Morse Oscillator Matrix Elements for HI Vibration—Rotation Lines

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Abstract
The treatment developed by Herman and Rubin for the calculation of the vibration—rotation matrix elements of the individual lines of a Morse oscillator whose electric dipole-moment function is expressed as a power series has been put into a form suitable for electronic computation. Calculations have been carried out for all of the hydrogen halides, and the results for hydrogen iodide are reported here in detail. Comparison with matrix elements obtained from experimental infrared line intensities indicates that the dipole-moment function coefficients for HI (taking M0=0.42 D) are M1= —0.51×10—11 esu and M2=0.16×10—2 esu/cm. The value for M2 is based primarily on the data of the overtone band from which an accurate determination of M2 is made possible by the accidental weakness of the M1 contribution. The J dependence of the matrix elements provided by the present calculation is qualitatively correct but not sufficiently strong to follow the trend of the data into the wings of the band. The neglect of higher-order terms in the expansion of the centrifugal stretching term is presumably responsible for this sluggish behavior of the calculated matrix elements at high values of J.