Vibration-rotational matrix elements for infrared transitions of diatomic molecules

Theoretical expressions for the vibro-rotational matrix elements corresponding to i.r. transitions vJ→v′J′ with v ⩽ v ′ ⩽ v + 6 are obtained in terms of quadratic polynomials in m, including contributions from the Dunham potential energy parameters a₁ to a₅ and from dipole-moment expansion coefficients M₀ to M₇. The formalism has been applied to vibrational transitions in the ground electronic state of CO and HCl. The Herman-Wallis coefficients have been derived for the bands 0-0 to 0-4 of CO and 0-0 to 0-6 of HCl and are compared with experimental data.