# C-N bond lengths in 2-bromo-1,3,5-trinitrobenzene

Are all the $\ce{C-N}$ single bonds in 2-bromo-1,3,5-trinitrobenzene the same or different? I am of the view that the $\ce{C_1-N}$ and $\ce{C_3-N}$ bonds are of the same length and they are longer than the $\ce{C_5-N}$ bond, due to steric hindrance. Am I right or am I missing out something?

structure of 2-bromo 1,3,5-trinitro benzene http://webbook.nist.gov/cgi/inchi?Struct=C4185539&Type=Color

• Seems you're right. – Mithoron Jun 25 '15 at 17:13
• Those pentavalent nitrogens are causing my eyes to bleed. – Lighthart Jun 25 '15 at 21:05
• Subhamon, I see that you are new here and that this is the first question you've asked. So let me mention that if an answer is helpful please consider accepting and\or up-voting it. Accepting \ upvoting an answer is a nice way to say "thank you". – ron Jul 4 '15 at 16:39

By rotating the molecule 180° about the $\mathrm{C_2}$ symmetry axis that passes through the bromine and the nitro group in the 5-position, you can interconvert $\ce{C_1-NO2}$ and $\ce{C_3-NO2}$. Groups that can be interconverted by a rotational axis must be equivalent. There is no symmetry element that interconcerts $\ce{C_1-NO2}$ (or $\ce{C_3-NO2}$) and $\ce{C_5-NO2}$, therefore these groups cannot be equivalent. So symmetry tells us that the $\ce{C_1-NO2}$ and $\ce{C_3-NO2}$ bond lengths are exactly the same, and both are different from the $\ce{C_5-NO2}$ bond length.

Symmetry can only tell us if things are the same or different, it can't tell us the magnitude of any difference. So I don't know for sure which set of carbon-nitro bonds is longer or shorter, but your argument based on steric strain seems reasonable. It is also possible that the bulky bromine causes the adjacent nitro groups to twist out of the plane of the aromatic ring, reducing resonance overlap between nitrogen and carbon and also lengthening those adjacent nitro bonds.

As I thought this could be interesting because I would have argued the same way as both of you did I have done some geometry optimizations.

The final niveau was B3LYP-D3/def2-QZVPP in the gas phase (no frequency calculation has been done because it would have taken too long for me to wait so I have to believe that it is a ground state) and the result from this one calculation with this single functional is that all three $\ce{C-N}$-bonds have de facto the same lengths: $1.482~\mathrm{\overset{\circ}A}$ "long" and $1.480~\mathrm{\overset{\circ}A}$ "short"

The two bromine-neighboring nitro-groups do indeed turn out of plane (dihedral angle is about 61...62°) as it was suggested by ron. This seems enough to compensate the proximity to the bromine.

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• What program are you using to generate that structure? – tkhanna42 Jun 27 '15 at 8:56
• The structure itself is made with Gaussview. – pH13 - Yet another Philipp Jun 27 '15 at 10:02

There is also a single crystal structure investigation (1) of polymorphism among picryl bromide structures. Geometry of the molecule in crystal structure is a little bit different, showing bigger difference in $\ce{C - N}$ bonds: 1.483 and 1.493 (ortho) vs 1.461 (para) in comparison with the calculated one for the gas phase:

I tried to align the molecule in the same way as it's been done by @pH13-Yet anotherPhilipp for better visual comparison. It's also worth noticing that in real crystal structure nitro groups are more tilted due to interlayer interactions:

(1) Parrish, D. A.; Deschamps, J. R.; Gilardi, R. D.; Butcher, R. J. Crystal Growth & Design 2008, 8 (1), 57–62. DOI: 10.1021/cg700727n

The bond lengths of carbon 1 & 3 are same and they are longer than that of carbon 5 and its attached nitrogen. This is due to resonance and in resonance we see 1 structure at a time.

• Welcome to Chemistry.SE. There is no need to address the poster or put in a signature. Every post is signed, and every answer is directed back to the asker. See here. I have edited your post to remove these and clean up your grammar. – Ben Norris Jul 4 '15 at 14:11
• While we're at it, do you have any additional data that makes your answer significantly different than PH13's, which makes the same point and has a DFT gas-phase structure to back it up? – Ben Norris Jul 4 '15 at 14:15