Cooperative optical phenomena. II. Spin-forbidden lifetime of the a 4Π state of nitric oxide

As an additional mechanism for the spin‐forbidden ${\mathrm{a\hspace{0.17em}}}^4{\mathrm{\Pi \; -x\hspace{0.17em}}}^2\Pi$ transition of nitric oxide, we consider the coupling of two nitric oxide molecules and the subsequent cooperative optical transition via a one‐photon, spin‐allowed, electric‐dipole mechanism. The feasibility of such a mechanism arises mainly through the exchange overlap of the orbitals. The coupled composite states of the dimer are constructed by projecting out the over‐all permutational symmetry (by antisymmetrization), the spin symmetry (by Clebsch‐Gordan vector coupling), and the point‐group symmetry of the dimer. For the point‐group symmetry, the state functions of the $D_{\mathrm{\infty \; h}}$ dimer are first constructed explicitly and are then combined upon descent in symmetry to give lower point‐group ($C_{\mathrm{\infty \; \nu }}$ , C_2ν, C_2h, C_s) state functions. The states obtained agree with the qualitative predictions of Kotani, Mulliken, and Herzberg, who did not give such explicit quantitative wavefunctions as we give. Exchange degeneracy between the ${}^4\Pi$ and ${}^2\Pi$ states in a dimer also gives rise to many new states not considered before. The oscillator strengths for the transition between the composite states are shown to give lifetimes comparable to experimental results, thus showing that this cooperative mechanism is as important as the conventional spin‐orbit interaction mechanism. The relationship between the intensities computed for a given geometry and the importance of such geometry in the dimer is discussed. Potential usefulness of the symmetry analysis and correlation with the composite (intermediate) state in chemical reactions is also discussed.