Henry Rzepa's blog

In the previous post[1] I followed up on an article published on the theme “Physical Organic Chemistry: Never Out of Style“.[2] Paul Rablen presented the case that the amount of o (ortho) product in electrophilic substitution of a phenyl ring bearing an EWG (electron withdrawing group) is often large enough to merit changing the long held rule-of-thumb for EWGs from being just meta directors into being ortho and meta-directors, with a preference for meta. I showed how Paul’s elegant insight could be complemented by an NBO7 analysis of the donor-acceptor interactions in the σ-complex formed by protonating the phenyl ring bearing the EWG. Both the o– and m– isomers showed similar NBO orbital patterns and associated E(2) donor/acceptor interaction energies and also matched the observation that the proportion of meta is modestly greater than ortho substitution (steric effects not modelled). These interactions were both very different from those calculated for the para isomer.

Here using the same NBO7 analysis, I look at what happens when you transpose the atoms of CN to form the isocyanide NC.

The orbital overlaps for NC as substituent can be seen as 3D rotatable models below (click on image to open model).

These effects (ωB97XD/Def2-QZVPP/SCRF=DCM) can be summarised in the table below.

What emerges is that the two groups cyanide (CN) and isocyanide (NC) can act as both π-electron acceptors and π-electron donors. For the former, the o– and m– electron acceptor interactions are larger, whilst for the latter the o– and m– electron donor effects dominate. However, the interactions for both o– and m– are qualitatively very similar and it is therefore correct to group them together, as was implied in the title of the recently published article.[2] In contrast it seems appropriate to treat p– direction as a qualitatively different effect.

This post has DOI: 10.59350/rzepa.29121

References

1. H. Rzepa, ""Typical Electron-Withdrawing Groups Are o, m-Directors Rather than m-Directors in Electrophilic Aromatic Substitution"", 2025. https://doi.org/10.59350/rzepa.28993
2. P.R. Rablen, "Typical Electron-Withdrawing Groups Are <i>ortho</i>, <i>meta</i>-Directors Rather than <i>meta</i>-Directors in Electrophilic Aromatic Substitution", The Journal of Organic Chemistry, vol. 90, pp. 6090-6093, 2025. https://doi.org/10.1021/acs.joc.5c00426

The title of this post comes from an article published in a special virtual issue on the theme “Physical Organic Chemistry: Never Out of Style“[1] There, Paul Rablen presents the case that the amount of o (ortho) product in electrophilic substitution of a phenyl ring bearing an EWG (electron withdrawing group) is often large enough to merit changing the long held rule-of-thumb for EWGs from being just meta directors into these substituents are best understood as ortho, meta-directors, with a preference for meta. I cannot help but add here a citation[2] to the earliest publication I can find showing tables of both o,p and m-directing groups and dating from 1887, so this rule is 138 years old (at least).

Here I thought I might show some computational models (ωB97XD/Def2-QZVPP/SCRF=Dichloromethane)[3] derived from the relative stability of the Wheland or σ-complex produced by protonating the Ph-EWG molecule in the three possible positions on the ring – and now taking the opportunity to add some unusual EWGs to the table to explore how far this effect might be pushed.

I start by looking at the results reported for benzonitrile (EWG = CN), for typical product distributions:

1. o– (~16%), m– (~82%) and p– (~2%) are cited for nitronium ion as electrophile
2. o– (23%), m– ( 74%) and p– (3% ) for chlorination
3. o– (34%), m– (55%) and p– (1%) for uncatalysed bromination (see [4] for an unexpectedly complex mechanism and kinetic analysis of this particular reaction)
4. σ-complex calculations [5] which result in values of o– (43%), m– (55%) and p– (2%) for benzonitrile.
   • The observation was made[5] that inclusion of a solvation correction substantially improved the agreement with the limited experimental information available to us regarding product distributions in EAS and the results below certainly confirm that (especially for benzonitrile). Solvent also has a significant effect on the optimised geometry of each system (see Table).

The calculations reported here[3] are similar to those reported using a slightly different model[5]. For the specific example of benzonitrile, the authors of the original report expressed surprise that their computations showed that “the ortho and meta σ-complexes were … about equally stable“. The results for this blog show a slightly larger and perhaps more realistic (?) discrimination in favour of meta by 0.51 kcal/mol in the free energy.

