Author: Henry Rzepa

In the previous post,[cite]10.59350/x5k75-t2m40[/cite] I was commenting that the transition state for borohydride reduction of a ketone contained some close contacts between the hydrogen of the borohydride and the hydrogen of water. A systematic search of the CSD reveals a modest number of such contacts have been observed in crystal structures (Table).  Since it is always good to have a reality check for constructed transition states, here I take a look at some of compounds showing the closest H…H contacts in the experimental database of structures.

The DFT procedures I used to calculate the geometries of the examples tabled below[cite]10.14469/hpc/15566[/cite] were

1. the classical B3LYP/Def2-TZVPP method, but enhanced with the D4 dispersion correction – the latter developed as a successor to the often used D3+BJ predecessor.
2. The DFT method named  r²scan-3c, a composite described by its developers as the “Swiss army knife of DFT methods” and  “r²SCAN-3c Works Well On Everything”.[cite]10.26434/chemrxiv.13333520.v2[/cite] rather grandly quotesThe specific features are described as  “The unaltered r2SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error“.[cite]10.1063/5.0040021[/cite] The method scales efficiently to several hundred atoms. Results for both types of DFT calculation are  collected here.[cite]10.14469/hpc/15566[/cite]

Table. Calculated and observed BH…HO interactions
Molecule	rH…H using B3LYP+D4/ Def2-TZVPP	rH…H using r2SCAN-3c/ Def2-mTZVPP	Crystal structure, rH…H, Å	angle, BH…H, °	angle, OH…H, °
JATMUN	1.531	1.544	1.519 (1.513) [cite]10.1016/j.jorganchem.2005.02.037[/cite],[cite]10.5517/cc8gcz1[/cite]	95.1	158.6
OLEVIL	1.612	1.654	1.806 (1.67) [cite]10.1016/j.tetlet.2010.12.106[/cite],[cite]10.5517/ccvkd70[/cite]	107.7	171.4
OLEVEH	1.623	1.666	1.857 (1.757) [cite]10.1016/j.tetlet.2010.12.106[/cite],[cite]10.5517/ccvkd6z[/cite]	105.1	176.6
OWUKID	1.685	1.770	1.871 (1.778) [cite]10.1002/cplu.202000427[/cite],[cite]10.5517/ccdc.csd.cc252bp9[/cite]	131.7	157.8
SASVAS	1.757	1.872	1.901 (1.807) [cite]10.1002/chem.200902915[/cite],[cite]10.5517/cct86qz[/cite]	94.3	155.0
BOTFOJ	1.741	1.810	1.976 (1.856) [cite]10.5517/ccdc.csd.cc2k93ww[/cite]	129.6	171.0
MOPXOG	1.888	1.966	1.990 (1.872) [cite]10.1021/om5005989[/cite],[cite]10.5517/cc136fzq[/cite]	95.4	159.5
FOLREF	1.881	1.966	1.998 (1.908) [cite]10.1021/ol500970x[/cite],[cite]10.5517/cc12tj5l[/cite]	110.2	160.8

OLEVIL@r2SCAN-3c
OLEVIL @B3LYP+D4

In general, the B3LYP+D4 method predicts slightly shorter H…H contacts than does r²SCAN-3c. Comparison with experiment is tricky, since OH and BH distances obtained directly from a classical crystal structure refinement tend to emerge as ~0.1A too short (see eg [cite]10.59350/5dy8w-0zs92[/cite] for more detailed discussion). A simple correction for these values is shown in parentheses in the table above. However, given that the angle subtended at the hydrogen atom varies  enormously, this correction may too simplistic. Better would be if the original crystallographic data could be re-refined using the non-spherical atom model model described in [cite]10.59350/5dy8w-0zs92[/cite]  A provisional conclusion without such treatment might be that r²SCAN-3c is somewhat more accurately predicting the H…H distances.

OLEVIL is interesting because it contains two OH groups, with only one interacting with a proximate BH group. Calculating (r2scan-3c) ν_OH gives values of 3477 cm^-1 as perturbed by the close BH vs a BH unperturbed value of 3801 cm^-1  or Δν 324 cm^-1. The corresponding values using B3LYP+D4 are 3700 vs 3803, Δν 103 cm^-1. This large difference in perturbation predicted by these two DFT methods could be easily tested experimentally. Unfortunately, the experimental information reported for this compound[cite]10.1016/j.tetlet.2010.12.106[/cite] does not contain the OH stretching values, which might have been a good test of the claim that “r²SCAN-3c Works Well On Everything”.

