Structural parameters from rotational spectrum

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

The study of the rotation-vibration spectra of polyatomic molecules in the gas phase can provide extensive information about the molecular structure, the force field and vibration-rotation interaction parameters. Such IR-spectra are sources of rotational information, in particular for molecules with no permanent dipole moment, since for these cases a pure rotational spectrum does not exist. Vibrational frequencies from gas phase spectra are desirable, because the molecular force field is not affected by intermolecular interactions. Besides, valuable support for the assignment of vibrational transitions can be obtained from the rotational fine structure of the vibrational bands. Even spectra recorded with medium resolution can contain a wealth of information hot bands , for instance, provide insight into the anharmonicity of vibrational potentials. Spectral contributions of isotopic molecules, certainly dependent on their abundance, may also be resolved. 

The principal application of the Kraitchman equations [Eq. (9)1 is for the determination of the atomic coordinates, at, bSi and cs. From a study of the rotational spectrum of the parent and of a species with single isotopic substitution the coordinates of the substituted atom may be determined. These coordinates are referred to as substitution coordinates or rs coordinates. Each new species yields new coordinates, and since all of the coordinates are in the same coordinate system, the calculation of substitution or rs bond distances and bond angles is a simple process. Costain,s demonstrated that there are definite advantages to the use of the Kraitchman equations to obtain molecular parameters. These advantages are sufficient to make the use of Kraitchman s equations the preferred method of structure determination from ground-state rotational constants. 

Structural parameters and interatomic distances derived from electron diffraction <77JST(42)121> and x-ray diffraction studies <76AX(B)3178> were given in CHEC-I. The molecular structure of pyrazine has been determined by combined analyses of data obtained by gas-phase electron diffraction (ED) and liquid-crystal NMR (LCNMR) <88JA2758>. The NMR spectrum gives structural information because the solute is partially oriented in the liquid-crystal solvent. The structural parameters determined from the ED, LCNMR data and in a joint analysis of both are listed in Table 2. There the C—C bonded distance is fixed since LCNMR data give no information on the absolute size of the molecule. Since pyrazine itself has no dipole moment, it should not show a microwave (pure rotation) spectrum. 

Since the symmetric top selection rules are A7 = 1, AK = 0, absorptive transitions will be observed from state J — 1, KM> to states JKMy and JKM + 1>, occurring at frequencies 2BJ according to Eq. 5.25. Hence, the microwave spectrum of NF3 yields no measurement of the rotational constant C. Since two structural parameters (/ and 0) enter in the rotational moment a... 

Because of the selection rule AK = 0, the rotational constant about the symmetry axis, A (C for an oblate top), cannot be evaluated from the rotational spectrum of a symmetric top. This selection rule follows because there is no dipole moment component perpendicular to the symmetry axis, and applies rigorously for a rigid molecule. Recent theoretical developments have shown that actually a very small dipole moment perpendicular to the symmetry axis can be induced through the effects of centrifugal distortion. This lifts the A AT = 0 selection rule and allows the observation of AK = 3, 6,... transitions with a sensitive spectrometer. This has enabled the structures of pyramidal XY3 molecules, which have only two structural parameters (see Table II), to be evaluated directly from and h without the need for isotopic information. The observation of so-called forbidden transitions often results... 

As can be seen from the above, the shape of the resolved rotational structure is well described when the parameters of the fitting law were chosen from the best fit to experiment. The values of estimated from the rotational width of the collapsed Q-branch qZE. Therefore the models giving the same high-density limits. One may hope to discriminate between them only in the intermediate range of densities where the spectrum is unresolved but has not yet collapsed. The spectral shape in this range may be calculated only numerically from Eq. (4.86) with impact operator Tj, linear in n. Of course, it implies that binary theory is still valid and that vibrational dephasing is not yet... 

---