Prolate top

In the symmetric top cases, Hrot can be expressed in terms of J2 and the angular momentum along the axis with the unique moment of inertia (denoted the a-axis for prolate tops and the c-axis of oblate tops) ... 

A=5.4+0.4GHz B+C=1445.2 0.5MHz of the per-deuterated acetic acid dimer (CD3COOD)2 were extracted. It was not possible to determine the rotational constants B and C independently due to the symmetric prolate top nature of the dimeric structure (Ray s asymmetry parameter k=-0.965). More detailed consideration of the fs DFWM spectra taken in the gas cell and in a supersonic expansion for the acetic acid dimer are under way in our laboratory and will be presented in a forthcoming publication. 

Fig. 53 Rotational levels for a prolate symmetric top with A =4.55 and for an oblate symmetric top with B=4.5C. Note the accidental degeneracy of the 7=2, Af 2, and 7=4, K =0 prolate-top levels.

FIGURE 2. Portion of H2CO spectra of the 2q4q transition (a) absorption spectrum with ordinate in absorbance unit (b) red HNO chemiluminescence excitation spectrum taken with the emission at 760 mm (1.0 torr H2CO/IO torr NO) (c) blue F CO fluorescence excitation spectrum taken from the emission at 380-500 mm (0.20 torr H2CO). The rotational subbranch assignment as a near prolate top is " with J" shown on top of the line the line for J"=ll of rR7 is not shown. (From ref. 237, Fig. 1). 

Before discussing the spherical rotor, it is appropriate to focus on the rotational energy levels for symmetric rotors (see also Tab. 4.3-2). For the rigid prolate top, the rotational energy is given by... 

A succession of levels like those of a linear molecule can be calculated for each quantum number K, which in this case describes the quantized component of the angular momentum about the unique a-axis. K cannot exceed 7, the quantum number for the total angular momentum, i.e., K = 0, 1,... dz7. For an oblate symmetric top the rotational constant A j has to be replaced by Q ]. In relation to the case of A" = 0, other K quantum numbers allowed will thus result in lower energies Ejk, which is in contrast to the prolate top with a positive term of (A[ j - 6 ]). Evidently, all rotational levels with 0 are doubly degenerate. It should be noted that each level still possesses an M-degeneracy of (27 -f 1) as discussed in connection with the linear molecule. This is due to space quantization. 

A -splitting of the lines in the branches. This is only minor as long as the difference between the rotational constants of the lower and the upper vibrational state is small. The infrared spectrum of CHyl (prolate top) shows examples of parallel band features with a PQR. structure like that for a linear molecule (.see Fig. 4.3-8). 

Equation (21) reduces to a simpler form for symmetric top and linear molecules, where for a prolate top, with the symmetry axis along a, we write... 

Figure 7.11 Parallel transitions in a /-resolved absorption. Note that the excited state is produced in a distribution of K levels and therefore in a distribution of internal energies. The example is for a prolate top in which the energy increases with K.

The rotational-orbital sum of states function ( ., J) depends upon the nature of the products, for example, two spheres, a sphere plus a prolate top, etc. Expressions for it and other rotational sums and densities will be given later. First we present the expressions for the product energy distributions. 

Symmetric Top, Ia - Iq (prolate top) or Ia=Ibrotational spectrum is still degenerate in the nij quantum number however, part of the k degeneracy is lift. Only those levels with k =0 are now doubly degenerate (in k). The rotational spectrom of symmetric top molecules (such as NH3, CgHg) can be written as... 

The aeeeptor switching splitting leads to a set of energy levels with symmetries Ai/Ei/Bi and another set of energy levels with A2/E2/B2. All transitions were fit to the foUowing rotational energy expressions appropriate for near prolate tops [03Keul] ... 

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