The upper electronic state of the 16O 3 molecule

Abstract

The main thing that we do in this paper is to predict the configuration of the ozone molecule in the excited electronic state associated with the Huggins' bands and to infer that the transition is 1A 1 → 1B 2 . First we observe that for the electronic ground state the known form of the kinetic energy operator together with the known molecular configuration alone produce a convergence of the levels of the ν 3 vibration which predicts a value of the third harmonic 3 ν 3 in very good agreement with the observed value of Wilson and Badger. To make the calculation we expand the entire Hamiltonian to second order and use a potential energy of the form kχ 2 2 . By using the known form of solution for the harmonic oscillator we obtain a formula for the energy which depends on k, but in which the coefficient, −11.234 cm −1, of the n 3 2 term depends only on the form of the kinetic energy operator and the equilibrium configuration and is independent of k. We determine k from the observed value of ν 3 (1043 cm −1). Jakowlewa and Kondratjew have proposed a formula for the Huggins' bands, which they interpret in terms of progressions of ν″ 1, ν′ 1, and ν′ 2 in the lower and upper state, respectively. However, the ground-state frequency is 1046 cm −1 in good agreement with the ν 3 fundamental, and moreover, the coefficient of ( n″) 2, 11.5 cm −1, agrees well with our calculated value. We give arguments for reinterpreting the progressions in the excited state as ν′ 3 and ν′ 2. We calculate the coefficient of ( n′ 3) 2 for several configurations and compare with the value in the empirical formula. The configuration, so found, has an apex angle of 90°36′, and a bond length of 1.383 Å, some-what larger than that of the ground state. This configuration has the same value of u as the ground state and we explain how this operates with the Franck-Condon principle to suppress the ν′ 1-mode. With this reinterpretation the transition is 1A 1 → 1B 2 as predicted by Walsh from electronic structure considerations. The transition is similar to one in SO 2 where the angle changes from the ground state value of 120° (116° ozone) to around 100° in the excited state. Thus we find a consistent picture which awaits the test of more extensive experimental work. Finally, we calculate, in the same manner as for the ground state, the effect of barrier penetration in the excited state.