Ab initio calculations of the spectra and lifetimes of the lead dimer

Abstract

Owing to the key role of the lead dimer (Pb₂) as a heavy element benchmark for the Group IV-A dimers the assignment of its spectroscopic properties and chemical bonding is an important undertaking. To meet this demand, the present work provides comprehensive and detailed information on electronic structure and properties comprising a wide set of Pb₂ states. Calculations are performed by a high-level ab initio approach. Firstly, the potential energy curves (PECs) of 19 Λ–S states as well as those of 24 ungerade Ω states are calculated by utilizing the multi-reference configuration interaction plus Davidson correction (MRCI + Q) method taking into account core–valence correlation (CV) and spin–orbit coupling (SOC) effect, where Ω is a quantum number of the total (Λ + S) angular momentum projection. Secondly, interactions between the bound F³Σ⁻_u, 2³Σ⁺_u states and repulsive 1⁵Π_u state induced by strong SOC are discussed based on the PECs analysis and calculated SOC matrix, which also indicates that the F³Σ⁻_u state is predissociative. Thirdly, based on the calculated electric dipole transition moments and energy gaps between the 0⁺_u(III), F0⁺_u(II), C0⁺_u(I) and X0⁺_g states, the intense absorption bands of Pb₂ due to these transitions are interpreted. Our results indicate that the trends in intensity of absorption spectra (F0⁺_u(II), C0⁺_u(I) ← X0⁺_g) in the range of 12 600–13 600 and 22 200–23 800 cm⁻¹ are consistent with the previously observed spectra of Pb₂ in the qualitatively similar regions (15 200–16 200 and 19 800–21 800 cm⁻¹). Finally, the calculated intensity of the weak magnetic-dipole transitions from the singlet excited b¹Σ⁺_g and a¹Δ_g states to the triplet ground X³Σ⁻_g state and their electric quadrupole components are presented for the Pb₂ molecule in terms of SOC perturbations for the calculated Ω states expressed in Λ–S state notation. Based on our theoretical assignment, we predict that the weak emission a¹Δ_g2 → X³Σ⁻_g1 bands could be observed experimentally. The present work provides comprehensive electronic structure information and sheds new light on the absorption and emission spectra of the Pb₂ dimer.