# Breaking degeneracy in phosphorus pentachloride

Recently, in a class discussion, the following point was brought up:

Although the axial and equatorial bond lengths in $\ce {PCl5}$ are inequivalent, when we consider the time-averaged $\ce {P-Cl}$ bond length, there should only be one value sincethe molecule is symmetric and thus, all the chlorine atoms interact with the phosphorus atom to the same extent.

The idea of "time-averaged" means that we are considering the $\ce {P-Cl}$ bond over a long duration. This bond length varies over time since the atoms are constantly in motion. When this bond length is "time-averaged", it means that we are taking the average of the bond lengths measured at infinitely many instants in time.

The argument is that although at any particular instant, the molecule would adopt a configuration with axial bonds being longer than equatorial bonds, when the bonds are time-averaged, they should all be the same length.

This has caused much dispute among members of the class and it has also led me to consult a professor who is well-versed with quantum chemistry. The professor mentioned that the argument put forward is not valid because in $\ce {PCl5}$, there is a breaking of degeneracy due to perturbation. He cited the Jahn-Teller distortion as a situation similar to that in $\ce {PCl5}$, where degeneracy is broken.

I am very confused by this. What exactly is this perturbation? Why does it exist for $\ce {PCl5}$ and not for similar molecules, such as $\ce {SF6}$ (as seen in the comments for this question)?

• The experimental data shows that the two axial bonds ($C_3$ axis) are significantly longer than the 3 equatorial ones i.e. outside expt. error different. So there is no time averaging going on here as that would predict similar bond lengths. Additionally, electronegative atoms preferentially fill the axial positions e.g $\ce{PCl3F2}$ indicating a difference in bonding between axial and equatorial positions. The proposed trigonal bipyramidal ($sp^3d$ bonding) is consistent with minimising electron pair repulsion; $sp^2$ along equatorial; $pd$ along axial bonds. – porphyrin May 24 '18 at 13:01
• @porphyrin I am completely aware of the 3c4e bonding scheme involved and I understand the rationale behind the difference in bond lengths and thus, I am not looking for this in the answer that I require – Tan Yong Boon May 24 '18 at 13:20
• Rapid pseudorotation on the observational time scale is what makes the bonds euivalent. – ron May 24 '18 at 13:27
• That being said, the pseudorotation appears rapid to some physical methods and slow to the others. – Ivan Neretin May 24 '18 at 13:31
• The molecule will undergo a Berry rotation , but that does not make the bonds equivalent it effectively just swaps them around, rather like the effect of rotating the axes. The experimental evidence is that the two types of bonds have different lengths. A similar, but simpler, effect occurs in ammonia inversion or $\ce{CH2}$ wagging in cyclopentene or any number of molecules with small barriers to rotation/inversion. – porphyrin May 24 '18 at 13:43