Jahn-Teller theory beyond the standard model

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.

Section: Introductionmentioning

confidence: 99%

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

Seidu

Goel

Wang

et al. 2019

“…10,11,13,14 This is the so-called intramolecular collision. 15 Also, when a JT/pJT problem involves bond dissociation, the diabatic potentials are anharmonic and require higher order expansions. 16 High-order Hamiltonians are of concern to both theoreticians and experimentalists.…”

Section: Introductionmentioning

confidence: 99%

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

Hickman

Lang

Zeng

2018

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn-Teller and pseudo-Jahn-Teller Hamiltonians in tetragonal symmetry. Symmetry information of all the vibronic Hamiltonian matrix elements is fully carried by up to only 4 eigenvalues of symmetry operators. This problem-to-eigenvalue reduction enables us to handle thousands of vibronic problems in one work. The derived bimodal formulas can be easily extended to cover problems with one or more than two vibrational modes. They lay a solid foundation for future vibronic coupling studies of tetragonal systems. More importantly, the efficient derivation can be applied to handle (pseudo-)Jahn-Teller Hamiltonians for all problems with one principal symmetry axis.

“…However, if the vibronically active modes are bending and torsional modes that feature anharmonic large amplitude motion or even tunnelling, higher order expansions are strongly desired. 19,20,29,31,37 The success of the case specific expansions up to 6-th ∼ 8-th order for some trigonal (E + A) ⊗ (e + a) problems and subproblems in these pioneering works, especially in calculating vibronic and photoelectron spectra, inspires us to pursue the general formalism for this important class of vibronic Hamiltonians. The objective of this work is to derive expansions in the vibrational coordinates for all the trigonal (E + A) ⊗ (e + a)…”

Section: Introductionmentioning

confidence: 99%

Revisiting the (E + A) ⊗ (e + a) problems of polyatomic systems with trigonal symmetry: general expansions of their vibronic Hamiltonians

Zeng

Seidu

2017

In this work, we derive general expansions in vibrational coordinates for the (E + A) ⊗ (e + a) vibronic Hamiltonians of molecules with one and only one C axis. We first derive the expansion for the lowest C symmetry. Additional symmetry elements systematically eliminate terms in the expansion. We compare our expansions with the previous results for two cases, the and the C (E + A) ⊗ e. The first comparison demonstrates the robustness, completeness, conciseness, and convenience of our formalism. There is a systematic discrepancy in the second comparison. We discuss the origin of the discrepancy and use a numerical example to corroborate our expansion. Our formalism covers 153 vibronic problems in 6 point groups. It also gives general expansions for the spin-orbit vibronic Hamiltonians of the p-type (E + A) ⊗ (e + a) problems.