Rotation Spectra

Make measurements of the transition wavenumbers in the rotational spectrum of silane from Figure 5.10 and hence determine the Si—H bond length. 

HC5N (cyanodiacetylene) interstellar, 120 rotational spectrum, 110 Na2S203 (sodium thiosulphate)... 

Fig. 0.5. IR absorption spectra of HC1 in different liquid solvents (a) in SF6 [16] (the triangles mark the positions of the rotational components in the resolved spectrum of the rarefied gas) (b) in He [15] (c) in CCU (the vertical lines mark the frequencies vj and the intensities of the Stark components of the linear rotator spectrum split by the electrical field of the cage)[17].

The envelope of the Stark structure of the rotator in a constant orienting field, calculated quantum-mechanically in [17], roughly reproduces the shape of the triplet (Fig. 0.5(c)). The appearance of the Q-branch in the linear rotator spectrum indicates that the axis is partially fixed, i.e. some molecules perform librations of small amplitude around the field. Only molecules with high enough rotational energy overcome the barrier created by the field. They rotate with the frequencies observed in the... 

Being applied for the relaxation of populations (k = 0), this equality expresses the demands of the detailed balance principle. This is simply a generalization of Eq. (4.25), which establishes the well-known relation between rates of excitation and deactivation for the rotational spectrum. It is much more important that equality (5.21) holds not only for k = 0 but also for k = 1 when it deals with relaxation of angular momentum J and the elements should not be attributed any obvious physical sense. The non-triviality of this generalization is emphasized by the fact that it is impossible to extend it to the elements of the four-index... 

We make use of the assumption which is conventional in kinetic theory of the harmonic oscillator [193] as well as in energy-corrected IOS [194]. All the transition rates from top to bottom in the rotational spectrum are supposed to remain the same as in EFA. Only transition rates from bottom upwards must be corrected to meet the demands of detailed balance. In the same way the more general requirements expressed in Eq. (5.21) may be met ... 

In the purely non-adiabatic limit the phase (5.52) coincides with that calculated in [203] and for very long flights (rt b,v" v) or high energies (.E e) it reduces to what can be obtained from the approximation of rectilinear trajectories. However, there is no need for these simplifications. The SCS method enables us to account for the adiabaticity of collisions and consider the curvature of the particle trajectories. The only demerit is that this curvature is not subjected to anisotropic interaction and is not affected by transitions in the rotational spectrum of the molecule. 

To compare this result with that obtained within perturbation theory [273, 279], one must additionally assume the perturbation correlation function to be exponential, as in [273, 279, 280]. In this case, the purely rotational spectrum [273, 279] and that obtained with Eq. (7.71) coincide, if the co-dependence of the / operator is neglected and ([Pg.247]

Let us consider the quasi-classical formulation of impact theory. A rotational spectrum of ifth order at every value of co is a sum of spectral densities at a given frequency of all J-components of all branches... 

Birnbaum G. Quantized rotational motion in liquids Far infrared rotational spectrum of HF and NH3 in liquid SF6, Mol. Phys. 25, 241-5 (1973). 

In addition, Winnewisser et al. [36] have demonstrated quantum monodromy for the NCNCS molecule, not only in the (vb, Ka) eigenvalues but also in the Bes = B + C)/2 rotational constant, which varies smoothly with Ka, at fixed Vb for Vb = 0-2, but shows a kink for Vb = 3-5. This observation is a key to the assignment of the extremely congested rotational spectrum of this interesting quasilinear molecule. 

The rotational spectrum has been calculated accuratly by ab-initio methods [2], and has been measured in the laboratory with high precision [3,4], so that the radio detection of C3H2can be done without ambiguity, encouraging its search in different environments as dense dark clouds [5], diffuse interstellar medium [6] or Hll regions [7]. 

Directly linked to the geometry and dipole moment of a molecule, the rotational spectrum is an unambiguous fingerprint that has enabled the radioastronomers community to identify more than a hundred species. Optimized geometries of C3H2calculated at increasing levels of theory (from RHF to MP4 [12]) are presented in Table 1. The rotational constants obtained for C3H2 and its deuterated isomers are presented in Table 2. 

Fig. 14 The experimental geometries of benzene- -HC1 and benzene- -ClF (to scale) and the n-electron model of benzene. See text for discussion of the motion of the C1F subunit, as inferred from an analysis of the rotational spectrum of benzene- -ClF. See Fig. 1 for key to the colour coding of atoms... 

Evidence for a significant contribution from the ionic form [BX] + - -Y in a gas-phase complex B- XY was first deduced from the spectroscopic constants of H3N- -ClF, as obtained by analysis of its rotational spectrum [63]. In particular, the value ka = 34.3 N m 1 of the intermolecular stretching force constant (obtained from the centrifugal distortion constant Dj in the man-... 

In view of the fact that complete methylation of F N- HX to give (CH3)3N- -HX leads to an increased extent of proton transfer from HX to the base when X is Cl and essentially complete transfer when X is I, it seemed reasonable to seek a more significant contribution from the ionic valence bond structure [(CH3)3NC1] + - F in (CT N- ClF by examining properties similarly derived from its rotational spectrum [68]. 

Figure 3.6 The energy-level diagram for a rotational spectrum...

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