Asymmetric rotor molecules

Although these molecules form much the largest group we shall take up the smallest space in considering their rotational spectra. The reason for this is that there are no closed formulae for their rotational term values. Instead, these term values can be determined accurately only by a matrix diagonalization for each value of J, which remains a good quantum number. The selection mle A/ = 0, 1 applies and the molecule must have a permanent dipole moment. 

At a simple level, the rotational transitions of near-symmetric rotors (see Equations 5.8 and 5.9) are easier to understand. For a prolate or oblate near-symmetric rotor the rotational term values are given, approximately, by 

2 ROTATIONAL INFRARED, MILLIMETRE WAVE AND MICROWAVE SPECTRA 

Dipole moments of asymmetric rotors or, strictly, their components along the various inertial axes, may be determined using the Stark effect. 

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Linear, symmetric rotor, spherical rotor and asymmetric rotor molecules... 

In, for example, the planar asymmetric rotor molecule formaldehyde, IT2CO, shown in Figure 5.1(f), it is possible by obtaining, say, and B in the zero-point level and in the V = 1 level of all six vibrations to determine and B. Two rotational constants are insufficient, however, to give the three structural parameters rg(CFI), rg(CO) and (ZFICFI)e necessary for a complete equilibrium structure. It is at this stage that the importance of... 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

Evaluation of the partition function in the general case of an asymmetric rotor molecule is rather tedious. However, for rigid diatomic or linear molecules characterized by the rotational constant B (in MHz), the partition function can be calculated by replacing the summation over the total quantum number J by an integral... 

Watson et al. [55] also described a procedure to take into account the axis rotation induced by isotopic substitution. Instead of three c parameters (one for each axis), six c parameters are necessary to correct the moments of inertia of a general asymmetric rotor molecule. 

The molecule behaves approximately as a T-shaped near-prolate asymmetric rotor molecule. Rem is the distance between Ar and the center of mass of CO and was determined from the ground state K = 0 rotational constant. 

Since asymmetric rotor molecules have three unequal moments of inertia, unless some symmetry can be found, the band contours for these tops are too complicated to permit any conclusions to be drawn concerning the structure of the molecule. 

Inversion doubling and intensity alternation can occur in the fine-line structure of asymmetric rotor molecules. If the fine lines of the bands were not perturbed or split, we should expect the interlinear spacing to be related to the three rotational constants of the molecule. Thus, for a C band of an asymmetric rotor in which the ratio of the two moments of inertia 7 /7 is nearly 1, the band would have the fine-line spacing 2A = 2B = 4C, where the three principal moments of inertia of the rotor are related so that A > B > C (7 < Ip < Iq) are the rotational constants. 

FIGURE 7 Rotational energy level diagram for H2CO, a typical asymmetric rotor molecule. The rotational quantum numbers J, K i, and K+i, along with the associated energy above the ground state, are indicated for each level. 

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