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The Jahn-Teller effect arises from the symmetry breaking (distortion) of the local environment for the crystal field of 3d transitional metal ions.The distortion result in energy saving of electronic energy from the splitting of the degeneracy energy levels of octahedron / tetrahedral environment. Jahn-Teller effect is responsible for the hopping mechanism between Mn3+ and Mn4+ in some solid state structure.

The question is that is there current computational methods available to model the Jahn-Teller effect in solid state structure? Is there any reference available?

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    $\begingroup$ I wonder if QM/QM or QM/QM' methods would be sufficient. For example, I guess you'd be interested in studying some crossing between electronic states which might require a multi reference calculation. The crossing might be localized on a single unit of the crystal. There have also been some nice advancements in including long range electrostatics to QM/QM' methods $\endgroup$ – Cody Aldaz Nov 9 '20 at 8:59
  • $\begingroup$ Can you give us some references? In which papers did you see it modeled for solid-state systems? You said it's responsible for some hopping in a solid-state structure, do you have a reference for that? $\endgroup$ – Nike Dattani Dec 3 '20 at 22:00
  • $\begingroup$ This question seem to needs additional detail to be answered. It can be reopened with clarifications from the OP or if another user wishes to post an answer. $\endgroup$ – Tyberius Dec 31 '20 at 16:49