Kluk was the first to obtain these results [269]. They differ drastically from (6.25). When the medium becomes more rarefied, intensity in the central part of the IR spectrum decreases to zero. Hence, tJ j shortens, unlike t, which lengthens. The time t e i behaves in the same manner for the case of weak collisions, though a formula quantitatively analogous to (6.63) is not found for this case. One can refer only to numerical calculations based on the general formulae by Sack or by Fixman and Rider. These calculations provide identical results [85]. Fig. 6.5 shows that, in rarefied media, the difference between weak and strong collision [Pg.214]

So, the calculation of the shape of an IR spectrum in the case of anticorrelated jumps of the orienting field in a complete vibrational-rotational basis reduces to inversion of matrix (7.38). This may be done with routine numerical methods, but it is impossible to carry out this procedure analytically. To elucidate qualitatively the nature of this phenomenon, one should consider a simplified energy scheme, containing only the states with j = 0,1. In [18] this scheme had four levels, because the authors neglected degeneracy of states with j = 1. Solution (7.39) [275] is free of this drawback and allows one to get a complete notion of the spectrum of such a system. [Pg.237]

In this paper, we have presented an application of the Lanczos method to the IR spectrum calculation of a polyatomic molecule The power of this approach comes from the use of the Lanczos algorithm, in conjunction with tailored dipole functions, which allows to tune selectively the calculation to some specific components of the spectrum it is equivalent to split the whole spectrum calculation into smaller, nearly independent parts This has been shown explicitly in the case of the C-H stretch overtones, which have been converged up to c a 16000 cm, in a region where the density of states is about 50 per cm Contrary to a previous conclusion drawn by Slbert 19, the Lanczos method is able to provide highly excited overtone line positions, by choosing an ad hoc dipole function in eq.(l), as discussed in sections 2 and 4 3 [Pg.257]

Finally, in Figure 11.6 we report the NMA IR spectrum calculated by the GLOB/ADMP trajectory as the power spectrum of the dipole-dipole autocorrelation function. [Pg.530]

A full IR spectrum calculation based on the computer data base of molecular parameters (geometry, force constants, electro-optical parameters) can be considered as an effective aid for the IR spectra prediction. At the same time this approach is not so fast as to be applied to a large structural file and in addition the spectrum prediction can not be carried out fully automatically. [Pg.1311]

Based both on the determined isotopic shifts and the comparison of the radical IR spectrum with the spectra of various substituted benzenes, the bands have been assigned to the normal modes and the force field of the benzyl radical calculated (Table 8). [Pg.43]

Computational part is comprised several steps. There were several steps in computational part. Firstly, geometry of AA was optimized to achieve molecule stable state. Then vibrational analysis was carried out. Parameters of the same computational method were used for subsequent IR spectrum calculation. Obtained IR spectra are shown in Figure 8.14. [Pg.215]

Fig. 7.1. Spectral characteristics of the (=Si-0)3Si-N = N-O radical, (a) EPR spectrum (the central component of the spectrum at 300 K is distorted by the superposition of the admixed signal and is not shown (b) optical absorption spectrum (c) IR spectrum (calculated form of two normal vibrations of the radical F3Si-N = N-O are shown). |

There are 78 vibrational degrees of freedom for TgHg and it has been shown that the molecule has 33 different fundamental modes under Oh symmetry, 6 are IR active, 13 are Raman active, and 14 vibrations are inactive. The experimental fundamental IR active vibrational frequencies have been assigned as follows 2277 (v Si-H), 1141 (vas Si-O-Si), 881 5 O-Si-H), 566 ( s O-Si-O), 465 (v O-Si-O), and 399 cm ( s O-Si-O). These generally agree well with calculated values The IR spectrum recorded in the solid state shows bands at 2300 and 2293 cm [Pg.16]

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