Section: 9 | Hindered Internal Rotation |
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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
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I. Ozier and N. Moazzen-Ahmadi

In asymmetric rotors such as methyl alcohol, CH3OH, and symmetric rotors such as CH3SiH3, the methyl group can undergo internal rotation relative to the rest of the molecule, traditionally called the frame (Refs. 1 and 2). Although various rotating groups are considered here, all have three-fold symmetry. In such cases, the potential V hindering the internal rotation can be written:

V(α)= V3(½)(1 – cos3α) + V6(½)(1 – cos6α) + V9(½)(1 – cos9α) + ...,

where α is the deviation from equilibrium of the angle between the top and frame that measures the torsional motion. If only the first two terms are retained, then V3 is the height of the hindering potential and V6 is the shape parameter. For symmetric tops such CH3CH3 where the top and frame are identical, α is replaced by and the origin for γ is often taken as the eclipsed configuration. In the expansion, –cos6 is then replaced by (–1)n+1cos6, where n = 1,2,... In cases where different forms of the expansion have been used in the original works, the values of the parameters published there have been converted to the conventions defined here.

In Tables 1 and 2, values are given for V3 for a selection of asymmetric and symmetric rotors, respectively. Column definitions for Tables 1 and 2 are as follows.

Column heading Definition
Mol. form. Molecular formula; molecules are listed alphabetically in Hill order according to the molecular formula 
Name Name of molecule
Line formula Formula written in terms of connectivity
Ref. Reference number
V3 Magnitude of hindering potential, in cm-1 (wavenumbers)
Comments Additional information as appropriate including V6 (shape potential), V9 isomer, state, and/or isotopomer

For ethane, three symmetric top isotopomers are listed to illustrate the isotopic dependence of V3 and V6. In all other cases, only one isotopomer is listed, even if several have been studied. In all but one of these cases, the isotopomer reported is the one with the highest natural abundance. However, CH3OCDO is listed because the results obtained are more precise than for CH3OCHO. 

The determinations listed for the potential parameters are effective values that incorporate to varying degrees effects from other molecular parameters. For example, the apparent value of V3 can be changed significantly if the reduced rotational constant F is calculated from the structure, rather than being determined independently (Ref. 1). Other examples include such mechanisms as coupling to excited skeletal vibrations (Ref. 2) and redundancies connecting some of the torsional parameters (Refs. 3 and 4). The experimental uncertainties quoted are taken from the original works; no attempt has been made to standardize the definitions. All the potential parameters are given in cm–1. Where the original work has reported these values in other units, the conversion to cm–1 has been carried out using standard factors: 1 calorie = 4.1868 joules and 1 calorie/mole = 0.34998915 cm–1 (Ref. 5).

A variety of different methods have been used to measure V3, V6, and V9 (Refs. 1 and 2); only a few of the more important will be discussed here. For asymmetric rotors, both the pure rotational spectrum and its torsion-rotation counterpart are electric dipole allowed and are affected in lowest order by the leading terms in the torsional Hamiltonian. Both types of spectra have been used extensively to determine V3 (Ref. 1). For symmetric tops with a single torsional degree of freedom, either the permanent electric dipole moment vanishes, as in CH3CH3, or the normal rotational spectrum is independent of V3 in lowest order, as in CH3SiH3. In the latter case, the molecular beam avoided crossing method can often be used (Ref. 2). The torsion-rotation spectrum is forbidden in lowest order but becomes weakly allowed through interactions with the infrared active skeletal vibrations (Ref. 2). By employing long absorption path lengths, this spectrum has been used to determine V3 in a number of molecules. For both asymmetric and symmetric tops, the most precise determinations of the molecular parameters have been made in cases where both rotational and torsion-rotation spectra have been investigated.


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TABLE 1. Asymmetric Rotor Potential Parameters

Mol. form.NameLine formulaRef.V3/cm–1Comments
Continued on next page...
CHF3STrifluoromethanethiolCF3SH5500.83 ± 0.03
CH3F2OPMethylphosphonic difluorideCH3P(=O)F26676 ± 25
CH4OMethanolCH3OH5373.594 ± 0.007V6 = –1.597 ± 0.051; V9 = 1.04 ± 0.20
CH4SMethanethiolCH3SH7443.029 ± 0.070V6 = –1.6451 ± 0.0144
CH4S2MethyldisulfaneCH3SSH8609.0 ± 14.0
C2F3NOTrifluoromethyl isocyanateCF3N=C=O547.8769 ± 0.0051
C2HF3OTrifluoroacetaldehydeCF3C(H)=O9298 ± 10
C2HF5PentafluoroethaneCF3CHF2101190 ± 4
C2H3BrOAcetyl bromideCH3C(Br)=O11456.7 ± 10.5
C2H3ClF21-Chloro-1,1-difluoroethaneCH3CClF2121311.8 ± 1.4
C2H3ClOAcetyl chlorideCH3C(Cl)=O5442.74 ± 1.0535Cl
C2H3FOAcetyl fluorideCH3C(F)=O13364.3 ± 2.1
C2H3FO2Methyl fluoroformateCH3OC(F)=O5374.1 ± 0.2
C2H3F3OMethyl trifluoromethyl etherCH3OCF35382 ± 10CH3
C2H3IOAcetyl iodideCH3C(=O)I14455.3 ± 10.5
C2H3NOMethyl cyanateCH3OC≡N5399.0 ± 17.5
C2H4ClF1-Chloro-1-fluoroethaneCH3CHClF51334.9 ± 3.8
C2H4F21,1-DifluoroethaneCH3CHF251163.0 ± 2.5
C2H4OAcetaldehydeCH3C(H)=O15407.716 ± 0.010V6 = –12.068 ± 0.037

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