The Rotation of Unsymmetrical-top Molecules

1 The hypergeometric function is discussed in Whittaker and Watson, Modern Analysis, Chap. XIV. 

Inasmuch as the known solutions of the wave equation for a symmetrical-top molecule form a complete set of orthogonal functions (discussed in the preceding section), we can expand the wave function p in terms of them, writing 

On substituting this expression in the wave equation 36-15, we obtain the equation 

1 The same result follows from the observation that J and M correspond to the total angular momentum of the system and its component along a fixed axis in space (see Sec. 52, Chap. XV). 

These values of W are then the allowed values for the rotational energy of the unsymmetrical-top molecule. Wang has evaluated the integrals Hue and shown that the secular equation can be further simplified. The application in the interpretation of the rotational fine structure of spectra has been carried out in several cases, including water, hydrogen sulfide, and formaldehyde.4 

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