Other noteworthy observations include that

5. compared with CN, the iso-electronic isonitrile group NC is a strong and conventional o/p director, with a preference for p.
6. The EWG R=BO (a known, albeit very unstable molecule[6]) is the next isoelectronic isomer of CN and it now reveals a very strong preference for meta-substitution, with only 3.5% ortho. So this group does NOT follow the proposed new rule of “ortho, meta-directors, with a preference for meta” although this is unlikely to ever be able to be tested experimentally due to the instability of this species (it readily trimerises).
7. Finally in this isoelectronic progression for R=BeF, the calculations seem now to show that this is a strong o– director (61%) and that m is only 29%, again not following the newly modified rule but probably untestable.
8. R=NO however does seem to be an example of the new modified rule, since the percentage of o– is as high as 23.8%. Here it is significant that for both the o– and m– σ-complexes, the NO group was calculated as being co-planar with the phenyl ring, thus indicating significant conjugation – but the p-isomer (2.3%) was twisted and hence un-conjugated (dihedral values shown below).
9. The same result is obtained for R=NO₂, with the p-isomer having a twist angle of 67°.

On to the suggested explanation,[1] where interaction of the π-electrons from the σ-complex with the π* orbital from the EWG was suggested to be stronger not only for the m-isomer but also the o-isomer as compared to the p-isomer. This can now be quantified using NBO7 analysis, which indicates the energy of interaction between pairs of filled donor and empty acceptor orbitals.

For the m-isomer[7] of protonated benzonitrile, the overlap of the two orbitals (CN acting as an acceptor and the phenyl ring as a donor) is shown below (click on the image to get a rotatable 3D model) with blue positively overlapping with purple and red with orange. The NBO E(2) interaction energy is 23.85 kcal/mol (green bond above interacting with R=CN π^*).

A reverse donation, from the π-system of the CN group now acting as a donor to the π^* of the benzene ring acting as an acceptor has a smaller E(2) = 9.4kcal/mol. This shows that CN can act as both a donor and as an acceptor, but the latter effect is stronger.

For the o-isomer[8] (below), the NBO E(2) interaction energy is somewhat reduced to 18.8 kcal/mol (orange bond above interacting with R=CN π^*). but is still considerable and more or less commensurate with the relative free energies of the o– and m-isomers.

A reverse donation, from the π-system of the CN group now acting as a donor to the π^* of the benzene ring acting as an acceptor has a smaller E(2) = 14.3 kcal/mol. This again shows that CN can act as both a donor and as an acceptor with the latter effect the stronger.

Things are quite different for the p-isomer[9]. The equivalent CN-acceptor/phenyl-donor orbitals are shown below; they has no real overlap and the associated value for E(2) of 0.23 kcal/mol (red bond above interacting with R=CN π^*) is tiny compared to that for the o- and m– isomers.

The reverse donation from the π-system of the CN group now acting as a donor to the π^* of the benzene ring acting as an acceptor is equally small, E(2) 0.15 kcal/mol.

Furthermore, the p-isomer NBO E(2) interaction energy for the same atoms as with o– and m– shows two instances of 3.0 kcal/mol (because of the C_2v symmetry), also very much reduced from 23.85 or 18.8 kcal/mol.

Although many other interactions can be found in the NBO analysis, this accounts for by far the largest difference between the o, m, and p isomers. These results also match with the observation made above that for R=NO, the o– and m-isomers are fully coplanar, but for the p-isomer the NO group is twisted by about 90° with respect to the phenyl ring. This is also reflected in the calculated torsional or twisting vibrations of the R group, being 89 cm^-1 for m-Nitroso vs 23 cm^-1 for o-nitroso and again 55 cm^-1 for m-nitro vs 38 cm^-1 for o-nitro.

So this new NBO7 orbital overlap analysis helps to quantify these effects (the reported qualitative analysis[1] was based on molecular orbitals rather than localised NBO orbitals) and confirms that for some EWG groups at least, the o-isomer is almost as favoured as the m-form. Well, an observation that is 138 years old gets new light shone on it!

