Spectrum phases

The ultraviolet absorption spectrum of thiazole was first determined in 1955 in ethanolic solution by Leandri et al. (172), then in 1957 by Sheinker et al. (173), and in 1967 by Coltbourne et al. (174). Albert in 1957 gave the spectrum in aqueous solution at pH 5 and in acidic solution (NHCl) (175). Nonhydroxylic solvents were employed (176, 177), and the vapor-phase spectrum was also determined (123). The results summarized in Table 1-15 are homogeneous except for the first data of Leandri (172). Both bands A and B have a red shift of about 3 nm when thiazole is dissolved in hydrocarbon solvents. This red shift of band A increases when the solvent is hydroxylic and, in the case of water, especially when the solution becomes acidic and the extinction coefficient increases simultaneously. 

Valence Vibrations. pCH and pCD. In the 3100 cm region the infrared spectrum of thiazole shows only two absorptions at 3126 and 3092 cm F with the same frequencies as the corresponding Raman lines (201-4) (Fig. I-IO and Table 1-23). In the vapor-phase spectrum of... 

Out-of-Plane Vibrations, yCH and yCD. In accordance with all the proposed assignments (201-203), the bands at 797 and 716 cm correspond to yCH vibrators, which is confirmed by the C-type structure observed for these frequencies in the vapor-phase spectrum of thiazoie (Fig. 1-9). On the contrary, the assignments proposed for the third yCH mode are contradictory. According to Chouteau et al. (201), this vibration is located at 723 cm whereas Sbrana et al. (202) prefer the band at S49cm and Davidovics et al. (203) the peak at 877 cm This last assignment is the most compatible with the whole set of spectra for the thiazole derivatives (203) and is confirmed by the normal vibration mode calculations (205) (Table 1-25). The order of decreasing yCH frequencies, established by the study of isotopic and substituted thiazole derivatives, is (203) yC(4)H > 70(2)13 > yC(5)H. Both the 2- and 4-positions, which seem equivalent for the vCH modes, are quite different for the yCH out-of-plane vibrations, a fact related to the influence observed for the... 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

On the contrary, according to Eq. (1.70) gM becomes zero for o) = 0, the width of a gap in the centre of the spectrum being about l/xj. Note that the total width of a gas phase spectrum is much larger, namely 1/tc. This narrow gap in the centre of gM(oj) points to the existence of intercollisional correlation. The same is valid for the spectrum of random... 

The phase spectrum 0(n) is defined as 0(n) = arctan(A(n)/B(n)). One can prove that for a symmetrical peak the ratio of the real and imaginary coefficients is constant, which means that all cosine and sine functions are in phase. It is important to note that the Fourier coefficients A(n) and B(n) can be regenerated from the power spectrum P(n) using the phase information. Phase information can be applied to distinguish frequencies corresponding to the signal and noise, because the phases of the noise frequencies randomly oscillate. 

Modem NMR software comes with very good automatic phase routines so most of the time you should end up with a beautifully phased spectrum. Sometimes, however, the software doesn t quite perform and you may need to tweak the phase manually. It can take a bit of familiarity to get this right but it is just a matter of practise. If you remember that the zero order adjustment works constantly across the spectrum and that the first order doesn t, it is quite easy to see what is going on. Normally the software gives you an option of setting the pivot point of the first order adjustment (i.e., the frequency in the spectrum where there is no effect from the first order adjustment). This pivot point is normally set to the largest peak. 

Spectrum 4.3 shows how the phase can be improved with a manual tweak. Note that in a poorly phased spectrum, the integrals will be distorted such that they are pretty much unusable. 

Spectrum 4.3 A well phased spectrum with reliable integrals (below) and a badly phased spectrum with unusable integrals (above). 

There is of course attenuation of the signal, as shown in Fig. 5, taken from Joyner and Roberts (28) The gas phase spectrum will also be obtained, but this usually can be separated easily from the signal of the solid. This sample cell arrangement thus permits the study of the stationary-state surface during catalysis and also its evolution in response to pulses and step functions in the gas composition. The temperature of the sample should be controlled so that the surface can be studied during temperature-programmed desorption and reaction. 

