Cooperative Optical Transitions in the Oxygen Dimer: Excimer States, Selection Rules, and Oscillator Strengths

An alternative and approximate method is used to compute the dipole intensity of the cooperative optical transition in an oxygen molecular dimer, O₄. This approximation attributes the interaction of the two oxygen molecules to the overlap of their valence electrons and constructs the composite molecular states of the dimer by permuting all four π_g valence electrons (two from each molecule) in a Slater determinant. The overall symmetry of the possible composite, dimeric and exciton states is determined for different collision geometry belonging to D∞_h, $C_{\text{2v}}^x{\mathrm{,\hspace{0.17em}C}}_{\text{2h}}^y{\mathrm{,\hspace{0.17em}C}}_{\text{2v}}^z$ , D_2h, $C_3^{\mathrm{yz}}$ , C₂, $C_3^{\mathrm{xz}}$ , and S₄ point groups. The polarization of the transition is determined from these overall symmetries of the dimer. The transition matrix elements of the dimer are weighted by overlap integrals and are expressed in terms of the angles between the two molecules. This is in contrast to the conventional method which gives transition matrix elements weighted by electrostatic matrix element divided by an energy factor. The latter conventional method mixes in allowed states by intermolecular electrostatic interaction plus electron exchange. The present computation provides an expedient way of giving the relative contribution to intensity of the various orientations and geometries of the collision complex. The present formalism may be used in the cooperative optical transitions of the dimers of other homopolar diatomic molecules. The group theoretical analysis of the excimer states will be useful in the study of molecular crystals of linear molecules in various lattice geometries, in polarization studies and in the nonadiabatic vibronic energy transfer and chemical reactions between two linear molecules.