The Centrifugal Distortion of Axial Molecules

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Abstract
The theory of the semi‐rigid rotator developed by Wilson and Howard has been applied to the axial molecules YX3 and ZYX3. It is found that the change in rotational energy, δW, caused by the centrifugal distortion, can be expressed in terms of the quantum numbers J and K and as a function of the potential constants and the molecular dimensions. The formula is evaluated explicitly for NH3, and ND3, and for the former is, in cm—1: δW JK hC =−0.000625J 2 (J+1) 2 +0.000950K 2 J(J+1) +0.000799J(J+1)−0.000630K 4 −0.00189K 2 . The pure rotation lines of NH3 and of ND3 are calculated and compared with the observations of Wright and Randall, and of Barnes. The agreement is very satisfactory. The theory predicts that the rotation lines are multiple. The spacing of this fine structure was too small to be observable in the region mapped by Wright and Randall but should be possible to detect in the case of the higher members of the rotation series. We have also calculated the pure rotation spectrum of PH3 by using Howard's approximate values of the dimensions and force constants of this molecule. The agreement with experimental values is as good as could be expected from such rough data.