A four-component relativistic perspective on an E ⊗ e Jahn-Teller model.

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• Current non-adiabatic dynamics methods primarily focus on refining dynamics algorithms.
• Spin-orbit coupling is typically treated as a perturbation in conventional models.

Purpose of the Study:

• To develop an improved description of spin-orbit coupling by incorporating its relativistic origins.
• To extend a standard one-electron triatomic Jahn-Teller model to the four-component relativistic domain.

Main Methods:

• Utilizing the Dirac-Coulomb Hamiltonian for electron treatment.
• Keeping nuclei non-relativistic, deviating from conventional Pauli spin-orbit coupling.
• Introducing vibronic coupling terms on the anti-diagonal of the diabatic potential matrix.

Main Results:

• The relativistic model reveals vibronic coupling terms scaling as 1/c², significant near avoided-crossings or with heavy nuclei.
• Nuclear motion is shown to influence electron spin direction, a novel feature absent in non-relativistic models.
• Adiabatic representation shows non-Abelian characteristics in the non-adiabatic coupling matrix, persisting even within the Born-Oppenheimer approximation.

Conclusions:

• A relativistic formulation enables a more complex interplay between electronic spin and nuclear degrees of freedom.
• This approach offers a more accurate description of spin-dependent non-adiabatic dynamics.
• The findings are particularly relevant for systems involving heavy elements and complex electronic structures.