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Chen BJ, Pradhan E, Nooijen M, Zeng T. Adiabat-to-Diabat Angle in Seam Space: Renner-Teller-Type and Pseudo-Jahn-Teller-Type Problems. Chemphyschem 2024; 25:e202400130. [PMID: 38427966 DOI: 10.1002/cphc.202400130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 02/29/2024] [Accepted: 03/01/2024] [Indexed: 03/03/2024]
Abstract
In this study, we examine the adiabat-to-diabat (ATD) angles for trajectories in 2-dimensional vibrational subspace of the seam space of two degenerate states. In circulating around the tangential touching degeneracy center, the ATD angle is changed by2 π ${2\pi }$ or 0, similar to the Renner-Teller problem and the pseudo-Jahn-Teller problem, respectively. These ATD angle profiles may be indistinguishable from those of circulating multiple conical intersections or a pseudo-Jahn-Teller center. Methods to discern those seemingly indistinguishable cases are proposed. A sharp zigzag variation of the ATD angle is seen as a feature for trajectories that graze a pseudo-Jahn-Teller-type tangential touching center, in contrast to the monotonic steep variation for grazing a conical intersection or a Renner-Teller-type tangential touching center.
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Affiliation(s)
- Benny Jun Chen
- Department of Chemistry, University of Waterloo, Waterloo, ON, N2 L3G1, Canada
| | - Ekadashi Pradhan
- Department of Chemistry, York University, Toronto, Ontario, M3 J1P3, Canada
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, ON, N2 L3G1, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario, M3 J1P3, Canada
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Pradhan E, Zeng T. The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries. J Chem Theory Comput 2023; 19:7776-7786. [PMID: 37847554 DOI: 10.1021/acs.jctc.3c00782] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2023]
Abstract
Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.
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Affiliation(s)
- Ekadashi Pradhan
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
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3
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Pradhan E, Yao G, Yang Z, Zeng T. Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries. J Chem Phys 2022; 157:064104. [DOI: 10.1063/5.0090053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.
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Affiliation(s)
| | | | | | - Tao Zeng
- Department of Chemistry, York University, Canada
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Brown J, Pradhan E, Zeng T. Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries. J Chem Phys 2021; 155:224108. [PMID: 34911326 DOI: 10.1063/5.0068044] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C1 to D∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.
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Affiliation(s)
- James Brown
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
| | - Ekadashi Pradhan
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
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Brown J, Lang RA, Zeng T. Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries. J Chem Theory Comput 2021; 17:4392-4402. [PMID: 34110818 DOI: 10.1021/acs.jctc.1c00419] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E3″⊗e1' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.
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Affiliation(s)
- James Brown
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
| | - Robert A Lang
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.,Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Tao Zeng
- Department of Chemistry, York University, Toronto, Ontario M3J1P3, Canada
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Vasilyev OA, Nandipati KR, Navarkin IS, Solomonik VG, Domcke W. Strong static and dynamic Jahn-Teller and pseudo-Jahn-Teller effects in niobium tetrafluoride. J Chem Phys 2021; 154:124305. [PMID: 33810698 DOI: 10.1063/5.0045905] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a first-principles study of the static and dynamic aspects of the strong Jahn-Teller (JT) and pseudo-JT (PJT) effects in niobium tetrafluoride, NbF4, in the manifold of its electronic ground state, 2E, and its first excited state, 2T2. The complex topography of the full-dimensional multi-sheeted adiabatic JT/PJT surfaces is analyzed computationally at the complete-active-space self-consistent-field (CASSCF) and multireference second-order perturbation levels of electronic structure theory, providing a detailed characterization of minima, saddle points, and minimum-energy conical intersection points. The calculations reveal that the tetrahedral (Td) configuration of NbF4 undergoes strong JT distortions along the bending mode of e symmetry, yielding tetragonal molecular structures of D2d symmetry with Td → D2d stabilization energies of about 2000 cm-1 in the X̃2E state and about 6400 cm-1 in the Ã2T2 state. In addition, there exists strong X̃2E-Ã2T2 PJT coupling via the bending mode of t2 symmetry, which becomes important near the crossing seam of the X̃2E and Ã2T2 potential energy surfaces. A five-state five-mode JT/PJT vibronic-coupling Hamiltonian is constructed in terms of symmetry-invariant polynomial expansions of the X̃2E and Ã2T2 diabatic potential energy surfaces in the e and t2 bending coordinates. The parameters of the Hamiltonian are determined by a least-squares fit of its eigenvalues to the CASSCF ab initio data. The vibronic spectra and the time evolution of adiabatic electronic population probabilities are computed with the multi-configuration time-dependent Hartree method. The complexity of the spectra reflects the effects of the exceptionally strong E × e and T2 × e JT couplings and (E + T2) × (e + t2) PJT coupling. The time evolution of the populations of the adiabatic electronic states after the initial preparation of the Ã2T2 state reveals the femtosecond nonadiabatic dynamics through a multidimensional seam of conical intersection. These results represent the first study of the static and dynamical JT/PJT effects in the X̃2E and Ã2T2 electronic states of NbF4.
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Affiliation(s)
- Oleg A Vasilyev
- Department of Physics, Ivanovo State University of Chemistry and Technology, 153000 Ivanovo, Russia
| | - Krishna R Nandipati
- Theoretical Chemistry, Institute of Physical Chemistry, University of Heidelberg, D-69120 Heidelberg, Germany
| | - Ilya S Navarkin
- Department of Physics, Ivanovo State University of Chemistry and Technology, 153000 Ivanovo, Russia
| | - Victor G Solomonik
- Department of Physics, Ivanovo State University of Chemistry and Technology, 153000 Ivanovo, Russia
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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Bersuker IB. Jahn–Teller and Pseudo-Jahn–Teller Effects: From Particular Features to General Tools in Exploring Molecular and Solid State Properties. Chem Rev 2020; 121:1463-1512. [DOI: 10.1021/acs.chemrev.0c00718] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Isaac B. Bersuker
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
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8
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Seidu I, Goel P, Wang XG, Chen B, Wang XB, Zeng T. Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries. Phys Chem Chem Phys 2019; 21:8679-8690. [DOI: 10.1039/c9cp01352k] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO3−.
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Affiliation(s)
- Issaka Seidu
- Department of Chemistry
- Carleton University
- Ottawa
- Canada
- Department of Chemistry and Biomolecular Sciences
| | - Prateek Goel
- Department of Chemistry
- University of Florida
- Gainesville
- USA
| | | | - Bo Chen
- Department of Chemistry
- Pennsylvania State University
- State College
- USA
| | - Xue-Bin Wang
- Pacific Northwest National Laboratory
- Richland
- USA
| | - Tao Zeng
- Department of Chemistry
- Carleton University
- Ottawa
- Canada
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9
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Wang K, Zeng T. Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries. Phys Chem Chem Phys 2019; 21:18939-18957. [DOI: 10.1039/c9cp03584b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.
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Affiliation(s)
- Kun Wang
- Department of Chemistry
- York University
- Toronto
- Canada
- Department of Chemistry
| | - Tao Zeng
- Department of Chemistry
- York University
- Toronto
- Canada
- Department of Chemistry
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