Rotation nonrigid corrections

For diatomic molecules, B0 is the rotational constant to use with equation (10.125), while Be applies to equation (10.124). They are related by Bq = Be 2 - The moment of inertia 70(kg-m2) is related to 50(cm ) through the relationship /0 = h/ 8 x 10 27r22 oc), with h and c expressed in SI units. For polyatomic molecules, /a, /b, and Iq are the moments of inertia to use with Table 10.4 where the rigid rotator approximation is assumed. For diatomic molecules, /0 is used with Table 10.4 to calculate values to which we add the anharmonicity and nonrigid rotator corrections. 

For diatomic molecules, lj0 is the vibrational constant to use with equation (10.125) for calculating anharmonicity and nonrigid rotator corrections, while J)e and tDe-Ve... 

Under most circumstances the equations given in Table 10.4 accurately calculate the thermodynamic properties of the ideal gas. The most serious approximations involve the replacement of the summation with an integral [equations (10.94) and (10.95)] in calculating the partition function for the rigid rotator, and the approximation that the rotational and vibrational partition functions for a gas can be represented by those for a rigid rotator and harmonic oscillator. In general, the errors introduced by these approximations are most serious for the diatomic molecule." Fortunately, it is for the diatomic molecule that corrections are most easily calculated. It is also for these molecules that spectroscopic information is often available to make the corrections for anharmonicity and nonrigid rotator effects. We will summarize the relationships... 

Anharmonicity and Nonrigid Rotator Corrections With the rigid rotator and harmonic oscillator approximations, the combined energy for rotation and... 

Ja Equations for obtaining anharmonieiiy and nonrigid rotator corrections are also summarized in Table A4.5 of Appendix 4. 

Table A4.5 summarizes the equations for calculating anharmonicity and nonrigid rotator corrections for diatomic molecules. These corrections are to be added to the thermodynamic properties calculated from the equations given in Table A4.1 (which assume harmonic oscillator and rigid rotator approximations).

Table A4.5 Anharmonic oscillator and nonrigid rotator corrections...

The following equations are used to calculate the anharmonicity and nonrigid rotator corrections to the thermodynamic properties of diatomic molecules. 

For diatomic molecules, corrections can be made for the assumption used in the derivation of the rotational partition function that the rotational energy levels are so closely spaced that they can be considered to be continuous. The equations to be used in making these corrections are given in Appendix 6. Also given are the equations to use in correcting for vibrational anharmonicity and nonrigid rotator effects. These corrections are usually small.22... 

Analyses of linear nonrigid rotators, anharmonic oscillators, and vibrating rotators, yielding first-order corrections for nonrigidity, anharmon-icity, and vibration-rotation interaction (nonseparability of vibrational and rotational modes), respectively, have also been completed and are conventionally used in obtaining corrections (which are most important at elevated temperatures) to the simple product form of the molecular partition... 

In a nonrigid rotating diatomic molecule, centrifugal distortion will elongate the bond as the rotational frequency increases. To accurately fit the energy levels, a correction term must be added to Eq. (1.55)... 

The same expressions have been obtained for diatomic molecules [see Eqs. (3.3.19) and (3.3.20)]. The molecule rotates around any axis perpendicular to the line through the nuclei and passing through the center of mass. As with a diatomic molecule, the nonrigid nature of the molecule requires a small correction term due to centrifugal distortion, DJ ( J + 1), to be subtracted from the right side of Eq. (3.4.9). 

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