Vibronic emissions and radiative lifetimes for a3Σ+, b3Π, c3Σ+, d3Δ, and e 3Σ– states of silicon monoxide. (December 2019) - Feng, Yanan; Zhu, Zunlue
Highlights: c 3 Σ + –a 3 Σ + and c 3 Σ + –b 3 Π transitions are strong. Lifetime is in the order of 10 −7  s for the c 3 Σ + state. b 3 Π–a 3 Σ +, d 3 Δ–b 3 Π, and e 3 Σ − –b 3 Π transitions are weak. Lifetime changes with the variation of j only over a small range. Lifetimes are 10 −1 –10 −4, 10 −2 –10 −4, and 10 −3 –10 −4  s for the b 3 Π, d 3 Δ, and e 3 Σ − states, respectively. Abstract: In this study, the potential energy curves of the a 3 Σ +, b 3 Π, c 3 Σ +, d 3 Δ, and e 3 Σ – states of the silicon monoxide are calculated and the transition dipole moments between them are computed using the complete active space self–consistent field, which is followed by the valence internally contracted multireference configuration interaction approach. The Davidson correction, core–valence correlation and scalar relativistic corrections are considered. The extrapolation of the potential energies to the complete basis set limit is included. The band origins, Einstein A coefficients, and Franck–Condon factors of all vibronic emissions between these five states are calculated. The rotationless radiative lifetimes are approximately 10 –1 to 10 –4  s for the b 3 Π state, 10 –2 to 10 –4  s for the d 3 Δ state, and 10 –3 to 10 –4  s for the e 3 Σ – state. The radiative lifetime quickly becomes shorter as the vibrational level increases for the three states. The lifetime is of the order of 100 ns for all vibrational levels of the c 3 Σ + state, indicating that the spontaneous vibronic emissions originating from this state occurs easily. Overall, the vibronic emissions of the b 3 Π – a 3 Σ +, d 3 Δ – b 3 Π, and e 3 Σ –  – b 3 Π systems are weak, suggesting that they are difficult to measure through spectroscopy. The vibronic emissions of the c 3 Σ +  – a 3 Σ + and c 3 Σ +  – b 3 Π systems are strong, indicating that they are easy to measure in a spectroscopy experiment. The radiative lifetime with the variation of rotational angular momentum quantum number is discussed briefly for υ ≤ 15 and J  ≤ 30 of the b 3 Π, c 3 Σ +, d 3 Δ, and e 3 Σ – states. The results indicate that the radiative lifetime changes only over a small range for each triplet state. The transition properties calculated in this study can be used to explain why only a few experimental transition properties are currently available for these triplet states. Graphical abstract: The PECs of the a 3 Σ +, b 3 Π, c 3 Σ +, d 3 Δ, and e 3 Σ − states of SiO are calculated and the TDMs between them are computed. The radiative lifetimes are in the orders of 10 −1 to 10 −4  s for the b 3 Π state, 10 −2 to 10 −4  s for the d 3 Δ state, and 10 −3 to 10 −4  s for the e 3 Σ − state. respectively. The radiative lifetime is approximately 10 −7  s for the c 3 Σ + state, indicating that the vibronic emissions originated from this state occurs easily. Overall, the c 3 Σ +  – a 3 Σ + and c 3 Σ +  – b 3 Π transitions are strong, whereas the b 3 Π – a 3 Σ +, d 3 Δ – b 3 Π, and e 3 Σ −  – b 3 Π transitions are weak. The radiative lifetime varying as the rotational angular momentum quantum number is discussed for υ ≤ 15 and J  ≤ 30 of the b 3 Π, c 3 Σ +, d 3 Δ, and e 3 Σ − states. The results indicate that the radiative lifetime changes only over a small range for each triplet state. Image, graphical abstract