Response theory calculations of singlet-triplet transitions in molecular nitrogen

Abstract

Abstract The probabilities and energetics of singlet-triplet absorption transitions in molecular nitrogen from the ground X 1 Σ g + state to all triplet states of ungerade symmetry in the range up to 13 eV, the A 3 Σ u + , W 3 Δ u , B ′ 3 Σ u − , C 3 Π u , C ′ 3 Π u , and D 3 Σ u + states, have been studied by multi-configuration quadratic response theory with complete account of spin-orbit coupling (SOC) perturbation. The vibrational Schrodinger equation has been solved for all states with the theoretical and RKR (where these are available) potentials, and vibrational averaged transition probabilities have been calculated and compared with experimental data for absorption from the lowest ν″ = 0 ground state to different ν′ vibronic upper-state levels. The Vegard-Kaplan (A3Σu+−X1Σg+) and the Ogawa-Tanaka-Wilkinson (B′3Σu−−X1Σg+) band intensities were calculated also in emission (ν′→ν″). Different types of correlating active spaces have been explored for the reference ground state. Although the use of single reference self-consistent field wavefunctions in the lowest level of response calculations (random phase approximation) in general is not sufficient, it is found that quite moderate complete active space (CAS) expansions of the valence orbitals lead to good transition probabilities and energies for the excited triplet states. Even the smallest active space gives a spin-averaged radiative lifetime of the Vegard-Kaplan phosphorescence band only twice as large as the experimental value (5.84 versus 2.4 s). The transition moment curves for the Vegard-Kaplan (A3Σu+) and for the Saum-Benesch (W3Δu) bands are quite similar, both changing sign in the region of the ground state internuclear equilibrium distance. The B′3Σu−−X1Σg+ Ogawa-Tanaka-Wilkinson system (B′ ← X) is predicted to be much more intensive (f = 1.6 × 10−8 for the most intensive vibronic bands (ν′=7–9)) than the A-X and W-X transitions, and the ratio of transition moments for the Ω=1 and Ω=0 sublevels has been qualitatively reproduced. The Tanaka band (the C3Πu ← X1Σg+ transition) is calculated as the most intensive singlet-triplet transition with an oscillator strength (f = 1.1 × 10−7) which is comparable with the spin-allowed, orbitally forbidden absorption in the Lyman-Birge-Hopfield band in the same wavelength region (105–112 nm). The highest in energy of the investigated states, the D3Σu+ state, has Rydberg character in the vicinity of re and is strongly mixed by SOC with Rydberg and valence 1Πu states. The calculated intensity of the D3Σu+−X1Σg+ transition as well as the hot nitrogen absorption C′3Πu ← X1Σg+ could be somewhat overestimated because of unrealistic S-T crossings. The relative vibronic transition intensities are well reproduced for a large variety of transitions for which experimental data are available.