This selection of compounds illustrates how one aspect of a transition state can be given a reality check by comparing a key interaction with experimentally determined crystal structures.

In the previous post[cite]10.59350/rzepa.29626[/cite] I mooted the possibility that a high energy form of the dimer of nitric oxide 1 might nonetheless be able to be detected using suitable traps (such as hydrogenation or cycloaddition). However, an interesting alternative is that this species could be trapped by nitric oxide itself. According to [cite]10.1016/0022-1902(65)80196-8[/cite] in an article entitled “Decomposition of nitric oxide at elevated pressures” the rate of this termolecular reaction 3NO → N₂O + NO₂ are said to obey third order kinetics. One plausible mechanism for this process is shown below.

So the question now arises as to whether this process would always intervene to prevent any trapping of species 1. Time for some calculated energies.[cite]10.14469/hpc/15549[/cite] The reaction occurs in two steps, TS1, forming Int, which then gives the product via TS2. The combined IRC for these processes is shown below,^† and the  total energy barrier from 1 + NO for this process is small (~7 kcal/mol).

The NN bond length along the course of these two steps is shown below,^† indicting that it starts and ends with an ~N≡N bond, as implied in the scheme above.

The dipole moment response is shown below.^†

Animation for the IRC for TS1 is shown below:

The intermediate, N₃O₃ has a spin density covering all six atoms (click on image below to see interactive 3D model) so is difficult to represent by e.g. a single valence bond structure as shown above.

The IRC for TS2 is animated below:

The high value for ΔG^‡ ~39.5 kcal/mol arises in large part because of the loss of entropy in reducing three molecules to one at the transition states – and can be compared with e.g. the value of ΔG^‡ 31.0 kcal/mol previously quoted for the bimolecular dimerisation of two molecules of NO.[cite]10.59350/rzepa.29429[/cite]

The story is not quite over yet, since other conformations for this reaction are still being explored. Currently it appears there is only a small free energy window between forming species 1 and it reacting further in the manner 3NO → N₂O + NO₂ as shown above, so it seems unlikely at this stage that 1 could be easily detected.

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^† The slight discontinuity visible at ~IRC +1 is due to a conformational change between the end point of the IRC for TS1 and the start point for TS2.

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DOI: 10.59350/rzepa.29665

Previously[cite]10.59350/rzepa.29429[/cite] I looked at some of the properties of the mysterious dimer of nitric oxide  1 – not the known weak dimer but a higher energy form with a “triple” N≡N bond. This valence bond isomer of the weak dimer was some 24 kcal/mol higher in free energy than the two nitric oxide molecules it would be formed from. An energy decomposition analysis (NEDA) of 1 revealed an interaction energy[cite]10.14469/hpc/15468[/cite] of +4.5 kcal/mol for the two radical fragments, compared to eg -27 kcal/mol for the equivalent analysis of the N=N double bond in nitrosobenzene dimer[cite]10.14469/hpc/15444[/cite] So here I take a look at another property of N≡N bonds via their hydrogenation energy (Scheme), mindful that the dinitrogen molecule requires forcing conditions to hydrogenate, in part because of the unfavourable entropy terms (See Wiki and also here^‡ for a calculation of ΔG₂₉₈).

Calculations at the ωB97XD/Def2-TZVPP/SCRF=water level[cite]10.14469/hpc/15516[/cite] that whilst hydrogenation of the triple bond in N₂ is strongly endo-energic, the same process for molecule 1 is exo-energic (ΔΔG -26.32 kcal/mol). The direct product is a zwitterion, but presumed rapid proton transfer to a neutral form 2 increases exo-energicity. Whilst the second hydrogenation step  of N₂ is  exo-energic, the equivalent second step for 1 to  give 3 is now mildly endo-energic. Overall however, the thermodynamic energies of these two types of triple bond hydrogenation could not be more different.

So forming a N≡N triple bond by forcing two nitric oxide molecules to dimerise (using high pressure) in water produces a system where hydrogenation of that “difficult” N≡N bond is made very much easier thermodynamically. Time for an experiment?^♥

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^‡This site reports a gas phase experimental value for ΔG -8.1 kcal/mol at 298K for this equilibrium, although the pressure is not given. The calculated value shown in the scheme above (-20.1 kcal/mol)  is for 298K and 1 atm for a model using water as solvent – which might be expected to differentially solvate the product ammonia and hence promote the reaction. In the limit of low pressure (0.0001M)[cite]10.12688/f1000research.22758.1[/cite] this reduces to -13.0 kcal/mol, increases to -26.6 kcal/mol at 10M and becomes -14.3 kcal/mol at 10M/800K, illustrating how higher pressures make the reaction more exo-energic and higher temperatures less exo-energic. This was of course the problem solved in the Haber process of finding the sweet spot between pressure and temperature.

