Spin-orbit coupling and vibronic transitions of two Ce(C₄H₆) isomers probed by mass-analyzed threshold ionization and relativistic quantum computation

Ce atom reactions with ethylene, 2-butene, and isobutene are carried out in a pulsed laser vaporization molecule beam source. Ce-containing species are observed with time-of-flight mass spectrometry, and Ce(C₄H₆) is characterized with mass-analyzed threshold ionization (MATI) spectroscopy and relativistic quantum chemical calculations. Two structural isomers are identified for Ce(C₄H₆): one is the tetrahedronlike Ce[C(CH₂)₃] in C_3v symmetry and the other is the five-membered metallocyclic Ce(CH₂CHCHCH₂) in C_s. The MATI spectrum of the C_3v isomer exhibits two vibronic band systems separated by 88 cm^-1, while that of the C_s isomer displays three split by 60 and 101 cm^-1. The multiple band systems are attributed to spin-orbit splitting and vibronic transitions involving metal-hydrocarbon and hydrocarbon-based vibrations. The splitting in the C_3v isomer arises from interactions of two triplet and two singlet states at the lowest energies, while each splitting in the C_s isomer involves two triplets and a singlet. Although the Ce atom has ground electron configuration 4f¹5d¹6s², Ce valence electron configurations in both isomers are 4f¹6s¹ in the neutral ground state and 4f¹ in the ion. The remaining Ce 5d electrons in the isolated atom are spin paired in molecular orbitals that are a bonding combination between Ce 5d_π and hydrocarbon π^∗ orbitals.