Fourier absorption spectra

Figure 20. The (So —> S2) absorption spectrum of pyrazine for reduced three- and four-dimensional models (left and middle panels) and for a complete 24-vibrational model (right panel). For the three- and four-dimensional models, the exact quantum mechanical results (full line) are obtained using the Fourier method [43,45]. For the 24-dimensional model (nearly converged), quantum mechanical results are obtained using version 8 of the MCTDH program [210]. For all three models, the calculations are done in the diabatic representation. In the multiple spawning calculations (dashed lines) the spawning threshold 0,o) is set to 0.05, the initial size of the basis set for the three-, four-, and 24-dimensional models is 20, 40, and 60, and the total number of basis functions is limited to 900 (i.e., regardless of the magnitude of the effective nonadiabatic coupling, we do not spawn new basis functions once the total number of basis functions reaches 900).

This effect induces a free induction decay (FID) signal in the detection circuit. The FID can be measured, and the normal absorption spectrum can be obtained by means of an inverse Fourier transform. A variety of experimental extensions have been developed for this approach. By means of particular pulse sequences it is possible to detect spin resonances selectively on the basis of a broad ensemble of properties such as spatial proximity and dipolar coupling strengths. The central fundamental quantity of interest is, however, still the energy spectrum of the nuclear spin,... 

In the diffuse reflectance mode, samples can be measured as loose powders, with the advantages that not only is the tedious preparation of wafers unnecessary but also diffusion limitations associated with tightly pressed samples are avoided. Diffuse reflectance is also the indicated technique for strongly scattering or absorbing particles. The often-used acronyms DRIFT or DRIFTS stand for diffuse reflectance infrared Fourier transform spectroscopy. The diffusely scattered radiation is collected by an ellipsoidal mirror and focussed on the detector. The infrared absorption spectrum is described the Kubelka-Munk function ... 

Figure 2. a) X-ray absorption spectrum near the Mo K-edge of the Co/Mo = 0.125 unsupported Co-Mo catalyst recorded in situ at room temperature b) normalized Mo EXAFS spectrum c) absolute magnitude of the Fourier transform d) fit of the first shell e) fit of the second shell. The solid line in d) and e) is the filtered EXAFS, and the dashed line is the least squares fit. 

In detector noise limited spectroscopies such as PAS it is advantageous to enhance the throughput of energy (Jacquinot s advantage) by utilizing a Michel son interferometer. One then Fourier transforms (FTs) the resulting interferogram to yield a PA spectrum that qualitatively resembles an absorption spectrum. 

Fourier transform spectroscopy spect A spectroscopic technique in which all pertinent wavelengths simultaneously Irradiate the sample for a short period of time, and the absorption spectrum is found by mathematical manipulation of the Fourier transform so obtained. fur e a tranz,form spek tras-ko-pe fp See freezing point. 

The EXAFS function is obtained from the X-ray absorption spectrum by subtracting the absorption due to the free atom. A Fourier transform of the EXAFS data gives a radial distribution function which shows the distribution of the neighbouring atoms as a function of internuclear distance from the absorbing atom. Shells of neighbours, known as coordination shells, surround the absorbing atom. Finally, the radial distribution function is fitted to a series of trial structural models until a structure which best fits the... 

The previous sections have dealt primarily with infrared absorption spectra, although the conclusions can in general be applied to other types of spectra. Here additional uses of deconvolution will be demonstrated. In the first example, a Fourier transform spectrum is simulated and several attempts to deconvolve this spectrum show limited success. In the second example, pressure-broadening effects in an infrared absorption spectrum and a Raman spectrum are simulated. An attempt at removing these effects by deconvolution shows some promise. 

Figures 26 and 27 show the results of using deconvolution to remove the sidelobes present in a Fourier transform spectrum. These two spectral sections are taken from the v2 absorption band of ammonia at about 848 and 828 cm-1, respectively. The unapodized spectrum exhibits a resolution of 0.125 cm-1, and is shown in trace (a). The spacing of the lines in Fig. 26 is such that the sidelobes when added together partially cancel, minimizing their effect. Sidelobes and the apparent negative absorption between the lines are both still present. The spacing of the lines in Fig. 27 is such that the sidelobes add constructively, accentuating their effect and producing...

Fig. 26 Fourier transform spectrum of v2 of ammonia. Trace (a) is a section of the infrared absorption spectrum of ammonia recorded on a Digilab Fourier transform spectrometer at a nominal resolution of 0.125 cm-1. In this section of the spectrum near 848 cm-1 the sidelobes of the sine response function partially cancel, but the spectrum exhibits negative absorption and some sidelobes. Trace (b) is the same section of the ammonia spectrum using triangular apodiza-tion to produce a sine-squared transfer function. Trace (c) is the deconvolution of the sine-squared data using a Jansson-type weight constraint.

