Spectrum calculator

Fig. 7. RAIR spectrum calculated from the ti and k spectra shown in Fig. 6.

Fig. 10. (a) Raman spectra (T = 300 K) of arc-derived carbons from a dc arc cobalt was absent (dotted line) and cobalt was present (solid line) in the carbon anode, (b) the difference spectrum calculated from (a), emphasbjng the contribution from Co-catalyzed nanolubes, the inset to (b) depicts a Lorentzian fit to the first-order spectrum (after ref. [27]). 

Pd4oCu4oP2o, Pd5oCu3oP2o, and Pd6oCu2oP20 alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. 

Problem 12.6 It s useful to develop a feeling for the amounts of energy that correspond to different parts of the electromagnetic spectrum. Calculate the energies of each of the following kinds of radiation... 

The spectrum calculated in the secular non-adiabatic approximation reproduces some special peculiarities of the spectra observed. In following papers (see Table 7.1) for diatomic molecules the dependence of the resolved spectra components on the rotational quantum number was described. As an example, the experimental dependence %(j) = Tj+1. /r is shown in Fig. 7.5. 

Fig. 12. Effect of a strong exchange interaction on the shape of the EPR spectrum displayed by a pair of centers A and B having identical g vEilues, = 1.89, g, = 1.96, g = 2.07, and rotated magnetic axes according to xjly, yglx, zJIzy,. (a) 9 GHz spectrum calculated with J = 0 (b) and (c) spectra calculated with J = 25 X 10 cm at 9 and 35 GHz, respectively. The spectra were calculated as described in Ref. 192) without including any dipolar terms, with the linewidths ui = cr, = oi = 0.01.

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. 

Fig. 6.—Measured Circular Dichroism Spectrum (-----), Calculated Circular Dichroism...

H atomic spectrum Calculation of the allowed transition frequencies in the... 

Figure 3. Infrared spectrum of carbene la, matrix isolated in argon at 10 K (bottom) compared to the spectrum calculated at the B3LYP/6-31 G(d) level of theory.

Two isomers of the cyclopropene, 3c and 3c with the methyl group in 3-and 1-position, respectively, have to be considered. Although the number of IR absorptions suggests that only one isomer is formed and the experimental spectrum is better matched by the spectrum calculated for 3c, the theoretical IR spectra of the two isomers are too similar to allow for a definitive assignment. According to DFT calculations, the isomer 3c is by 3.6 kcal/mol more stable than the isomer 3c with the methyl group at the bridgehead carbon atom, which is in line with the preferentially formation of 3c (Scheme 8). 

In support of Chapman s assignment7 of the matrix infrared spectrum of the product formed from la, the calculations of Matzinger et al. found that the experimental IR spectmm agrees well with the spectrum calculated for 3a, but not with that computed for 2a.55 The calculations for 3a reproduced the weak allene stretching band that Chapman et al. observed at 1823 cm-1. 

In Fig. 1 level spacing distributions for different temperatures are plotted (w = 0.01 and 9) for the energy spectrum calculated by diagonalizing of the matrix R. It is clear from this plot that the system is regular at 9 = 0. However, the increase of temperature leads to a chaotization of the system and P(S) becomes closer to the Gaussian distribution. 

Figure 5.19 A plot of a typical relaxation spectrum calculated from Equation (5.59)...

Figure 6.9 Observed opto-thermal spectrum of the Avcw = 3 overtone of benzene (points with error bars) and a stick spectrum calculated by means of the algebraic theory. Labels indicate the most important states involved in borrowing intensity from the CH overtone. Adapted from Bassi et al. (1993).

Although this equation only applies when the coalescence point is reached, rate constants for the exchange between two or more exchanging sites are accessible by analysis of line widths at half height, Avip, and shift differences, Ar, in Hz. The comparison between the experimental spectrum and the spectrum calculated by use of a simulation package for line shapes provides the mechanism for determining the rate constant of exchange [161, 162]. 

Calculation of the MCD intensity of a closed-shell molecule through the imaginary Verdet constant produces a result as a function of w but no further breakdown of the intensity. There are advantages to this approach but it does mean that individual and A term parameters are not calculated. An MCD spectrum calculated from Im[V] can yield A and term parameters by fitting the spectrum with suitable band-shape functions in much the same way the parameters can be extracted from an experimental spectrum. 

Models for SN1987a have recently been extensively discussed by Woosley [1 ]. We have used model 10H from that paper for the spectrum calculation. As discussed there in detail, this model is the core of a 20 Mg, star which has lost 4 M 0f mass in a wind. The core collapse and subsequent explosioh produces ejecta with 1.4xl051 ergs and 0.08 M of ssNi. As discussed in an earlier section of this paper, this model is not thin in the continuum until roughly 300 days after explosion. In fact, the situation is worse than this, since... 

We assumed that tau neutrinos are emitted from their neutrino-sphere with the speotrum of Fermi-Dirac distribution with zero ohemical potential determined by the temperature at the neutrino-sphere. This temperature is estimated to be 5 MeV from the spectrum calculated by Wilson and his collaborators. 

Medium Component. The elementary spectra for the medium component were derived by Bergmann and Nawotki12,13 on the basis of a spectrum calculated by Gutowsky and Pake52) for paired protons such as in 1,2-dichloroethane with hindered rotation around the C—C bond. 

Fig. 21.7 Photoexcitation spectrum of the 6sl5d D2 —> (6p3/2 d) 7 = 3 transition in Ba as a function of the frequency of the third laser. All three lasers are circularly polarized in the same sense. The broken line is the spectrum calculated from Eqs. (21.15) and (21.16). The energy level inset is not to scale (from ref. 9).

Figure 5. Left Frame Comparison between a measured post-Pinatubo bimodal size distribution (solid line) and that retrieved by the LUT from its best-fit extinction spectrum (i.e., at = 1.6) (dashed line). The fitting parameters of the measured bimodal and the LUT retrieved uni-modal are shown in the table. Right Frame Calculated extinction spectra for size distributions in the left frame The error bars on the spectrum calculated from the measured bimodal (open circles) are derived from the relative errors on coincident SAGE II and CLAES measure-...

Line spectrum calculated in the low temperature approximation, valid at both 4 °K and 1.2 °K. There are no free parameters the lack of sharp lines in the observed spectra is attributed to spin relaxation (After Lang and Marshall, Ref. 103))... 

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