Rigid Rotor Results

Finally, we recall that the wave function of the rigid rotor is a product of ( )) and (0). The 

We also note that m must be an integer and m 1 for a degeneracy of (21 + 1) different m values. We show this form here to achieve a combined single eigenfunction, but you can see that the factor of 

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That result is included in Fig. 4.4. For precise comparison with experiment harmonic oscillator rigid rotor results should be corrected for the effects of nonclassical rotation and anharmonicity. In the region of the maximum (Fig. 4.4) these corrections (see Appendix 4.2), which are temperature dependent, lower the calculated results by several percent. The spectroscopic data employed for the calculation reported in Fig.4.4 are shown in Table4.2. 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

There is a well-known precedent for the difference in the results predicted by stiff and rigid models. The constant-volume heat capacity of a diatomic ideal gas is predicted to be jkT per molecule for a stiff classical model and jkT for a classical rigid rotor. A quanmm mechanical analysis of a diatomic gas yields the... 

Recall that semiempirical methods were parameterized in such a way that the computed electronic energies were equated with heats of formation, not computed enthalpies. Thus, when a semiempirical electronic structure program reports a 298 K heat of formation for AMI, for instance, the reported value derives from adding the atomization energy AE to the experimental 298 K heats of formation of the atoms. Inspection of Figure 10.1 indicates that this will differ from the rigid-rotor-hannonic-oscillator computed result by ZPVE and the differential thermal contributions to the enthalpy of the molecule compared to the atoms. 

To consider the quantum mechanics of rotation of a polyatomic molecule, we first need the classical-mechanical expression for the rotational energy. We are considering the molecule to be a rigid rotor, with dimensions obtained by averaging over the vibrational motions. The classical mechanics of rotation of a rigid body in three dimensions is involved, and we shall simply summarize the results.2... 

Figure 8.16. Tunneling splitting of the A level of the rigid rotor in the water dimer (left) results from permutations between the stable configurations shown at the lower right.

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... 

Although the value of A = 17.2 keV is small (it corresponds to a mo-ment of inertia of about 90 % of the rigid rotor value) it is not unexpected, since a value of A = 18.0 keV has been deduced for the ground state band of the odd-mass neighbour A = 99. If K = 1 or K = 3 were used for the fit with the classical rotational formula then values of A 27 keV and 12 keV would result which are not compatible with the knowledge about other nuclei in this mass region. Hence, K = 2 is proposed for the band in 98Y. 

The reliability of the newly-developed rigid-rotor potential was tested by means of close-coupling calculations of rotational state-to-state integral cross sections. The MOLSCAT code was used [66]. The results were compared with those obtained using the semiempirical potential of Buck, and with the available experimental data. 

This is an important result. It tells us that the total angular momentum determined in the laboratory frame is the sum of a centre-of-mass contribution and the total angular momentum tiJ measured in the centre-of-mass frame. In a rigid rotor the velocity vector of the kW particle in the centre-of-mass frame is related to the angular velocity, u>, of the rotating particle by... 

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