# How to know which kind of distortion takes place due to Jahn-Teller effect

I have gone through a few videos and a few articles (including Wikipedia's) about Jahn-Teller distortion effect and I'm not able to follow if there is a rule which governs which kind of distortion will take place in which compound. If I want to remember which compound has which distortion, should I remember a rule or memorise the whole list?

• The Jahn-Teller theorem does not predict the exact form of the distortion that will take place - it only states that such systems are unstable with respect to distortion. Honestly I would say the only one worth memorising is $\ce{Cu^2+}$, which is of course an axial elongation. – orthocresol Apr 30 '16 at 21:27
• I recently came across a question which asked the electronic configuration for a chromium compound and asked where the electron would be in dz^2 or dx^2-y^2 orbital. And I wasn't able to answer. Isn't this related to Jahn Teller? – user29557 Apr 30 '16 at 21:45
• If it is Cr(II) then probably yes. I don't fully understand that question though :/ – orthocresol Apr 30 '16 at 22:21

If you read and watched videos, you probably already know that the Jahn-Teller effect causes stabilisation in the case of unevenly populated orbitals. Reducing the symmetry of the system renders the orbitals no longer symmetrically equivalent thereby creating an energy difference used to the compound’s advantage.

Let’s separate two cases: 1) octahedral complexes with $\mathrm{d^4}$ and $\mathrm{d^9}$ configuration, in which the $\mathrm{e_g}$ orbitals are unevenly populated; and 2) all the other cases.

# Uneven $\mathbf{e_g}$ population

In an octahedral complex with four or nine d-electrons, there will be either one or three within the $\mathrm{e_g}$ orbitals ($\mathrm{d}_{x^2-y^2}$ and $\mathrm{d}_{z^2}$). It is unfavourable for orbitals of the same energy (as symmetrically equivalent orbitals have) to have different populations so the system distorts itself. The distortion will always be along a single axis and per defintion this axis is always the $z$ axis. Thereby, ligands on the $z$-axis (negative charges in the most simple crystal field model) move away from the metal centre stabilising any orbital with a contribution in $z$ direction and most significantly the $\mathrm{d}_{z^2}$ one.

The effect is greatest in this case because the $\mathrm{e_g}$ orbitals actually point towards the ligands thus rendering them most susceptible to distance effects.

# All other cases

In all other cases, the effect is much weaker. This is mainly because no other orbitals are known to point directly at the ligands; even for tetrahedral complexes the $\mathrm{t_2}$ orbitals point in-between them. Therefore, moving a ligand away slightly has much less effect on the electronics of the system.

What exactly happens really depends on the system itself and how it can be stabilised. If you are speaking of an octahedral complex, it will usually distort itself to $D_{\mathrm{4h}}$, i.e. equivalently to the former case because that is the distortion that keeps the highest possible symmetry. In that case again, one would say that the ligands in $z$ direction are moved away. Otherwise you need to figure it out by drawing, thinking and guessing or by studying crystal structures.

# Tl;dr

Instead of memorising a list remember the first case and $z$-distortion. Ignore all the other cases for being weak.

• Very lucid answer @Jan but for questions like this- jahn teller effect is not observed in high spin complexes of : a) d^4 b)d^9 C)d^7 D) d^8 what strategy should be used? As you've written here options a and b can be ruled out but how to decide between C and D.is there any other way to find whether jahn teller distortion happens when provided with specific orbitals like these along with their spins? – Harini Apr 24 '17 at 4:27
• @Harini Draw out the hypothetical octahedral state. Only in the case of $\mathrm{d^8}$ can you achieve fully evenly populated orbitals. All other cases require degenerate orbitals of uneven population: $\mathrm{d^4}$ and $\mathrm{d^9}$ have $\mathrm{e_g}^1$ and $\mathrm{e_g}^3$, respectively; $\mathrm{d^7}$ has $\mathrm{t_{2g}}^5$. This last case is contained in all other cases of my answer. – Jan Jun 7 '17 at 20:35