This post has DOI: 10.59350/rzepa.28993

References

1. P.R. Rablen, "Typical Electron-Withdrawing Groups Are <i>ortho</i>, <i>meta</i>-Directors Rather than <i>meta</i>-Directors in Electrophilic Aromatic Substitution", The Journal of Organic Chemistry, vol. 90, pp. 6090-6093, 2025. https://doi.org/10.1021/acs.joc.5c00426
2. H.E. Armstrong, "XXVIII.—An explanation of the laws which govern substitution in the case of benzenoid compounds", J. Chem. Soc., Trans., vol. 51, pp. 258-268, 1887. https://doi.org/10.1039/ct8875100258
3. H. Rzepa, "Cationic intermediates in electrophilic substitution of benzene substituted with electron withdrawing groups", 2025. https://doi.org/10.14469/hpc/15341
4. A.V. Shernyukov, A.M. Genaev, G.E. Salnikov, H.S. Rzepa, and V.G. Shubin, "Noncatalytic bromination of benzene: A combined computational and experimental study", Journal of Computational Chemistry, vol. 37, pp. 210-225, 2015. https://doi.org/10.1002/jcc.23985
5. P.R. Rablen, and A. Yett, "The relative favorability of placing substituents ortho or para in the cationic intermediate for electrophilic aromatic substitution", Journal of Physical Organic Chemistry, vol. 36, 2022. https://doi.org/10.1002/poc.4457
6. D.S.N. Parker, B.B. Dangi, N. Balucani, D. Stranges, A.M. Mebel, and R.I. Kaiser, "Gas-Phase Synthesis of Phenyl Oxoborane (C₆H₅BO) via the Reaction of Boron Monoxide with Benzene", The Journal of Organic Chemistry, vol. 78, pp. 11896-11900, 2013. https://doi.org/10.1021/jo401942z
7. H. Rzepa, "Protonated benzonitrile- m G = -324.706886 + DCM => -324.791810 Cavity surface area= 172.569 Ang**2 Cavity volume = 166.107 Ang**3", 2025. https://doi.org/10.14469/hpc/15354
8. H. Rzepa, "Protonated benzonitrile- o, G = -324.709093 + DCM => G = -324.791005 Cavity surface area= 172.048 Ang**2 Cavity volume 165.997 Ang**3", 2025. https://doi.org/10.14469/hpc/15355
9. H. Rzepa, "Protonated benzonitrile- p, G = -324.708521 + DCM G = -324.789846 Cavity surface area= 171.955 Ang**2 Cavity volume = 165.449 Ang**3", 2025. https://doi.org/10.14469/hpc/15353

I am in the process of revising my annual lecture to first year university students on the topic of “curly arrows”. I like to start my story in 1924, when Robert Robinson published the very first example[1] as an illustration of why nitrosobenzene undergoes electrophilic bromination in the para position of the benzene ring. I follow this up by showing how “data mining” can be used to see if this supports his assertion. I have used the very latest version of the CSD crystal structure database to update the version originally posted here in 2020.[2]

I then discuss some possible reasons why Robinson might have thought that bromination goes in the para position, including the observation[3] that nitrosobenzene is in equilibrium with its dimer, and that such a dimer might be expected to more reactive towards electrophiles than the “deactivated” monomer.

Not part of the main lecture, but held in reserve for any questions at the end, is the following curly arrow pushing for the dimerisation.

This raises a simple question – do both the red and blue arrows shown below participate at the same time, or do they go sequentially? Time then for some calculation to answer this last question. An ωB97XD/Def2-TZVPP/SCRF=chloroform calculation[4] using a closed shell wavefunction (to correspond to two-electron curly arrows) appears to show a smooth reaction profile. The N-N bond length also converges from no bond to a double bond shortly after the transition state (NN = 1.3Å) without anything intermediate (this for the (Z)-stereochemical isomer, not the one shown above and which will be discussed later). The reported activation free energy for this process ΔG₁₉₈ is 15.7 kcal/mol[3] whilst the calculated value by this method is 25.5 kcal/mol. Even allowing for a concentration effect (1M) and quasi-harmonic corrections to the free energy, it is still 23.9 kcal/mol.

In a previous post[5] when an overly large barrier was computed, one reason is that the wavefunction might have “biradical” character and that the appropriate curly arrows might not be the appropriate two electron variety at all, but instead one-electron ones, as shown below.

The degree of biradical character is given by the spin-expectation operator <S²>, which has a value of 0.0 for no biradical character and 1.0 for a pure biradical. This time the transition state for the dimerisation is calculated to have a value of <S²> = 0.5418 and ΔG₁₉₈ is now calculated as 21.8 kcal/mol (20.3 with quasi-harmonic corrections).

The energy and N-N bond length profiles for the reaction coordinate using “one-electron” curly arrows are shown below, the former being around 4 kcal/mol lower than for the two-electron arrows.

The dihedral at the central C-N-N-C bond shows it almost entirely twisted at the transition state (as might befit a biradical) and then a smooth rotation to co-planarity (as befits a double bond) as the second bond forms.

Because the system has C₂-symmetry and importantly no plane of symmetry, the π and σ electrons are now allowed to mix together and this can be seen in the two (equivalent) orbital overlap models below at the transition state, each nitrogen lone pair managing to overlap constructively (blue with purple, red with orange, click on the diagram to load the orbitals) with the N-N π^* orbital of the second nitrosobenzene.

Why is this simple system better described (energetically) by the use of one-electron arrows rather than two electron ones? A simple explanation might be that the electrons like to move consecutively simply to reduce the electron repulsion that the two-electron model would impose on it (reducing the electron correlation incurred in the process). It’s probably more complicated than this, but it shows a rare example where two-electron arrows are not the most appropriate for describing a chemical reaction.

