INO-18

Jahn–Teller snapshot

E_JT ≈ 2 δ for an elongated d⁹ octahedron. Distortion lowering.

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Crystal fieldJahn–Teller

Governing equation

E_{\mathrm{JT}}\approx 2\delta

where

\delta: Tetragonal δ (cm^{-1})
E_{JT}: JT lowering (cm^{-1})
E_{JT}: JT in kJ/mol (kJ/mol)

Lecture brief

Historical brief

Pauling and Allred–Rochow electronegativity, Kapustinskii lattice energy, CFSE and Goldschmidt radii organise the periodic solid. The sheets predict bond character and crystal packing. This sheet (INO-18 — Jahn–Teller snapshot) is the form associated with Jahn–Teller. Working symbols: $\delta$ $\rightarrow$ $E_{JT}$ , $E_{JT}$ . A degenerate electronic ground state distorts to lift the degeneracy. Strongest for eg¹/eg³.

Purpose

Purpose: compute

E_{JT}

E_{JT}

from

\delta

in Inorganic chemistry via

E_{\mathrm{JT}}\approx 2\delta

E_JT ≈ 2 δ for an elongated d⁹ octahedron. Distortion lowering. Use it when a real inorganic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\delta = 1500.000\,\mathrm{cm^-1}

, the governing relation

E_{\mathrm{JT}}\approx 2\delta

yields

E_{JT} = 3000\,\mathrm{cm^-1}

E_{JT} = 35.89\,\mathrm{kJ/mol}

. Enter the tetragonal splitting parameter δ (cm⁻¹). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Tetragonal δ \delta1500 cm^{-1}

Outputs

JT lowering E_{JT}3000 cm^{-1}
JT in kJ/mol E_{JT}35.89 kJ/mol

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Narration of this film

Enter the tetragonal splitting parameter δ (cm⁻¹).

A degenerate electronic ground state distorts to lift the degeneracy. Strongest for eg¹/eg³.

Reading speed

Watch on YouTube