Spectrum of the Model

on the special lines the stripe ground state of the considered model is asymptotically degenerated with an excited spiral singlet state in the thermodynamic limit. It is not clear if the degeneracy is exponentially large or not. This consideration is valid for any integer or half-integer x = j, but it is not valid for 

It is interesting to note that the singlet wave function (26) can be also represented in a special recurrent form [14, 11] 

The norm of the wave function (44) and expectation values can be also calculated with the use of the recursion technique developed in [14, 11], Certainly, it gives the same expressions (37,42) for spin correlation functions. 

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The structural unit associated with an electronic transition m UV VIS spectroscopy IS called a chromophore Chemists often refer to model compounds to help interpret UV VIS spectra An appropriate model is a simple compound of known structure that mcor porates the chromophore suspected of being present m the sample Because remote sub stituents do not affect Xmax of the chromophore a strong similarity between the spectrum of the model compound and that of the unknown can serve to identify the kind of rr electron system present m the sample There is a substantial body of data concerning the UV VIS spectra of a great many chromophores as well as empirical correlations of sub stituent effects on k Such data are helpful when using UV VIS spectroscopy as a tool for structure determination... 

Cover Illustration Atomic force microscopy image of molybdenum oxide particles on flat, silicon dioxide substrate, which serves as a model system for a supported catalyst. The area shown corresponds to one square micrometer the maximum difference in height is approximately 10 nanometer. The superimposed curve is the secondary ion mass spectrum of the model catalyst, showing the caracteristic isotopic patterns of single molybdenum ions and of molybdenum oxide cluster ions. 

Fig. 10.13. MALDI-TOP spectrum of the model oligo(ethylene terephthalate diol)s. The inset shows an expanded view of the low-intensity peaks in the circle m/z 940-1120). Adapted from Ref. [126] by permission. John Wiley Sons, 1995.

Phenolic Hydroxyl Group. An ethanolic solution of 3,4,5-tri-methoxybenzyl alcohol (4-0-methylsyringyl alcohol) and sodium hydroxide was prepared, and ultraviolet spectra of the solution were recorded immediately and 3 days after preparation. These spectra were compared with the spectrum of the model compound in neutral ethanol. The three spectra were identical with the absorption curve possessing a broad maximum in the 270-280 m/x region. Further visual observation of the alkaline solution for 2 weeks revealed no color formation. This suggests that phenoxide ion formation may be a necessary initial step in reactions leading to the development of chromophoric structures from lignin model compounds. 

In hydrastinine (15) the aromatic chemical shifts were assigned by comparison with the spectrum of the model compound, methylenedioxybenzene... 

AXH NMR spectrum of the model compound (CH3CH2)3NGH2CH2COOCH3 Ie contained peaks at d = 1.2 and 3.8, which are assigned to CH3C-N and -C-CHy-N, respectively. Similar peaks were evident in the spectrum of the polymer formed with triethy-lamine, their intensity corresponding to one ammonium group per chain. 

In order to confirm the structure for the LO cofactor, model compounds mimicking the proposed enzymic structure were synthesized (13, 24). The UV-Vis abso tion spectrum of the model compound, with a A-max of 504 nm which is red-shifted compared to other TPQ-containing amine oxidases, corresponded almost exactly to that of native LO (13). Under the same conditions, the resonance Raman spectrum of the phenylhydrazine derivative of the model compound was found to be superimposable with that of the isolated LO peptide labeled with phenylhydrazine, yet very different from the phenylhydrazine derivative of a TPQ model compound (13). 

Fig. 23 Simulated RI82 spectrum of the model spin system (shown in Fig. 19a with coordinates as in Table 4). The 180° pulse pairs were replaced by the composite pulse unit 90S590 3590 590° 4590° 13590° 45 = 180gol80° 90. o i/27r was lOOkHz andcc r/27r was 14.81kHz...

As a result of solving the Schrodinger equation for the model Hamiltonian (9.3) one gets anharmonic frequencies and relative IR intensities (if the dipole moment function is available) in the particular region of the IR spectrum [23-25]. It should be noted, however, that in many theoretical studies only the energy spectrum of the model 2D Hamiltonian was considered [26, 27]. 

For a more detailed analysis of the absorption properties, the UV spectrum of the model compound (Scheme 7), which was also synthesized, was calculated using semiempirical methods (MOPAC/ZINDO). The experimental UV spectrum of the model compound is nearly identical to the spectrum of the polymer. From the calculation it was derived that four UV transitions contributed to the absorption maximum at 330 nm. In detail, these are the HOMO LUMO, the HOMO->LUMO+l, the HOMO LUMO+2, and the HOMO—LUMO+3 transitions. The first two orbital excitations showed a large involvement of the triazene group, whereas the other two are mainly localized at the phenyl moieties. Similar results were previously reported for aryl dialkyl triazenes [119, 184] which have the same structural unit. Starting from simple chemical considerations, it could be thought that the number of chromophores responsible for the absorbance at around 300 nm is a low value, for example 2 or 4 per unit. On the other hand, the semiempirical calculations indicated the involvement of the phenyl moieties in the absorption properties therefore, the chromophore number in the calculation was not restricted to low values. As a starting point for the calculation, numbers close to the expected value were chosen. 

Rgure 13 The calculated spectrum of the model dimer of figure 10 at 5 A. Lines drawn with negative oscillator strength indicate the positions of transitions with no calculated oscillator strength. Y is the long axis of figure 10. 

For the determination of the methoxycarbonyl chain end fimctionality, a model compound was synthesized under similar conditions to that of the telechelic polymer. TMPCl was capped with DPE, followed by end quenching with MTSMP. This model compound was used for the assignments of both the H NMR and the NMR chemical shifts corresponding to the methoxycarbonyl chain end, as well as for calibration for IR measurements. The H NMR spectrum of the model compound is shown with the assignments in Figure 1. The peaks corresponding to protons c-i are... 

Among the most commonly used fluorescent probes for biochemical and biological systems are l-dimethylamino-5-sulfonamidonaphthalenes (DNS derivatives) (SCHEME IV). The emission spectrum of the model compound l-dimethylamino-5-(S-isobutyroyl-aminoethyl)sulfonamidonaph-thalene (IB DNS) in absolute methanol is characterized by one band with an emission maximum at 538 nm which corresponds to the excited state of IB DNS, with a nonprotonized dimethylamino group. The emission spectrum was independent on the exciting radiation for wavelengths from 250 to 380 nm. 

Figure 8. Response spectrum of the model as generated (black) and modified (red). 

The UV spectrum of the model compound and of the corresponding copolymers are very similar. By contrast the only detectable Cotton effect in the CD spectrum of the model compound, centered at about 260 nm, shows a very low Ae ax with respect to the copolymer and in the same order of magnitude (0.01—0.05) as other non rigid phenyl-alkanes (II). 

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