Postscript. The 1-electron transition state (<S²> = 0.981) for formation of the trans stereochemical (E) isomer is higher than the cis (Z) by ~4 kcal/mol.

References

1. "Forthcoming events", Journal of the Society of Chemical Industry, vol. 43, pp. 1295-1298, 1924. https://doi.org/10.1002/jctb.5000435208
2. H. Rzepa, "The first ever curly arrows. Revisited with some crystal structure mining.", 2020. https://doi.org/10.59350/c6thp-wqe69
3. K.G. Orrell, V. Šik, and D. Stephenson, "Study of the monomer‐dimer equilibrium of nitrosobenzene using multinuclear one‐ and two‐dimensional NMR techniques", Magnetic Resonance in Chemistry, vol. 25, pp. 1007-1011, 1987. https://doi.org/10.1002/mrc.1260251118
4. H. Rzepa, "The mechanism of nitrosobenzene dimerisation", 2025. https://doi.org/10.14469/hpc/15278
5. H. Rzepa, "Mechanism of the Masamune-Bergman reaction. Part 4. Why was the DFT energy barrier too high for the Calicheamicin reaction?", 2024. https://doi.org/10.59350/k4340-t6971

The topic of dicarbon, C₂, has been discussed here for a few years now. It undoubtedly would be a gas! This aspect of the species came to the fore recently[1] when further experiments on a potential chemical precursor of dicarbon, the zwitterion X(+)-C≡C(-), showed that different variants of X(+), such as not only X=PhI(+), but also e.g. X=dibenzothiophenium(+) appeared to generate a gaseous species, which could be trapped as “C₂” in a solvent-free connected flask experiment.

Part of the mystery is that C₂ itself is an extremely high energy species, its dimerisation to C₄ being around 107 kcal/mol exoenergic in free energy. Now, earlier calculations[2] had revealed that the reaction of the precursor PhI(+)-C≡C(-) with itself can occur on a relatively low energy pathway which avoids the very high energy of C₂. The IRC for this reaction is shown below, showing a modest barrier and a very exothermic reaction to the species PhI(+)-CCCC(-) and IPh. 

Here I bring your attention to an odd feature on the IRC, in the region of -5. In this region, effectively “free C₄” is formed (at an energy some 60 kcal/mol lower than the reactants and 167 kcal/mol lower than two molecules of free C₂), but this species is immediately trapped by a PhI to form the final products with a further decrease in energy of ~20 kcal/mol. Suppose however, in a molecular dynamics sense, some proportion of this “C₄” could take a different trajectory and free itself at this point, hence escaping being trapped by PhI? This reaction would then generate what again is presumably a gaseous C₄.

Here I explore what might happen next, to answer the question of whether linear C₄ is stable, or will it convert into something else? The scheme below shows some of the possible pathways, leading to the bicyclic form which I have previously discussed extensively in terms of its stabilising aromaticity. Calculations are at the CCSD(T)/Def2-TZVPPD gas phase level, allowing biradicals to form (FAIR Data DOI: 10.14469/hpc/11956).

You can see that C₄ is in a modest thermal well, with a free energy barrier to cyclisation of ~22 kcal/mol. So generated at relatively low energies, it might retain its linear structure, whereas at room temperatures or higher, it will probably end up as the bicyclic aromatic species.

The key calculation might be that dimerisation reaction shown above. Would molecular dynamics show that a proportion of the reaction allows the escape of C₄? Would that be temperature/pressure dependent? I am not about to try these calculations, but offers of doing so gladly accepted! But that does not necessarily solve the mystery of this reaction, alluded to above.[1] Is the trapped gaseous species C₂ itself, C₄ in some form, or indeed something else entirely?

This post has DOI: 10.14469/hpc/11959

References

1. H.S. Rzepa, M. Arita, K. Miyamoto, and M. Uchiyama, "A combined DFT-predictive and experimental exploration of the sensitivity towards nucleofuge variation in zwitterionic intermediates relating to mechanistic models for unimolecular chemical generation and trapping of free C ₂ and alternative bimolecular pathways involving no free C ₂", Physical Chemistry Chemical Physics, vol. 24, pp. 25816-25821, 2022. https://doi.org/10.1039/d2cp01214f
2. H.S. Rzepa, "Routes involving no free C ₂ in a DFT-computed mechanistic model for the reported room-temperature chemical synthesis of C ₂", Physical Chemistry Chemical Physics, vol. 23, pp. 12630-12636, 2021. https://doi.org/10.1039/d1cp02056k