Geometry of Condon Loci of Molecular Spectra

Abstract

IT is well known that if the positions of the most intense (v′, v″) bands of a diatomic molecular spectrum are indicated on the usual Deslandres diagram the axes of which are the upper (v′) and the lower (v″) quantum numbers involved, then the set of points (v′, v″) so plotted trace out a set of nested, open-limbed curves called the primary and subsidiary Condon loci, some aspects of the geometry of which have been previously discussed^1,2. In particular, it was suggested² that the position of the primary locus could be predicted from a consideration of those vibrational wave functions for which two respective antinodes are located at the same internuclear separation r. It was further suggested that the subsidiary loci could be located from a similar consideration of those wave functions for which one primary antinode and one appropriate subsidiary antinode, respectively, lie at the same value of r. These criteria ensure significant overlap between the two wave functions and thus a relatively large value of the Franck–Condon factor (square of the vibrational wave function overlap integral) which controls all transition probability and intensity parameters of the band.