Theoretical study of the intensity of the spin- or dipole forbidden transitions between the c ¹∑⁻ u , A′ ³Δ u , A ³∑⁺ u and X ³∑⁻ g , a ¹Δ g , b ¹∑⁺ g states in O₂

The transition moments between the three lowest gerade X 3∑- g , a 1Δ g and b 1∑+ g and ungerade states c 1∑- u , A′ 3Δ u and A 3∑+ u of the oxygen molecule have been calculated as a function of internuclear separation from 2·1 a.u. to 3·5 a.u. The wavefunctions have thereby been expanded in a perturbation sum whereby the individual terms are large-scale MRD-CI wavefunctions and the expansion coefficients are the spin-orbit coupling coefficients obtained by using the Breit-Pauli one- and two-particle operator. A total of 18 states has been considered in the perturbation expansions; the corresponding potential energy curves are also given for all states. The AO basis set was of double-zeta plus polarization and Rydberg quality and involves a total of 56 contracted gaussians. The absorption oscillator strengths are also determined; the predicted values are 0·06 × 10-7 for c 1∑- u — X 3∑- g , 0·32 × 10-7 for A′ 3Δ u (Ω = ± 1) — X 3∑- g and 1·6 × 10-7 calculated for the strongest A 3∑+ u — X 3∑- g transition, whereby the latter is in excellent agreement with the measured value of 1 × 10-7. The radiative lifetimes for the upper three ungerade states are calculated to be 6 s for c 1∑- u , 1 s for A′ 3Δ u and 0·07s for the A 3∑+ u state. A vibrational analysis of the various emission systems c 1∑- u — X 3∑- q (Herzberg II), A′ 3Δ u — X 3∑- g (Herzberg III), A′ 3Δ u — a 1Δ g (Chamberlain) and A 3∑+ u — X 3∑- g (Herzberg I system) is also undertaken and the most likely transition mechanisms are analysed. The strongest Herzberg I system borrows its intensity from the Schumann-Runge (B 3∑- u — X 3∑- g ) system since the B state occurs as perturber in the A 3∑+ u wavefunction.