Comparison with experiment linear molecules

The quasi-classical description of the Q-branch becomes valid as soon as its rotational structure is washed out. There is no doubt that at this point its contour is close to a static one, and, consequently, asymmetric to a large extent. It is also established [136] that after narrowing of the contour its shape in the liquid is Lorentzian even in the far wings where the intensity is four orders less than in the centre (see Fig. 3.3). In this case it is more convenient to compare observed contours with calculated ones by their characteristic parameters. These are the half width at half height Aa)i/2 and the shift of the spectrum maximum ftW— = 5a +A, which is usually assumed to be a sum of the rotational shift 5 u that is nonlinear in density and a linear shift of larger scale A determined by vibrational dephasing. 

In the case of the isotropic spectrum it is useful to consider the functional dependence of Acoi/2 and 5gj on rE, since it is rotational energy relaxation that causes frequency modulation in this spectrum. Such a 

In both models the rotational shift of the line 5co is the same either in the static limit, where it is equal to zero, or in the case of extreme narrowing where it reaches its maximum value coq. A slight difference in its dependence on tE is observed in the intermediate region only. The experimentally observed density dependence of the shift shown in Fig. 3.5 is in qualitative agreement with theory. 

In the pioneering work the same information was extracted from the extremum position assuming it is independent of y [143]. This is actually the case when isotropic scattering is studied by the CARS spectroscopy method [134]. The characteristic feature of the method is that it measures o(ico) 2 not the real part of Ko(icu), as conventional Raman scattering does. This is insignificant for symmetric Lorentzian contours, but not for the asymmetric spectra observed in rarefied gas. These CARS spectra are different from Raman ones both in shape and width until the spectrum collapses and its asymmetry disappears. In particular, it turns out that 

Consider the dependence of the spectral width on the dimensionless parameter T, which in the framework of impact theory linearly increases with increase in density. Then, according to the theory expounded in the preceding section, the extremum is at the point 

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In a more conventional CNDO/2 calculation. Hush and Williams calculated the parallel and perpendicular components of a for a series of first-row diatomics, and also calculated a for all first-row atoms using a similar formula. In view of the errors in their formulae as published, it is not clear whether their results are correct or not, although our own experience is that CNDO/2 gives in general very low values for a. Hush and Williams have also extended their CNDO/2 calculations to hyperpolarizabilities (elements only) for several linear molecules together with HjO, NHj, and CHj. The results are unimpressive where comparison with experiment is possible. Meyer and Schweig have published an extensive comparison of MINDO/... 

Photolysis of H3NBH3 with 121.5 nm radiation yields imidoborane, HBNH, which has been of theoretical interest Spectral shifts observed for several isotopic species containing °B, N, and D show clearly that the spectrum is due to HNBH which is isoelectronic with HBO, HCN and HCCH. From the spectrum of the isolated species two of the and one of the tr-type vibration frequencies for a linear molecule have been obtained. The location of the missing S (B-H stretch) frequency has been calculated. A comparison of observed and calculated frequencies for HBNH is given in Table 7. Another isolated product observed in these experiments is identified as HNB. This radical may be generated by photodissociation of HNBH subsequent to its formation. In this respect the photolysis mechanism would be similar to the formation of C2H from acetylene. 

Reis et al. report theoretical studies of the urea250 and benzene251 crystals. Their calculations start from MP2 ab initio data for the frequency-dependent molecular response functions and include crystal internal field effects via a rigorous local-field theory. The permanent dipolar fields of the interacting molecules are also taken into account using an SCF procedure. The experimental linear susceptibility of urea is accurately reproduced while differences between theory and experiment remain for /2). Hydrogen bonding effects, which prove to be small, have been estimated from a calculation of the response functions of a linear dimer of urea. Various optoelectronic response functions have been calculated. For benzene the experimental first order susceptibility is accurately reproduced and results for third order effects are predicted. Overall results and their comparison with studies of liquid benzene show that for compact nonpolar molecules environmental effects on the susceptibilities are small. 

Comparison of Theory for Linear Molecules with Experiment... 

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