Computed spectrum

Figure 12. Quantum monodromy in the accurately computed spectrum of LiCN/LiNC. Taken from Ref [9] with permission of Elsevier.

Fig. 38. The agreement between simulated and experimental CD spectra for the PD complex was very good after a red-shift of 0.25 eV was applied to the excitation energies. Analysis of the computed spectrum showed the intense bands to originate predominately from n-to-n transitions within an extended n framework of the phosp-hole-helicene ligands. Unlike initially expected, the various bands in the CD spectrum cannot be assigned to transitions centered separately on the helicene and phosphole moieties, respectively. The experimentally measured molar rotation of the Pd complex was 23.1 103 deg cm2 dmol 1 2% in dichloromethane. For an analogous Cu complex it was 13.1 103 2%, a staggering 104 deg cm2 dmol 1 lower.

Fig. 7.6. The linear scale X-ray spectrum of helium-like Ar16+ W4, wb and W6, with satellites, and hydrogen-like Ar17+ Ly, is shown in the top frame. In the bottom frame is the log scale observed spectrum and the computed spectrum for Ar16+, Ar17+, and Arle+...

In fact, these procedures (EMIRS or SNIFTIRS) should be used only when the system under study undergo reversible changes with potential [16]. Bipolar bands are obtained in the difference spectrum for species irreversibly adsorbed, if the band-center frequency is shifted with the potential, e.g., CO adsorbed on platinum (Fig. 8 a). But the situation is problematic when the frequency shift with potential is negligible. Then signals cancel out in the computed spectrum. This question has giv-... 

Silvestrelli et al. (1997) used Car-Parrinello molecular dynamics to obtain the IR spectrum of D2O. They did so by determining the time autocorrelation function for the dipole moment of their cell and then relating this function to the absorption coefficient as a function of frequency. Their computed spectrum and comparison to experiment are displayed in Fig. 11, taking into account corrections introduced by the authors. The essential features of the experimental spectrum, particularly the low-frequency peak, are reproduced well. The authors were then able to assign specific modes of the spectrum. 

Fig. 11. (a) Computed IR adsorption spectrum of D2O. (b) Comparison of the computed IR adsorption spectrum with experiment. The solid line is the computed spectrum, the dashed line is the computed spectrum with Egelstaff quantum corrections, and the inset shows an experimental IR spectrum of H2O. Reprinted with permission from Silvestrelli et al. (1997). 

Let us now turn to the intensity errors and discuss the most frequent ones in detail Figs. 39a)—d) demonstrate some of them in the interferogram and the effect in the spectrum. A minor intensity error is that sometimes the computed spectrum happens to be wrong by a constant factor due to some change in the amplifier gain between background and sample measurement (Fig. 39 a). Tliis does not affect the structures in the spectrum but is important when refractive index or absorption coefficient are evaluated from the reflectance or transmittance, respectively. 

Calculations by semi-empirical quantum mechanics of the INS of water on nickel clusters also refer to the riding modes [10,11]. The cluster Niii(H20), comprising a single layer of 11 nickel atoms with the water molecule bound to the central nickel atom, was modelled. The water molecule on top of the central nickel atom was at an optimised distance of 0.22 nm it was not dissociated. The INS of nickel particles with adsorbed water molecules was assigned with the aid of the computed spectrum peaks above 350 cm, to two external and two internal vibrations of the adsorbed water molecules peaks below 350 cm, to adsorbent (i.e. nickel) vibrations enhanced by hydrogen atoms... 

A catalytic center can be created in a zeolite cage by the incorporation of a transition metal compoimd, e.g. ferrocene, [Fe(CsH5)2], which may be the catalyst or the precursor. To assess the strength of the interaction between the encapsulated ferrocene and the zeolite the INS spectrum of ferrocene in the supercage of potassium zeolite Y has been compared with the INS of solid ferrocene [122]. The spectra are shown in Fig. 7.29 and the assignments, according to the INS and computed spectrum of solid ferrocene [123] in Table 7.20. 

All chosen approaches yielded qualitatively the same energetic order D3d < D2h< D4h. No genuine minima with Oh symmetry were found. Force constant analysis at the UBP86 level confirmed that the D3d and D4h species are minima on the potential surface, whereas the D2h structure is a transition state connecting equivalent D3d species. The infrared spectra of "V(CO)6 was in reasonable agreement with the computed spectrum of the D3d structure. 

Fig. 24. CD spectra of the hinge-peptide (curve 1), [Nle15]-gastrin-[2-l 7] (curve 2) and hinge-peptide/[Nle15]-gastrin-(2-l 7) (curve 3) in aqueous solution. The computed spectrum (curve 4) was obtained by addition of the CD curves 1 and 2. The CD spectrum of hinge-peptide/[Nle15 -gastrin-[5-17] is almost superimposable to that of curve 3.

Fig. 6. The p.m.r. spectrum of methyl 3,4-dichloro-4-deoxy-a-D-g/ycero-pent-2-enopyranoside (a), in deuterochloroform at 100 Mc./sec. (b), the computed spectrum. The methoxy resonance is not shown. (From Coxon et...

However, recently the spectrum of M9 was calculated using the CASPT2 level of theory. The computed spectrum was in very good agreement with experiment (Figure 5.13). The improved correspondence is a result of the combination of an improved description of the reference wave function and an adequate treatment of the dynamical electron correlation by the CASPT2 procedure. 

The CH (v = 3) spectrum and survival probability computed with the Maslen et al. force field will now be compared with the experimental results. The computed overtone spectra in Figure 9a have a slightly higher intensity over the interval —50 to +70 cm 1 when compared with the experimental spectrum of Scotoni et al. (127). The Scotoni et al. spectrum shows several absorption features in the interval -60 to —90 cm, the most intense of which is about 40% of the peak intensity. The computed spectrum shows a secondary structure near -80 cm 1 with an intensity that is about 25% of the peak intensity. The overtone spectrum of Page et al. (6,125,126) has a lower intensity over the interval —30 to —100 cm 1 compared with either the computed spectrum or the experimental spectrum of Scotoni et al. 

The extraction of individual component spectra from the spectrum of mixtures is less straightforward. Thus the computed spectrum of the product in Eq. (1) was well reproduced (see Fig. 12) in general although the features in the region used for fit-... 

If one chooses radius to be the smallest, the density of spheres with radius is a fractal function of the radius r of the sphere in which it is contained. That such a structure indeed gives a power-law dependence on K is shown for the theoretically computed spectrum in Fig.(5.24b)I J. 

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