Calculated spectrum

Theoretical calculations were performed with the linear muffin tin orbital (LMTO) method and the local density approximation for exchange and correlation. This method was used in combination with supercell models containing up to 16 atoms to calculate the DOS. The LMTO calculations are run self consistently and the DOS obtained are combined with the matrix elements for the transitions from initial to final states as described in detail elsewhere (Botton et al., 1996a) according to the method described by Vvedensky (1992). A comparison is also made between spectra calculated for some of the B2 compounds using the Korringa-Kohn-Rostoker (KKR) method. 

To produce a calibration using classical least-squares, we start with a training set consisting of a concentration matrix, C, and an absorbance matrix, A, for known calibration samples. We then solve for the matrix, K. Each column of K will each hold the spectrum of one of the pure components. Since the data in C and A contain noise, there will, in general, be no exact solution for equation [29]. So, we must find the best least-squares solution for equation [29]. In other words, we want to find K such that the sum of the squares of the errors is minimized. The errors are the difference between the measured spectra, A, and the spectra calculated by multiplying K and C ... 

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.

Ultimately, it was the strong agreement between He l Cl excitation spectra calculated by McCoy and co-workers and experimental He I Cl action spectra, such as shown in Fig. 2(b), that corroborated the proposed assignments of the newly observed He - -ICl features in the spectra [39, 40]. 

Fig. 32. Fe-M6ssbauer spectra of [Fe(6-Mepy)3tren](PF )2 for various temperatures recorded at p = 150 MPa. Full lines are spectra calculated using the stochastic theory of lineshape by Blume with sgn(F J sgn(Fh.). According to Ref. [169]...

Fig. 36. Fe-M6ssbauer spectra of [FefmtziJfPFglj at the temperatures of 150, 213, 243, and 300 K. Solid lines are spectra calculated with account of texture but without consideration of relaxation effects. According to Ref. [174]...

As an example, we give in Table 36.1 data on calibration spectra at 10 wavelengths of 4 calibration standards for 3 analytes. The corresponding spectra are shown in Fig. 36.1a at a 10-fold higher resolution. The pure spectra calculated according to eq. (36.5), using all 100 wavelengths, are displayed in Fig. 36.1b. 

Fig. 9.22 NFS spectra calculated with S YNFOS for different values of the asymmetry parameter j . Other conditions are as described in Fig. 9.21a. (Taken from [13])...

Fig. 14.2 (a) Emission spectra calculated for excited Cr at different temperatures, normalised with respect to the peak at 424 nm. 

Figure 16 Comparison of the F projections of the multiplicity-edited GHSQC, 60 Hz 1,1-ADEQUATE, the UIC calculated HSQC-1,1-ADEQUATE, and GIC calculated HSQC-1,1-ADEQUATE spectra (power 0.5) of strychnine (1). While Snyder and Bruschweiler have noted52 that signal-to-noise (s/n) measurements of covariance spectra may not be the most viable means of making comparisons, in the present example, the differences are so dramatic that they still allow valid conclusions to be drawn. The C12 (77.6 ppm) resonance provides a convenient s/n comparator. The region from 80 to 100 ppm, which is devoid of responses in the spectrum of strychnine, was used to define the "noise" region for the measurement. There is certainly no question that multiplicity-edited GHSQC is a high-sensitivity experiment as attested by a s/n for the C12/H12 correlation response of 290 1. In comparison, the C12 resonance of the 60 Hz 1,1-ADEQUATE spectrum is a much more modest 22 1. In contrast, the s/n for the C12 resonance in the HSQC-1,1-ADEQUATE spectra calculated using UIC and GIC methods was 293 1 and 257 1, respectively.

Figure 17 Signal-to-noise measurements for selected resonances of strychnine (1) in HSQC-1,1-ADEQUATE spectra calculated as a function of data acquisition time for the 1,1-ADEQUATE spectra used in the calculation.50...

ADEQUATE spectra calculated from the 1,1-ADEQUATE spectra demonstrates the advantage inherent in the covariance calculated... 

Microwave spectra Calculation of reduced mass, rotational constant, bond... 

Fig. 12.10. Comparison of the observed spectrum of the gravitationally lensed LBG MS 1512-cB58 (bold), with a redshift of 2.7, with synthetic spectra calculated with Starburst 99 together with the theoretical spectral library WM-basic for various metallicities (faint). The left panels show the region of the A. 1425 complex (a blend of Si, C and Fe photospheric lines), while the right panels show photospheric features of Fe hi between 1900 and 2000 A. After Rix etal. (2004).

The ability to measure small index perturbations, (I/Ven. depends on the depth (i.e., the extinction ratio at resonance) and width of these resonances. The depth and width in turn depend on the relative values of the coupling coefficient t and the resonator loss a. Figure 9.16 shows typical ring resonator spectra calculated for two different loss values. The maximum extinction ratio is obtained at critical coupling when t = a, and the output intensity at resonance is exactly zero. The width of the resonances depends on the total round trip resonator loss, at, which is the product of waveguide losses within the ring (a) and coupling loss (t) at the coupler. 

D17 Paetzold, R., A-El-Mottalab J. Mol. Str. 24, 357 (1975) The absolute IR intensities of v(CO) features, bond polarizations (MC and CO) and other quantities (13C chemical shifts, charge-transf< spectra, calculated CO 2pir populations) are correlated... 

Figure 57 Absorption spectra calculated for architectures with 26 Si atoms.362 Reprinted with permission from Watanabe, A. Fujitsuka, M. Ito, O. Miwa, T. Mol. Cryst. Liq. Cryst. 1998, 316, 363-366, 1998 Gordon and Breach Ltd.

As a result of these unfavourable interactions, i.e., opposition to bond strain i.e., between the pair of hydrogens shown at the bottom) and also due to bowsprit interaction, the potential energy of the boat form becomes high and this is why the boat conformation is not the preferred one. Hassel in 1947 established by means of electron diffraction studies that cyclohexane exists predominantly in the chair form. This has also been confirmed by electron diffraction studies and results obtained from Raman and I.R. spectra. Calculations made on the basis of entropy show that only about one molecule in a thousand will be in the boat form. 

A similar ab initio computational and VCD study in the 800-1500 cm-1 range using (55)-1 -azabicyclo[3.1.0]hexane (55 )-115] gave VCD spectra calculated at three different computational levels which are well reproduced in the experimental VCD spectrum151. 

Figure 15a. S-band, X-band, and Q-band EPR spectra for 1/2-met Br hemocyanin and spectra calculated using the parameters given in Table 4.

Figure 1. ESR spectra of Cu(II) at X-band and 77 K in chemically cross-linked polyacrylamide gels with pore diameters of 1.3 nm (A) and 4.0 nm (B). Solid lines are experimental spectra dotted lines are spectra calculated using the appropriate values of AH, and given in Table I and with 2.408, gj = 2.080, A,= 0.0134 cm, Aj,= 0.0009 cm, and AH = 30.0 Gauss.

Figure 4.12 FDIR spectra of (a) aniline and (b) a dihydrogen-bonded aniline-BTMA complex. The bottom lines correspond to the spectra calculated. (Reproduced with permission from ref. 21.)...

---