The infrared spectrum of GeF2 has also been reported 10 3 It was necessary to study the matrix-isolated spectrum for two reasons. First, the examination of the ultraviolet absorption spectrum of GeF2 indicated that at least ten of the bending states were populated, and second, germanium has five abundant isotopes. These suggested that the gas phase spectrum would be broad and ill de-... 

A more detailed description of the working principle of the multichannel YI is given for a four-channel device (N = A). The distances between the channels have been chosen such that di2 k d23 i=- d34 / di3 =/= d24 / dl4. There are six possible different channel pairs corresponding to six different distances of dx2 = 60 pm, d23 = 80 pm, d34 = 100 pm, d13 = 140 pm, d24 = 180 pm, and d14 = 240 pm. These distances match the realized YI sensor structure described in Sect. 10.3. The final interference pattern will thus be a superposition of six two-channel interference patterns. The calculated interference pattern for the four-channel YI is shown in Fig. 10.6a. The amplitude spectrum (lower graph) and the phase spectrum (upper graph) of the Fourier-transformed interference pattern are presented in Fig. 10.6b. 

As one might expect, there are six different peaks in the amplitude spectrum of the Fourier-transformed interference pattern located at six different spatial frequencies ky, each of them corresponding to the interference pattern obtained as a result of overlap of the channels that are separated by the specific distance dy. Looking at the selected spatial frequencies at the phase spectrum of the Fourier-transformed interference pattern, the phase of each two-channel sensor can be monitored simultaneously and independently from each other. The difference between distances dy should be designed such that they allow a good separation of the six different peaks. 

Here a third selection rule applies for linear molecules, transitions corresponding to vibrations along the main axis are allowed if Aj = 1. The A/=0 transition is only allowed for vibrations perpendicular to the main axis. Note that because of this selection rule the purely vibrational transition (called Q branch) appears in the gas phase spectrum of C(X but is absent in that of CO. In both cases, two branches of rotational side bands appear (called P and R branch) (see Fig. 8.3 for gas phase CO). 

Fig. 19. Pulse scheme of the MP-HNCA-TROSY experiment. Delay durations A = 1/(4/hn) 2T a = 27 ms 2Ta= 18-27 ms 2TN = 1/(2JNC-) <5 = gradient + field recovery delay 0 < k < Ta/t2,inax- Phase cycling scheme for the in-phase spectrum is 0i = y 02 = x, — x + States-TPPI 03 = x 0rec = x, — x 0 = y. For the antiphase spectrum, f is incremented by 90°. The intraresidual and sequential connectivities are distinguished from each other by recording the antiphase and in-phase data sets in an interleaved manner and subsequently adding and subtracting two data sets to yield two subspectra.

If li,max is kept rather short (i.e., < 10-12 ms), both the intra- and interresidual correlations exhibit ca. fl times higher intensity in the in-phase spectrum than in the subspectra because the 1Jco coupling is not resolved. 

From these viewpoints, it is advantageous to use the in-phase spectrum for assigning the resonances in the usual HNCA manner in the first place, thanks to its higher intensity when short tljmax is used. The subspectra can then be used to distinguish between the intra- and interresidual correlations in an ambiguous case.73,76... 

Fig. 8.4 Schematic representation of the pulse program IPAP-[ l-l-15N]-HSQC. Narrow and wide bars represent 90° and 180° pulses, with phase x unless indicated. The white bars represent pulses that are applied only when the anti-phase spectrum is acquired. The anti-phase and in-phase...

This point is illustrated by a second example. A vapor-phase spectrum of propionitrile was obtained and its digitization is shown in Table III. For the sake of example, assume the scientist entered the 2246 cm peak as average rather than sharp. The interpretation would result in likelihoods of 0.90 for isocyanate and 0.30 for nitrile. Performing the interpretation with the tracing function turned on would quickly show that the rules base the distinction between isocyanate and propionitrile very heavily on the width of the peak in the vicinity of 2260 cm . Reinterpreting this spectrum with the correct, sharp width entered for the 2246 cm peak results in a nitrile likelihood of 0.50 and isocyanate of 0.40. 

The gel phase spectrum is assumed to be the superposition of two components a three narrow Lorentzian-lines component, which is the spectrum of free radical in the fluid part of the gel phase, and a broad Lorentzian componint, which is the spectrum of radicals involved in the network (see Figure 3, in which the nitrogen hyperfine splitting is = 14.55 C-. . ... 

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