Line strengths, line widths, and dipole moment function for HCl

Previous expressions for the dipole moment matrix elements of the vibration-rotation bands of diatomic molecules, based on a quintic anharmonic oscillator potential, a cubic dipole moment function, and third order perturbation theory, are extended for the 1-0 and 2-0 bands to include second-order contributions. Line intensities in the 1-0 band of HCl are measured with 0.02 cm ^-1 resolution and analyzed to obtain a band intensity S ₀¹ of 135 cm ^-2 atm ^-1 at 300°K and the following Herman-Wallis factor: F ₀¹(m) = 1 - 0.0260 m + 4.5 × 10 ^-4m ². Similar measurements are made in the 2-0 band of HCl with 0.04 cm ^-1 resolution and yield S ₀² = 3.73 cm ^-2 atm ^-1 and F ₀²(m) = 1 - 0.0086 m + 4.1 × 10 ^-4m ². These results and the previous 3-0 band intensity data are incorporated with the dipole moment matrix elements above to obtain the following dipole moment function for HCl: M( r) = 1.095 + 0.905( r - r_e) - 0.066( r - r_e) ² - 0.73( r - r_e) ³, where r - r_e is in angstroms and M( r) is in Debyes. The half-widths of self-broadened lines of HCl in the 2-0 band are measured directly. The results are somewhat lower than previous measurements for | m| < 8. Previous results for the dipole moment function of HCl are discussed as is the importance of second-order contributions to the dipole moment matrix elements. It is pointed out that the Morse oscillator results for HCl for a quadratic dipole moment agree reasonably well with those of the anharmonic oscillator.