^♥Perhaps not, given the report that at high pressures, nitric oxide can become explosive.[cite]10.1016/0022-1902(65)80196-8[/cite]

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I started adding citations to my blog posts around 2012 using the Kcite plugin.^‡ Rogue Scholar is a service that monitors registered blog sources and adds all sorts of value to the original post, including identifying such citations and creating a list of them.

I show the results for the previous blog[cite]10.59350/rzepa.29523[/cite] here.

Martin Fenner has just added some interesting new features[cite]10.53731/yjq4w-5yr32[/cite] which I thought would be useful to share with you here.

1. If you go to the Rogue Scholar archive of the post and scroll down to the References list, then click on the title of any of the references, you will get a list of all Rogue Scholar posts citing that reference: https://rogue-scholar.org/search?q=doi:10.1038/sdata.2016.18+references:10.1038/sdata.2016.18+citations:10.1038/sdata.2016.18
2. If you click on the author name in any of the entries from the previous search, you get a list of all the posts published by that person.
   https://rogue-scholar.org/search?q=orcid:0000-0002-8635-8390&sort=newest

I think this idea of adding citations to a blog post can result in a considerably enhanced discovery process – if only you could do this with journals themselves!

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^‡ This is temporarily not functional due to a php update on the site. I hope to get it working again soon. Update. Thanks to Martin Fenner, the Kcite plugin is working again at version 1.7.11 and upwards.[cite]10.53731/326tr-95k32[/cite]

Previously, I pondered about the strange N=N double bond in nitrosobenzene dimer[cite]10.59350/rzepa.29383[/cite] as a follow up to commenting on the curly arrow mechanism of the dimerisation.[cite]10.59350/rzepa.28849[/cite] By the same curly arrow method, one can produce the below, showing how the simpler nitric oxide radical could potentially dimerise to a species with a N≡N triple bond!^† This involves a total of six electrons entering the N-N region, and hence raises the question of whether these all move in a single concerted/synchronous bond forming reaction, or whether they might go in (asynchronous) stages. Here are some calculations[cite]10.14469/hpc/15483[/cite]) which might shed some light on this aspect.

The structure[cite]10.1021/ja00381a052[/cite] of a nitric oxide dimer was shown in 1982 to have a very long (rather than short) N-N bond length of 2.237Å and a theoretical analysis[cite]10.1016/j.cplett.2007.11.084[/cite] showed it to be a weak complex with a very complex wavefunction showing multi-reference character.

Firstly, an IRC-based reaction path (method: uωB97XD, scrf=(cpcm,solvent=water) guess=(mix,always) def2tzvpp to allow either an open shell biradical to form and also to encourage any ion pair formation). As you can see, the (total) energy goes up to a very  shallow transition state (with a tiny reverse barrier) to form a biradical  with <S²> 0.628. This species, as noted existing in a very shallow energy well, has an N-N bond length of 1.725Å.

The bonding for this species is complex (analysis for a later post), but the calculated biradical spin density below shows the unpaired electrons are in the π-system (click on the image to get a 3D rotatable model).

Further contraction of the N-N length results in an IRC energy potential to a transition state with a N-N length 1.294Å across a further barrier of ~12 kcal/mol (ΔE; ΔG 13.6 kcal/mol). The overall barrier from two nitric oxide molecules is ΔG 31.0 kcal/mol with the overall thermochemistry summarised in the table. Basically, this barrier is unsurmountable at normal temperatures and the reverse barrier of ΔG 6.7 kcal/mol ensures that the N≡N triple bonded species shown above is not likely stable and will not be observed experimentally.^‡ However this product is NOT a biradical but a normal closed shell singlet molecule.[cite]10.14469/hpc/15474[/cite]

So to answer my first question, the six electrons appear to move in two stages, firstly two electrons form a weak N-N bond and then a further four electrons contract this to a triple bond. Their motion is effectively concerted, but asynchronous.

