The Jahn-Teller Effect

Overview

The Jahn-Teller Effect, named after Hermann Arthur Jahn and Edward Teller, is a distortion in the geometric configuration of a molecule that results in a lower overall energy state. This effect is typically observed in molecules and ions with a degenerate electronic ground state.

Introduction to Symmetry and Degeneracy

Before delving into the Jahn-Teller effect, it’s crucial to understand the concepts of symmetry and degeneracy in the context of molecular physics.

Symmetry refers to the unchanged characteristics of a molecule when subjected to transformations like rotation or reflection. Degeneracy, on the other hand, is a condition in quantum systems where two or more different states have the same energy.

The Principle of the Jahn-Teller Effect

At the heart of the Jahn-Teller effect lies the principle that any non-linear molecular system in a degenerate electronic state will undergo a distortion that removes the degeneracy and minimizes the total energy of the system.

In mathematical terms, if we represent the electronic energy of the system as a function of nuclear coordinates :

where is the energy at the symmetric configuration, are force constants, and the sum is over all nuclear coordinates. The Jahn-Teller theorem states that if the energy has a degeneracy (multiple values with the same energy), the system will distort along the coordinate with the smallest force constant to break the symmetry and minimize the energy.

Consequences and Examples of the Jahn-Teller Effect

The Jahn-Teller distortion can lead to several notable changes in the properties of the molecule, such as changes in the electronic spectra, magnetic properties, structural deformations, and vibrational spectra.

A common example of the Jahn-Teller effect is the distortion of octahedral transition metal complexes, such as

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