Non-rigid rotor

It is possible that the complexes benzene- -HX can be described in a similar way, but in the absence of any observed non-rigid-rotor behaviour or a vibrational satellite spectrum, it is not possible to distinguish between a strictly C6v equilibrium geometry and one of the type observed for benzene- ClF. In either case, the vibrational wavefunctions will have C6v symmetry, however. 

In fact, the frequency ofthe torsional oscillation mode V4 is found to be more than double that ofthe ground state. The frequency ofthe torsional oscillation mode was reevaluated by Mukheijee et al [56], using a very accurate representation of the one-dimensional vibrational Hamiltonian of the non-rigid rotor in terms of a Fourier series [76-78], and other spectroscopic parameters calculated for the first time taking care of anharmonicity. A new assignment of the experimental spectrum was given. The results are displayed in Table 8. For reference purpose the vibrational frequencies of the ionic states are also listed... 

We have already seen that, in quantum mechanics, the eigenvalue of J is J(J + 1) so that from (6.194) we obtain, for the non-rigid rotor,... 

The thermodynamic functions of this table are analogous to those in the JANAF table for H20(g) (j ) both tables are taken from Freidman and Haar (1 ). Friedman and Haar applied their non-rigid-rotor, anharmonic-oscillator treatment (with vibrational-rotational coupling terms and low-temperature rotational corrections) to the infrared-spectra analyses of Benedict et al. (J ), and... 

The 2-3 splitting is of the order of a typical low-J rotational spacing and non-rigid-rotor spectra result. The rovibrational levels were therefore computed from the Hamiltonian of Eqs. (4.9a, b) with the help of a second-order perturbation correction used by Butcher and Costain66 for cyclopentene rather than by direct matrix... 

MW Double minimum potential function determined from the variation of rotational constants and from analysis of the non-rigid rotor spectra in the v = 0, 1 and 2,3 inversion states. Barrier =241 cm-1 125)... 

Figure 4.4 Dependence of NOE, nTi and nT2 upon rotational correlation time Tr, for a proton-decoupled resonance in a rigid rotor, in spectrometers with proton resonance frequencies of 250 and 500MHz. The dotted curve represents nT for a non-rigid rotor with an internal motion which rapidly halves the angular order parameter, S. The curves for other values of may be estimated by interpolation.

In a similar fashion to the description of vibrational energy levels, a simple model can be used to approximate the rotational motion. In general, that of a non-rigid rotor is used (because the atoms are able to change their relative intemuclear positions). In general, the rotation energy Ej (frequently, F(J) instead of / is used) is written as... 

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