Gaussians, component

Fig. 4 Spectral changes upon incremental additions of Pr4N+Br (from 0 to 208 mM) to the 5 mM solution of TCP in acetonitrile showing the appearance of the new charge-transfer band at Act = 400 nm. Insert-, deconvolution of the 400-nm band into two Gaussian components [23]... 

FIGURE 27. The photoelectron spectra of compounds 40 and 42. The solid line refers to the experimental data the dashed line shows the Gaussian components the points refer to the convoluted Gaussian components. Reproduced by permission of Elsevier Science from Reference 141... 

As shown in the figures, the spectral contour in the OH stretching region can be represented as the sum of contribution from four Gaussian components. Since... 

Table 5. Temperature variation of Gaussian component parameters in the OH stretching region of amorphous solid H2O and in the OD stretching region of amorphous solid DsO8...

This result is not as satisfactory as it seems. The reader will notice that the behavior of the Gaussian components appears different from that described on p. 130. MN use the data of H. A. Lindner [Ph. D. dissertation, University of Karlsruhe (1970)], and his spectral decomposition must differ from that of Wal-rafen judging from the frequencies (see Table 2) as well as the temperature dependences of the components (see also the comments by Walrafen 30>). Until this difference is resolved, and better spectra are available, the findings of MN must be viewed with reserve. 

Proton n.m.r. investigations of coals swollen in deuterated pyridine showed that the free induction decay /FID/ consists of Gaussian and Lorentzian components related to two populations of protons which have widely different degrees of rotational mobility (1-5). The Gaussian component of FID has been unanimously ascribed to the macromolecular part of the coal matter that is supposed to have very limited rotational mobility. These publications as well as the ensuing debates (6-9) however, reflected the controversy regarding the nature of the Lorentzian /mobile/ protons in coals. 

It is worthy of note that in the complexes with Csv symmetry such as [CuBr(Meetren)]Br (47, 42) (Fig. 10) the spectra still have two d—d bands and have much the same appearance as those of Dsh chromophores (Fig. 14). In the above compound the two bands, when resolved into Gaussian components, are found at 10.3 (e 450, P = 5.4-10 3) and 13.5 kK (e 180, P=1.4-10 3) ( ). Their separation of 3.2 kK is in this case too large to be attributed solely to spin-orbit couphng and the two bands are therefore assigned as - 2 (1) and - 2 (2) (8). This spectrum is very similar to that of the chromium(II) analog (d< configuration). 

Only in the simplest cases—a single Gaussian component, for example— may conventional linear least-squares method be employed to solve for u. More commonly, either approximate linearized methods or nonlinear methods are employed. 

Fig. 8. Curve decomposition of the SANS intensity function of NIPA gd (G083) at 29 °C. The solid squares, dashed line, and dotted line indicate the observed data points, the Lotentzian and Gaussian components, respectively...

When conventional methods of manual optimisation are no longer sufficient, it is possible to use deconvolution software or fuzzy logic to deconvolute unresolved peaks into Gaussian components for which the area can be easily measured (see Fig. 1.12). 

Figure 18. The normalized electronic transition frequency correlation function M(t) 1= S(i)] obtained from the experimental three-pulse photon echo peak shifts and transient grating data for IR144 in ethanol (—) total W(t) ( ) ultrafast Gaussian component in M(t) ( ) oscillatory component that arises from intramolecular vibrational motion.

Fig. 2. Emission line profiles of M1-5, M1-9, K3-66, and K3-67. Crosses and real lines are observational results, broken lines are Gaussian components.

Figure 10. The calculated total friction (C(0) as a function of time, along with the relative contributions to it from the binary ( and the density relaxation Rpp t) terms for the system CH3 in CH3I. The reduced temperature T (= kaT/e) is 1.158 and the reduced density p for CH3I is 0.918. The time-dependent frictions are scaled by t 2, where = [mirTj/fcgT]1/2 1.1 ps. i and j represent the solute atom and the solvent atom, respectively. The plot shows a clear Gaussian component in the initial time scale for the binary part (r) and slower damped oscillatory behavior for the Rpf t) part.

The subquadratic n dependence clearly arises from the nonexponential component of (Q(t)Q(0)) (shown in Fig. 12) in the initial time scale which increases with increase in the quantum number n, which strongly reflects the presence of the Gaussian components of binary friction. This dominant Gaussian behavior is responsible for the nearly linear n dependence in the higher quantum levels. 

K and (4) 403 K. The inset shows a deconvolution of the 1.82-eV band in two individual Gaussian components. (Reproduced with permission from Korsunska et al. (2004).)... 

The presence of hard and soft domains in segmented polyurethanes also has been confirmed by experimental results using pulsed NMR and low-frequency dielectric measurements. Assink (55) recently has shown that the nuclear-magnetic, free-induction decay of these thermoplastic elastomers consists of a fast Gaussian component attributable to the glassy hard domains and a slow exponential component associated with the rubbery domains. Furthermore, the NMR technique also can be used to determine the relative amounts of material in each domain. 

Figure 15 The evolution of the transient spectra is shown here for a 0.17 M mixture of ethanol and CCI4 and the anisotropic (a-c) and isotropic (d-f) components. With increasing delay time from —2 ps (a,d) to 0 ps (b,e) and finally 11 ps (c,f), clearly a short-living spectral hole (a, dotted line) as well as a completely isotropic Gaussian component (d, dashed line) is noticed. 

Similar experiments have also been performed on a higher concentrated mixture of 1.2 M ethanol and CCI4. Again spectral holes could be identified from the transient spectra with a width of 25 cm-1 and lifetime of 1 ps. From transient spectra taken for different excitation frequencies in the OH band, evidence for a faster hole relaxation with increasing red shift (bond strength) is inferred, which is accompanied by the differences in the temporal evolution of the isotropic Gaussian component related to level 2. 

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