Herman-Wallis factor

Thus with the operator (2.128), the Herman-Wallis factors are... 

One may recognize that, in the limit of large N, one recovers the Herman-Wallis factors for the harmonic limit Rv v = const, Fv v(m) = 1. 

From Eq. (2.141) one obtains the Herman-Wallis factor for the operator (2.140), in the large-A limit,... 

This leads to the most general expansion for the Herman-Wallis factor... 

The rotational Herman-Wallis factor Fv< v(m) of the operator (2.140) is still that of a rigid rotor. In order to describe rotational-vibrational interactions, one must introduce explicitly the angular momentum J. To lowest order, the dipole operator that includes rotational-vibrational interactions is... 

Figure 2.9 Herman-Wallis factors observed in HC1 (dots) and compared with Eq. (2.145) (dotted lines) adapted from Iachello, Leviatan, and Mengoni (1991).

From Eqs. (2.149) one can see that the rotational Herman-Wallis factor is linear in m when v v, and quadratic in m when v = v. An example is shown in Figure 2.10. 

Picque et al. [OOPic] have measured relative intensities in the 1-0, 2-1, 3-2, and 4-3 vibration-rotation bands between 1800 and 2830 cm using FTS in a discharge tube. The Herman-Wallis factors and in turn the absolute values of the vibrational transition moments could be determined without knowing the ionic concentrations. The results are, relative to the permanent dipole moment po = 1.42(4) D [87Lau]... 

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