Species	ΔG	ΔH	ΔΔG	ΔΔH	T.ΔS	rNN, Å	<S2>	DOI
2*Nitric oxide	-259.83494	-259.78839	0.0	0.0	29.2	∞	0.753	15472[cite]10.14469/hpc/15472[/cite]
Singlet biradical	-259.80716	-259.77615	17.4	7.7	19.5	1.725	0.628	15476[cite]10.14469/hpc/15476[/cite]
Triplet biradical	-259.80865	-259.77672	16.5	7.3	20.0	1.779	2.016	15475[cite]10.14469/hpc/15475[/cite]
Singlet TS	-259.78550	-259.75579	31.0 (13.6)	20.5 (12.8)	18.6	1.294	0.000	15483[cite]10.14469/hpc/15483[/cite]
Singlet N≡N dimer	-259.79614	-259.76693	24.3  (7.8)	13.5	18.3	1.114	0.000	15467[cite]10.14469/hpc/15467[/cite]

Now for a NEDA energy decomposition analysis[cite]10.1063/1.466432[/cite]

Electrical (ES+POL+SE) :  -9414.608
   Charge Transfer (CT) :  -1363.597
       Core (XC+DEF-SE) :  10782.725                      
  Total Interaction (E) :      4.520 kcal/mol.

Normally NEDA total interaction energies are -ve, but this one is positive! So the triple bond dissociation energy is not merely small, but actually negative. That is a weak triple bond and as the title implies, a very mysterious bond. In some aspects however it is conventional. Thus calculated r_NN 1.114Å and ν_NN 2604 cm^-1. However partial occupancies of NBO antibonding BD* orbitals results in a calculated Wiberg bond order of only 1.01; there is still a great deal of mystery left about this species! Probably what is fairly certain is that the closed shell single-reference wavefunction used here is not appropriate for a full explanation and more complex multi-reference procedures would have to be used to get a more complete picture of this strange non-existing^‡ little molecule. It may even be that such procedures remove the small reverse barrier noted above, thus preventing the molecule from even existing in an energy well.

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^†This species does not appear to have been previously discussed or suggested, according to SciFinder/CAS.
^‡Might it exist at very high pressures in water?

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To find all blog posts authored here, along with their DOIs, try https://rogue-scholar.org/search?q=orcid:0000-0002-8635-8390&sort=newest

In the previous post,[cite]10.59350/rzepa.29383[/cite] I introduced the N=N double bond in nitrosobenzene dimer, arguing that even though it was a formal double bond, its bond dissociation energy made it nonetheless a very weak double bond! This was backed up by a technique known as energy decomposition analysis or EDA. Here I use a variant of this method  known as  NEDA to look at some other strained alkenes, including the famously non-existent tetra t-Butyl ethene.

The NEDA procedure gives a fragment interaction energy (decomposing it into fundamental quantum mechanically derived energies if required) with respect to a reference state for the fragments. In this case, the fragments are obtained by cutting the double bond, resulting in triplet state carbenes as the reference state. The calculations (B3LYP+GD3+BJ/Def2-TZVPP) are available here.[cite]10.14469/hpc/15463[/cite]

1. Compound 1, a relatively unstrained alkene, ΔE = -177.0 kcal/mol, R_CC 1.341Å
2. Compound 2 (PUVQUE, [cite]10.1107/S0108270198099247[/cite], [cite]10.5517/cc4cx7m[/cite]), ΔE = -164.3 kcal/mol, R_CC 1.362Å, CC torsion 16.5°
3. Compound 3 (CUBVOK, [cite]10.1016/S0040-4039(00)98504-6[/cite]) ΔE = -167.9 kcal/mol, R_CC 1.351Å, CC torsion 9.2°
4. Compound 4 (currently unknown) ΔE = -135.8 kcal/mol, R_CC 1.380Å, CC torsion 54.5°

The NEDA interaction energy is directly proportional to both the CC bond length and the C-C=C-C torsion angle. What is interesting however is the large interaction energy gap in ΔE between the two known hindered alkenes (2 and 3) and the unknown tetra-t-butyl ethene 4. It seems moving from say compound 2 by converting the two iso-propyl substituents to full t-butyl ones is just too large a change to bridge. Unless one day isolated as a very very unstable species, compound 4 seems destined not to exist!

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This post has DOI: 10.59350/rzepa.29410

In an earlier blog, I discussed[cite]10.59350/rzepa.28849[/cite] the curly arrows associated with the known dimerisation of nitrosobenzene, and how the N=N double bond (shown in red below) forms in a single concerted process.

