The Structure of Electronic Bands of Polyatomic Molecules. I. Prolate Approximation for XY2Molecules

Abstract

A study has been made of the rotational structure of electronic bands of polyatomic molecules whose moments of inertia are related approximately like those of a symmetrical top, with the object of facilitating the interpretation of observed (resolved or unresolved) structures. The present discussion concerns non-linear X${\mathrm{Y}}_2$ molecules, but it is also valid for all polyatomic molecules that come approximately under the prolate symmetrical top classification. The four characteristic cases of changes in dimensions during the electronic transition are considered and yield four typically different band structures. The variation in band structure with bond distance and apex angle is worked out in detail for S${\mathrm{O}}_2$ molecules and theoretical quantitative diagrams of band structures are given, for a temperature of 200°K. The intensity distributions shown in these diagrams are valid (for some adjusted temperature) for any polyatomic molecules in which the moments of inertia of the ground state have the same ratio as those in S${\mathrm{O}}_2$. If, in addition, the same is true of the moments of inertia in the upper states, then the entire band structure is identical at some adjusted scale. The correlation between rotational structure and vibrational intensity distribution is worked out, from which conclusions about the changes in dimensions of the X${\mathrm{Y}}_2$ molecule in the transition can be made. It is shown how a qualitative examination of the observed (resolved or unresolved) rotational structure may guide or confirm the associated vibrational analysis. Finally a comparison with the available data on S${\mathrm{O}}_2$ and Cl${\mathrm{O}}_2$ is made.