines correspond to the theoretical spectrum for 12 conformers (3 lines for each) with intensities computed as described in the main text. The experimental spectrum is presented as a dark line (with the highest energy intensity also normalized to 1). The inset shows the near-UV absorption in greater detail. Adapted from Ref. [18]...

Figure 29 compares the calculated40 and experimental photoelectron spectra. Figure 29(a) compares the calculated spectrum from the ground state of HsO with the experimental spectrum that was obtained with a zero angle between the laser polarization and direction of electron detection,... 

Figure 29(b) compares the calculated spectrum from an excited initial state of H3O-, which corresponds to H2 OFP, with the experimental spectrum that was obtained for 0 = 90. The sharp intense experimental feature at about 1.83 eV in Fig. 29(b) is due to OFP and is ignored here. There has been no adjustment to the energy scale for the theoretical results, so the coincidence of the peaks in the spectra is a measure of the agreement between theory and experiment and attests to the quality of the PESs. 

Figure 3 Crystal field states (left-hand panel) and potential energy surfaces (right-hand panel) for an octahedral complex of nickel(II) in the 3Tig/1Eg energy range. Calculated spectra for the transition to each electronic state are shown in the central panel. Lines with markers connect electronic states and their corresponding calculated spectra. The total calculated spectrum (calc.) is obtained as the sum of the four individual spectra and is compared to the experimental spectrum of Ni(H20)62+ measured at 5K336 (reprinted with permission from ref. 336 1998, American Chemical Society).

Carotenoid neutral radicals are also formed under irradiation of carotenoids inside molecular sieves. Davies and Mims ENDOR spectra of lutein (Lut) radicals in Cu-MCM-41 were recorded and then compared with the simulated spectra using the isotropic and anisotropic hfcs predicted by DFT. The simulation of lutein radical cation, Lut +, generated the Mims ENDOR spectrum in Figure 9.7a. Its features at B through E could not account for the experimental spectrum by themselves, so contribution from different neutral radicals whose features coincided with those of the experimental... 

FIGURE 9.5 CW ENDOR spectrum of 1-carotene radicals, (a) Experimental spectrum of Figure 9.4. (Reported in Wu, Y. et al., Chem. Phys. Lett., 180, 573, 1991.) (b) Simulated ENDOR powder pattern (using linewidth of 0.6MHz) for the sum of radical cation and neutral radicals in 5 3 1 1 ratio. (Reported in Gao, Y. et al., J. Phys. Chem. B, 110, 24750, 2006. With permission.)... 

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