Because of this mathematical step, the technique is usually called Fourier transform infrared spectroscopy or FTIR spectroscopy. The Fourier transformation is a mathematical procedure that enables one to convert from the results of an interfero-gram back to intensities of a given wavelength. It is performed in a computer connected to the spectrometer. The result is the absorption spectrum of the sample, that is, the intensity of the absorbance as a function of the wavenumbers. 

In reality the individual lines obtained after the Fourier transformation are composed of both absorptive A(f) and dispersive D(f) components. This non-ideality arises because of a phase shift between the phase of the radiofrequency pulses and the phase of the receiver, PHCO, and because signal detection is not started immediately after the excitation pulse but after a short delay period A. Whereas the effect of the former is the same for all lines in a spectrum and can be corrected by a zero-order phase correction PHCO, the latter depends linearly on the line frequency and can be compensated for by a first-order phase correction PHCl. Both corrections use the separately stored real and imaginary parts of the spectrum to recalculate a pure absorptive spectrum. 

H2OS3(CO)io. Figure 5 presents a proton NMR absorption spectrum for H2Os3(CO)io that was obtained by Fourier transformation of the free induction decay. The spectrum was taken at room temperature, but no difference was... 

Vibrational spectroscopy [3, 4] The infrared absorption spectrum of zaleplon, obtained in KBr disk is shown in Fig. 8.5. The spectrum was recorded on Jasco FT/IR 460 plus Fourier transform infrared spectrometer model. 

The electronic absorption spectrum in the frequency domain is the fourier transform of the overlap in the time domain. 

This expression for the complete overlap is Fourier transformed to give the electronic emission spectrum. In order to carry out the calculation it is necessary to know the frequencies and the displacements for all of the displaced normal modes. In addition, the energy difference between the minima of the two potential surfaces E0 and the damping r must be known. As will be discussed below, the frequencies and displacements can be experimentally determined from pre-resonance Raman spectroscopy, and the energy difference between the ground and excited states and the damping can be obtained from the electronic absorption spectrum and/or emission spectrum. 

Structures in the absorption spectrum are related to structures in the autocorrelation function. There are many cases in which an unambiguous assignment of structures in the absorption spectrum is essentially impossible in the energy domain. Figure 4.4(a) depicts an intriguing example. The corresponding autocorrelation function, however, obtained by Fourier transformation of the measured spectrum has a much simpler... 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

Spectral Manipulation Techniques. Many sophisticated software packages are now available for the manipulation of digitized spectra with both dedicated spectrometer minicomputers, as well as larger main - frame machines. Application of various mathematical techniques to FT-IR spectra is usually driven by the large widths of many bands of interest. Fourier self - deconvolution of bands, sometimes referred to as "resolution enhancement", has been found to be a valuable aid in the determination of peak location, at the expense of exact peak shape, in FT-IR spectra. This technique involves the application of a suitable apodization weighting function to the cosine Fourier transform of an absorption spectrum, and then recomputing the "deconvolved" spectrum, in which the widths of the individual bands are now narrowed to an extent which depends on the nature of the apodization function applied. Such manipulation does not truly change the "resolution" of the spectrum, which is a consequence of instrumental parameters, but can provide improved visual presentations of the spectra for study. 

Figure 5.4, one can easily understand why the interfacial electron transfer should take place in the 10-100 fsec range because this ET process should be faster than the photo-luminescence of the dye molecules and energy transfer between the molecules. Recently Zimmermann et al. [58] have employed the 20 fsec laser pulses to study the ET dynamics in the DTB-Pe/TiC>2 system and for comparison, they have also studied the excited-state dynamics of free perylene in toluene solution. Limited by the 20 fsec pulse-duration, from the uncertainty principle, they can only observe the vibrational coherences (i.e., vibrational wave packets) of low-frequency modes (see Figure 5.5). Six significant modes, 275, 360, 420, 460, 500 and 625 cm-1, have been resolved from the Fourier transform spectra of ultrashort pulse measurements. The Fourier transform spectrum has also been compared with the Raman spectrum. A good agreement can be seen (Figure 5.5). For detail of the analysis of the quantum beat, refer to Figures 5.5-5.7 of Zimmermann et al. s paper [58], These modes should play an important role not only in ET dynamics or excited-state dynamics, but also in absorption spectra. Therefore, the steady state absorption spectra of DTB-Pe, both in...

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