AA’BB’MX Spin System? The 19F NMR Spectrum of Tris(p-fluorophenyl)phosphine

I came across an interesting multiplet pattern. And when I am looking into exotic multiplet patterns I always end up on this fabulous website of Professor Reich from University of Wisconsin-Madison: https://www2.chem.wisc.edu/areas/reich/chem605/index.htm – you should absolutely check it out if you haven’t already.

So, let’s have a look at the ¹⁹F NMR spectrum of tris(p-fluorophenyl)phosphine.

Figure 1. In the ¹⁹F NMR of P(4-F-C₆H₄)₃ a nearly symmetrical multiplet is observed.

The beauty of this multiplet lies in the 18 peaks arranged in an almost perfect mirror symmetry. Even more, there are a lot of spin I = ½ nuclei present in this molecule, namely, ¹³C, ¹H, ¹⁹F, and ³¹P (in this blog post I will focus on the latter three ones). Clearly love at first sight but trying to rationalize this signal might require some effort.

Let’s start it off easy.

1. Let’s say each of the two aromatic hydrogen atoms in ³J (H^A and H^A’) and ⁴J (H^B and H^B’) distance would have the same coupling constant
2. The hydrogen atoms in closer proximity to the fluorine atom (H^A & H^A’) give the higher coupling constant (see Figure 2)

Figure 2. Rationalizing the H-F coupling constants.

This would mean that the fluorine signal is being split to a triplet by the ³J distant hydrogens (H^A & H^A’), and this triplet splits to another triplet by the ⁴J distant hydrogens (H^B & H^B’) as the number of lines equals the equivalent neighbouring atoms plus one (n+1 rule). Actually, this already makes lot of sense, check out this animation:

Figure 3. Simplification of the H-F couplings of the ¹⁹F NMR multiplet signal. The animation was done for clarity.

We can see that there are two triplets of triplets present in this signal – the multiplets 1 (green) and 2 (blue). Each set of a total of 6 triplets is highlighted by circles. So far so good.

It should be noted that the four splitting patterns in the triplet of triplets show different coupling constants which already gives us a hint that the H-F couplings have four instead just two different coupling constants and the simplification
J_(H^A-F)=J_(H^A'-F) is not allowed.

As a result, each assumed triplet corresponds to a doublet of doublets (with two different coupling constants), so, instead of two tt we have two dddd !

Why do we have two sets of “triplets of triplets” or “doublets of doublets of doublets of doublets”? Because of the phosphorous atom which contributes a P-F coupling doublet (n+1). This means the dddd splits by another d.

So, we end up with a ddddd, namely a doublet of doublets of doublets of doublets of doublets. Sounds like a hanging vinyl record, right?

If you think that’s complicated wait for the following resolution. Let’s check out the coupling constant of this last doublet, contributed by the ⁵J_PF coupling. We can do that by measuring the distance in Hz from the center of multiplet A to the center of multiplet B. So, speaking in numbers (and this is a bit rough due to rounding) we can calculate the last missing coupling constant by the following equations:

We could also just have measured the coupling constant with an NMR processing software, but I always like to keep this easy conversion in people’s minds.

Now check out what we observe in the ³¹P{¹H} NMR spectrum – getting rid of the H-F and H-P couplings by turning on the decoupler in the ¹H channel during acquisition (check our blog post on decoupling modes here) – it’s a quartet (the three fluorine atoms split the signal to a quartet (n+1) with a coupling constant of ⁵J_PF = 4.5 Hz which corresponds very good with our measured coupling constant from the ¹⁹F NMR spectrum.

Figure 4. ³¹P{¹H} NMR spectrum of tris(p-fluorophenyl)phosphine.

Having rationalized this multiplet we can double-check if we were correct by picking all the relevant J couplings (following the J tree of our “triplet of triplets assumption” compare Figure 3) in the Multiplet Manager inside Mnova and check the Simulate Multiplet button to receive a satisfying direct comparison of the experimental (green line) and the simulated (purple area) spectrum, Figure 5.

Figure 5. Comparison of the experimental (green line) and the simulated (purple area) ¹⁹F NMR spectrum of tris(p-fluorophenyl)phosphine.

The interested reader may find some more information in a publication ^[1] from 1971, which refers to the spin system of tris(p-fluorophenyl)phosphine as AA’BB’MX. Inside this, you can find a 94.07 MHz ¹⁹F NMR spectrum of the same compound as well as some information on AA’BB’ and AA’BB’MX spin systems along with the functions and Hamiltonian matrix elements for those.

To my great regret, while writing this blog post, I got to know that Professor Hans J. Reich, died on May 1 ^st of 2020.^[2]

[1] Batterham, T. J. and Bramley, R. Org. Magn. Reson., 1971, 3, 83-99.

[2] https://www.chemistry.ucla.edu/news/remembering-professor-hans-j-reich-1943-2020 (accessed 2020-08-13).