One of the properties of this molecule is that the equilibrium between the monomer and dimer can be detected[cite]10.1002/mrc.1260251118[/cite], with significant concentrations of the dimer observed below 10°C. This dimer can even be crystalised, with around 20 well defined crystal structures known for the dimeric structure in the current version of the CSD crystal structure dataset. Nitrosobenzene dimer itself forms a cis isomer, but others are known as trans (see below).

This detectable equilibrium means that the formal bond dissociation energy of that N=N bond must be very low – close to zero. This makes it an unusually weak double bond! Let’s explore how unusual by adopting a technique for analysing the energies in the molecule known as Natural Energy Decomposition Analysis or NEDA[cite]https://doi.org/10.1063/1.466432[/cite] (there are several other well-used methods for this, but I will concentrate on this one in this post at least). To explain what it is, I will paraphrase the NBO7 manual:

Natural energy decomposition analysis is an energy partitioning procedure for molecular interactions with contributions from Electrical interaction (EL), charge transfer (CT), and core repulsion (CORE) terms as evaluated for self-consistent field (SCF) wavefunctions.

1. The electrical term EL = ES + POL + SE arises from classical electrostatic (ES) and polarization interactions (POL+SE). SE is the linear response self energy (energy penalty) of polarization.
2. The CORE contribution CORE = EX + DEF − SE results principally from intermolecular exchange interactions (EX) and deformation (DEF), where the latter is the energy cost to distort a fragment wavefunction in the field of all other fragments of the complex. For DFT-based analysis, EX is replaced by the exchange-correlation interaction (XC).
3. The total interaction energy is then given by 
4. ΔE = EL + CT + CORE

So now for some calculations[cite]10.14469/hpc/15455[/cite]. To do this, one has to consider an appropriate reference state[cite]10.1021/acs.organomet.5b00429[/cite] for the two fragments of the molecule, in this case nitrosobenzene itself. This is expressed via a set of charge,multiplicity definitions for the supermolecule and all the fragments. For the nitrosobenzene dimer, two possibilities can be considered

1. 0,1 0,1 0,1 (which defines singlet states for all three species)
2. 0,1 0,3 0,-3 (which defines triplet states for the two fragments, with a “spin flip” for the second).

Firstly  I will calculate ΔE  (Z)-1,2-diphenylethene, which is a classical C=C double bond alkene.

1. For the reference state 0,1 0,3 0,-3

   Electrical (ES+POL+SE) :  -8691.975
      Charge Transfer (CT) :   -809.587
          Core (XC+DEF-SE) :   9327.995
                           ------------
     Total Interaction (E) :   -173.567 kcal/mol

2. For the reference state 0,1 0,1 0,1 (which represents two carbenes)

    Electrical (ES+POL+SE) :  -7878.192
      Charge Transfer (CT) :   -918.005
          Core (XC+DEF-SE) :   8473.018
                           ------------
     Total Interaction (E) :   -323.179 kcal/mol

So this classical C=C double bond partitions into two interacting triplet carbenes, with a spin flip to align their interaction. Now for nitrosobenzene.

1. For the reference state 0,1 0,1 0,1 (which represents two nitrosobenzenes each with a lone pair of electrons)

   Electrical (ES+POL+SE) : -18230.176
      Charge Transfer (CT) :   -818.925
          Core (XC+DEF-SE) :  19021.537
                           ------------
     Total Interaction (E) :    -27.564 kcal/mol

2. For the reference state 0,1 0,3 0,-3

   Electrical (ES+POL+SE) : -17567.592
      Charge Transfer (CT) :   -677.676
          Core (XC+DEF-SE) :  18197.205
                           ------------
     Total Interaction (E) :    -48.063 kcal/mol

This shows completely different behaviour for the nitrosobenzene dimer and (effectively) the phenyl carbene dimer, with a different reference state for the two species. The electrical and charge transfer terms for the former are much larger than for the latter and this analysis does indeed conform the supposition made at the start that the N=N bond in nitrosobenzene dimer is indeed very unusual and very weak! Perhaps the weakest double bond known? If there are other candidates, I would love to hear about them!

Finally, I note that the relatively low NEDA energy for a triplet reference state for the nitrosobenzene dimer also matches with the observation made previously[cite]10.59350/rzepa.28849[/cite] that open shell (biradical) wavefunctions are needed to describe the curly arrows for the process.

Energy decomposition analysis is a good tool to have in one’s toolbox for analysing molecular behaviour and no doubt I will use it more in the future! Next, tetra-t-butylethene!

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This post has DOI: 10.59350/rzepa.29383