Dipole Moment Function and Vibration—Rotation Matrix Elements for CO

Electric dipole matrix elements for vibration—rotation transitions in CO have been calculated using a computer program developed by Cooley for the solution of the radial Schrödinger equation. By means of this program four possible cubic dipole moment functions M(r) for CO were obtained from room‐temperature measurements of the integrated intensities of the fundamental and first two overtone infrared bands. Relative measurements of rotational line intensities in the overtone bands indicate clearly that the most linear of these four functions is the correct one: ${\text{M(r)=±0.112+3.11(r−r}}_e{\text{)−0.15(r−r}}_e{)}^2{\text{−2.36(r−r}}_e{)}^3\mathrm{D}$ . (The internuclear separation r and its equilibrium value, r_e, are in angstroms.) Using this expression we find in the case of the overtone bands that there is an appreciable deviation of the vibrational matrix elements from the usual binomial expression, and that the matrix elements have a significant rotational dependence.