Infrared band intensities: a comparative study of the transition moment matrix elements for fundamentals and overtones: Part I. General

A complete survey of the various expressions reported by different authors for transition moment matrix elements for infrared transitions of diatomic molecules has been made. The different expressions for fundamentals and overtones are presented in uniform coordinates. Although the expressions look different when compared in their original forms it is found that with the uniform coordinates, several of them are similar in the first few terms. Expressions obtained from the consideration of Morse potential as well as those obtained from inclusion of anharmonic potential are discussed. From the various expressions presented in uniform coordinates general remarks about the effects of inclusion of mechanical and electrical anharmonicity on the intensities of the fundamental and first two overtones are made. Since the effects of inclusion of mechanical and electrical anharmonicity are opposite in sign for the first overtone, it is further discussed that an increase in the intensity of the fundamental band on hydrogen bonding and a slight weakening of the intensity of the first overtone or no change in its intensity can be explained on the basis of an increase in the first and second derivatives of dipole moments on hydrogen bonding. Some general remarks are made regarding the dipole expansions and intensity expressions for polyatomic molecules