Symmetric top molecules

In a symmetric top molecule such as NH3, if the transition dipole lies along the molecule s symmetry axis, only k = 0 contributes. Such vibrations preserve the molecule s symmetry relative to this symmetry axis (e.g. the totally symmetric N-H stretching mode in NH3). The additional selection rule AK = 0... 

St. Pierre A. G., Steele W. A. Collisional effects upon rotational correlations of symmetrical top molecules. J. Chem. Phys. 57, 4638-48 (1972). 

Although the hypergeometric functions are useful in spectroscopy, as they describe the rotation of a symmetric top molecule (Section 9.2.4), their importance is primarily due to their generality. If, for example, a = 1 and fi say, Eq. (154) becomes a +i — a for all values of n. The result is the ordinary geometric series... 

Recent experiments11 have shown that for symmetric top molecules, such as methyl chloride, electron impact ionization is more probable at the positive end of the dipole. This follows intuitively from simple electrostatics, since it would be expected that an electron should be more strongly attracted to the positive end of the dipole, leading to a greater ionization probability at this end of the molecule. The effect may be quantified in terms of a steric ratio R. 

A small step rotational diffusion model has been used to describe molecular rotations (MR) of rigid molecules in the presence of a potential of mean torque.118 120,151 t0 calculate the orientation correlation functions, the rotational diffusion equation must be solved to give the conditional probability for the molecule in a certain orientation at time t given that it has a different orientation at t = 0, and the equilibrium probability for finding the molecule with a certain orientation. These orientation correlation functions were found as a sum of decaying exponentials.120 In the notation of Tarroni and Zannoni,123 the spectral denisities (m = 0, 1, 2) for a deuteron fixed on a reorienting symmetric top molecule are ... 

Sell rod I tiger s equation for the rotation or a symmetrical-top molecule is... 

Hougen, J. T. (1962), Classification of Rotational Energy Levels for Symmetric-Top Molecules, 7. Chem. Phys. 37, 1433. 

Molecules for which two of the three principal moments of inertia are equal are called symmetric top molecules. Prolate symmetric tops have Ia < lb = Ic oblate symmetric tops have Ia = lb < Ic (it is convention to order the moments of inertia as Ia < lb < Ic ) ... 

Symmetric tops with no dipole moment have no microwave spectrum. For example, planar symmetric-top molecules have a C axis and a ak symmetry plane such molecules cannot have a dipole moment. Thus benzene has no microwave spectrum. For a symmetric top with a permanent electric dipole moment, the selection rules for pure-rotation transitions are... 

Finally, we should note that a number of formulas for anharmonic constants and vibration-rotation interaction constants for symmetric-top molecules given in the spectroscopic literature are incomplete. The problem is that relatively few complete anharmonic analyses have been carried out, and the available examples are not adequate to cover all combinations of degenerate and nondegenerate modes. A detailed discussion is given by Lee and co-workers [35]. 

When the overall motion is not isotropic, the diagonal elements of the rotational diffusion tensor are no longer equivalent and rotation about the three principal axes of the diffusion tensor may be described by different diffusion coefficients or correlation times. For anisotropic motion, the correlation time in Eqs. 16 and 25 is an effective correlation time, r ff, containing contributions from the various modes of reorientation. Partitioning of the various components of rff can be achieved through appropriate dynamic models. The simplest case of anisotropic motion is that for a symmetric-top molecule. The r ff of a rigid ellipsoid is expressed in terms of two parameters, Dn and DL these two parameters respectively describe the rotational diffusion about the C3 symmetry axis (major axis) and the two perpendicular axes (minor axes), which are assumed to be equivalent25-44 (Fig. 4) ... 

Fig. 1.4. Rotational motion and moments of inertia in symmetric top molecules (of the type of CH3F or its halogensubstitutes).

The above results may be extended to electronic transitions in the case of symmetric top molecules [156, 374, 402], where, in molecule-fixed coordinates, the rotational state of the molecule is characterized by two values, namely the modulus (J) of the total angular momentum, and the projection (K) of the momentum J on the symmetry axis of the molecule (the x-axis see Fig. 1.4). In the case of an electronic transition where... 

For polar polyatomic molecules one has to ascertain the orientation of molecular symmetry axes (x-axis in Fig. 1.4 for a symmetric top molecule). As was established by Novakoski and McClelland [299] it is more likely for a CF3H molecule to desorb from an Ag(lll) surface with the F end of the symmetry axes pointing directly away from the surface, and a degree of orientation of 0.27 (averaged value of (cos )) was observed. 

Fig. 6.5. (a) Angular momentum orientation via beam deflection in a magnetic field. (6) Figure axis orientation for symmetric top molecules via beam deflection in an electric field, (c) Figure axis orientation in hexapole focussing field. 

---