Vibronic interaction in CO₃⁻ photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Abstract

Recently, the negative ion photoelectron spectrum of CO − 3 was reported and the second lowest energy band is assigned to the close-lying 3 E and 3 E states that undergo Jahn-Teller distortions (Chem. Sci., 2016, 7, 1142. This assignment is based on the Born-Oppenheimer approximation and the assumption of a static Jahn-Teller effect that distorts the CO 3 structure from D 3h to C 2v symmetry. In this work, we employ a 4 states 6 modes vibronic coupling model to investigate the triplet band and uncover the dynamic and non-adiabatic nature of the Jahn-Teller and pseudo-Jahn-Teller interactions in the triplet states. The apparent four peaks progression in the band is studied in depth, and is found to consist of more than four transitions. By comparing the simulated spectra using the full model and the reduced-dimension 2 states 2 modes models, we characterize those transitions. The origin of the complexities of the spectrum is traced to the C-O nonbonding character of the orbitals that lose electron in the photo-detachment process. Methodology-wise, we derive and present the formalisms for arbitrary order expansions of all bimodal trigonal Jahn-Teller and pseudo-Jahn-Teller Hamiltonians in vibrational coordinates.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

“…All bimodal expansion formulas that feature the symmetry eigenvalues summarized in ) = (0, ±1), have been derived before in the context of non-SO pJT/JT interactions in trigonal 57,61 and tetragonal 59 symmetries. The trigonal formulas are summarized in Table . A. I-Table . A. VI in Appendix, and the tetragonal formulas in Table . A.…”

“…The idea and approaches have been employed in our recent derivations of arbitrarily high order expansion formulas for non-SO JT/pJT problems in trigonal, tetragonal, and cubic symmetries. 57,58,59,60,61 They can be equally employed in deriving SO JT/pJT formulas, and the resultant formulas can be similarly summarized in a set of look-up tables. Each independent Hamiltonian matrix element of a SO JT/pJT problem carries a set of symmetry eigenvalues, which guide us to retrieve the element's expansion formulas in the tables.…”

Unified Hamiltonian Formalism of Jahn–Teller and Pseudo-Jahn–Teller Problems in Axial Symmetries

“…In this work, we make a larger stride forward to derive a unified JT/pJT Hamiltonian formalism that covers all problems in all axial symmetries with arbitrary numbers of all types of vibrational modes. The resultant more inclusive formalism turns out to adopt a simpler form than the previous ones for trigonal and tetragonal bimodal problems. − …”

“…The resultant more inclusive formalism turns out to adopt a simpler form than the previous ones for trigonal and tetragonal bimodal problems. [43][44][45] In Section 2, we briefly overview axial symmetries and the conventional symbols of JT/pJT problems in those symmetries. The mathematical symbols that are used in our derivations are also introduced.…”

“…These pioneering studies motivated us to derive JT/pJT expansion formulas that are of arbitrarily high orders and are as inclusive as for one class of symmetries, instead of one symmetry. So far, we have successfully derived arbitrarily high order expansion formulas for all bimodal JT/pJT problems in trigonal symmetries, , tetragonal symmetries, cubic group symmetries, , and spin–orbit JT/pJT problems in trigonal and tetragonal symmetries . These formalisms are inclusive, yet not enough.…”