Rigid asymmetric

That AEs is nonzero is not so much a result of rotation-vibration mixing, as it is a result of S02 being an asymmetric top. This conjecture is verified by plotting AEA as a function of the expectation value of the rigid asymmetric top Hamiltonian given by Eq. (7). These results are displayed in the second row of Fig. 7. We find that AEA is... 

The rigid asymmetric rotor Hamiltonian may be written [84Gor] ... 

According to Kivelson and Wilson [52Kiv, 84Gor] the Hamiltonian for a non-rigid asymmetric rotor may be written ... 

A. Rotational Partition Function for a Rigid Asymmetric Molecule 441... 

A. ROTATIONAL PARTITION FUNCTION FOR A RIGID ASYMMETRIC MOLECULE... 

There are several different theoretical approaches to the problem. The Landau molecular field theory was applied by de Gennes to liquid-crystal phase transitions. (89) The Maier-Saupe theory focuses attention on the role of intermolecular attractive forces.(90) Onsager s classical theory is based on the analysis of the second virial coefficient of very long rodlike particles.(91) This theory was the first to show that a solution of rigid, asymmetric molecules should separate into two phases above a critical concentration that depends on the axial ratio of the solute. One of these phases is isotropic, the other anisotropic. The phase separation is, according to this theory, solely a consequence of shape asymmetry. There is no need to involve the intervention of intermolecular attractive forces. Lattice methods are also well suited for treating solutions, and phase behavior, of asymmetric shaped molecules.(80,92,93)... 

Figure 14.1 The SVRT model for polyatom-polyatom reactive collision between the target (reacting) molecule T and the reactant molecule R. The target molecule T is composed of two rigid parts B and C whose centers of mass are connected by the reactive coordinate r which describes the generalized vibrational motion responsible for breaking the B-C bond. The reactant molecule R is treated as a rigid asymmetric rotor.

For the reactant molecule R with mass rriji, we treat it as a rigid asymmetric rotor whose quantum Hamiltonian (with zero kinetic energy for the center-of-mass) is given by ... 

For the sake of brevity, only the simplest case of plane rotating oscillator has been considered here. Nevertheless, more involved situations like polyatomic molecules modelled with non-rigid asymmetric tops with the account of intramolecular vibrational-vibrational and vibrational-rotational couplings, may be studied in the framework of the same formalism (Dubrovskiy et al. 1983 Bogdanov et al. 1985b). Some of the cases where cross effects determine the physical picture of scattering are discussed below (Sect. 2.4). 

Table 4 Energies of the rigid asymmetric rotor. Analytic expressions for the total rotational energy in terms of the rotational constants A, B and C. As the rotational transitions involving low Jean often be observed, these relationships can be of considerable use in making a preliminary determination of molecular constants...

The three rotational constants completely determine the energy level scheme of a rigid asymmetric top. This scheme may be considerably more complex than that of a symmetric rotor, especially if k is close to zero. Like it has already been shown for linear and symmetric-top molecttles, the mrmber of parameters reqttired to theoretically reproduce accurately measirred rotational spectra may increase considerably if effects of rotation-vibration interaction, spin coupling, or internal rotation must be taken into account. Details of practical importance will be considered below. 

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