Determination of the Dipole Moment Function from Infrared Band Intensities of Diatomic Molecules

A discussion is given of the relations which exist among vibrational matrix elements for diatomic molecules represented as Morse oscillators. This is done according to the wave function approximation of Trischka and Salwen. It is shown how the matrix element of the dipole moment ${\mathfrak{M}}_v^{i^{\prime }}$ is related to the matrix elements ${\mathfrak{M}}_0^i$ where v′—v≤i≤v′+v with v′>v. This relation is examined for the case of the 1–2 band of HCl. It is also shown how the matrix element ${\mathfrak{M}}_0^1$ for DCl can be related to the matrix elements of HCl. Finally, the influence of the vibration‐rotation interaction is incorporated in the wave function approximation. In an example, it is shown that the matrix element $\{{\mathfrak{M}}_{\text{0,J}}^{\text{i,J+1}}$ can be expressed in terms of the set of matrix elements$\{{\mathfrak{M}}_{\text{0,0}}^{\text{i,1}}\text{},i=0,1,···}$ .