Henry Rzepa's blog

How does silane invert (its configuration)?

March 16th, 2017

In the previous post, I found intriguing the mechanism by which methane (CH₄) inverts by transposing two of its hydrogens. Here I take a look at silane, SiH₄.

It appears it is a three-stage process! Firstly, silane eliminates molecular hydrogen to form a molecular complex between H₂and SiH₂ (DOI: 10.14469/hpc/2290). The barrier (~60 kcal/mol) is very much lower than with methane.

The H₂ component of this complex then rotates (DOI: 10.14469/hpc/2289) transposing atoms 1 and 2. The barrier for this process is tiny (~4 kcal/mol).

Finally, the rotated H₂/SiH₂ complex goes back to silane by the first route, but now with the two hydrogens transposed.

So this inversion is a stepwise process in contrast to methane which was concerted, albeit with “frustrated” elimination of hydrogen. Again a little molecule can show us so much chemistry, in this case also illustrating the avoidance of a Woodward-Hoffmann forbidden cheletropic elimination by desymmetrisation.

Tags: Chemistry, Industrial gases, Methane, SiH2 complex, Silanes
Posted in reaction mechanism | No Comments »

How does methane invert (its configuration)?

March 16th, 2017

This is a spin-off from the table I constructed here for further chemical examples of the classical/non-classical norbornyl cation conundrum. One possible entry would include the transition state for inversion of methane via a square planar geometry as compared with e.g. NiH₄ for which the square planar motif is its minimum. So is square planar methane a true transition state for inversion (of configuration) of carbon?

The history of this topic is nicely told as far back as 1993[1], when square planar methane was shown to be a 4th-order saddle point (i.e. four negative force constants) and not the first order one required of a transition state. A true transition state was located,^‡ and here I show it as part of an animated IRC (intrinsic reaction coordinate). Go to DOI: 10.14469/hpc/2288 for the calculation outputs.

To convince yourself that the configuration really does invert, focus on the CIP rule. With atom 1 pointing behind, atoms 2 → 3 → 4 rotate in a clockwise direction. Now focus on the final point at the end of the IRC, when 2 → 3 → 4 rotate anti-clockwise. The configuration has inverted! The barrier as can be seen below is ~118 kcal/mol. At this value the half-life for the process would be far longer than the age of the universe.

The process can be described as an interesting variation on pseudorotation, for which the classic example is of course PF₅.^† Alternatively it can be thought of as the partial extrusion of H₂ to give carbene, followed by re-addition of the H₂ to reform methane. Partial because the extrusion is never fully achieved.

I have to say I did not expect anything quite so interesting to be associated with methane; one can learn from the simplest of molecules!

^‡ It was not entirely trivial to recover appropriate coordinates for recomputing this TS from the article. But it is in fact an easy one to find from scratch. Hopefully with the files at 10.14469/hpc/2288 to help, this will not be an issue here.

^†There are many kinds of pseudo-rotations. For others see here.[2] and [3]

References

M.S. Gordon, and M.W. Schmidt, "Does methane invert through square planar?", Journal of the American Chemical Society, vol. 115, pp. 7486-7492, 1993. https://doi.org/10.1021/ja00069a056
H.S. Rzepa, and M.E. Cass, "A Computational Study of the Nondissociative Mechanisms that Interchange Apical and Equatorial Atoms in Square Pyramidal Molecules", Inorganic Chemistry, vol. 45, pp. 3958-3963, 2006. https://doi.org/10.1021/ic0519988
H.S. Rzepa, and M.E. Cass, "In Search of the Bailar and Rây−Dutt Twist Mechanisms That Racemize Chiral Trischelates: A Computational Study of ScIII, TiIV, CoIII, ZnII, GaIII, and GeIV Complexes of a Ligand Analogue of Acetylacetonate", Inorganic Chemistry, vol. 46, pp. 8024-8031, 2007. https://doi.org/10.1021/ic062473y

Tags: Chemistry, Methane, Molecular geometry, Orbital hybridisation, Planar, Square planar molecular geometry, Stereochemistry
Posted in reaction mechanism | 2 Comments »

Expanding on the curious connection between the norbornyl cation and small-ring aromatics.

March 12th, 2017

This is another of those posts that has morphed from an earlier one noting the death of the great chemist George Olah. The discussion about the norbornyl cation concentrated on whether this species existed in a single minimum symmetric energy well (the non-classical Winstein/Olah proposal) or a double minimum well connected by a symmetric transition state (the classical Brown proposal). In a comment on the post, I added other examples in chemistry of single/double minima, mapped here to non-classical/classical structures. I now expand on the examples related to small aromatic or anti-aromatic rings.

Examples of symmetric energy potentials
System	Classical with 1 imaginary normal mode	Non-classical with 0 imaginary modes
Norbornyl cation	TS for [1,2] sigmatropic	Minimum, this post
Singlet [6], [10]; 4n+2 annulenes	–	Minimum with Kekulé vibration
Singlet [4], [8]; 4n annulenes	TS for bond shift, 1 imaginary normal mode	–
Triplet [4], [8]; 4n annulenes	–	Minimum, with Kekulé vibration (?)
Semibullvalenes	TS for [3,3] sigmatropic	Minimum
Strong Hydrogen bonds	TS for proton transfer	Minimum
S_N2 substitutions	TS for substitution (C)	Minimum (Si)
Jahn-Teller distortions	Dynamic Jahn-Teller effects	No Jahn-Teller distortions

In the table above, you might notice a (?) associated with the entry for (aromatic) triplet state 4n annulenes. Here I expand the ? by considering triplet cyclobutadiene and triplet cyclo-octatetraene (ωB97XD/Def2-TZVPP, 10.14469/hpc/2241 and 10.14469/hpc/2242 respectively). Each has a normal vibrational mode shown animated below, which oscillates between the two Kekulé representations of the molecule with wavenumbers of 1397 and 1744 cm^-1 respectively. These Kekulé modes are both real, which indicates that the symmetric species (D_4h and D_8hsymmetry) is in each case the equilibrium minimum energy position (r_CC 1.431 and 1.395Å). For comparison the aromatic singlet state 4n+2 annulene benzene (r_CC 1.387Å) has the value 1339 cm^-1. Notice that both the triplet state wavenumbers are elevated compared to singlet benzene, because in each case the triplet ring π-bond orders are lower, thus decreasing the natural tendency of the π-system to desymmetrise the ring.[1]

To complete the theme, I will look at singlet cyclobutadiene. According to the table above, the symmetric form should be a transition state (TS) for bond shifting, with one imaginary normal mode. To calculate this mode, one has to use a method that correctly reflects the symmetry, in this case a CASSCF(4,4)/6-311G(d,p) wavefunction (DOI: 10.14469/hpc/2244). The mode (r_CC 1.444Å) shown below has a wavenumber of 1477i cm^-1;its vectors of course resemble those of the triplet mode, but its force constant is now negative rather than positive!

At first sight any connection between the property of the norbornyl cation at the core of the controversies all those decades ago and aromatic/antiaromatic rings might seem tenuous. But in the end many aspects of chemistry boil down to symmetries and from there to Évariste Galois, who started the ball rolling.

References

S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l

Tags: antiaromaticity, aromaticity, Carbocation, Chemistry, equilibrium minimum energy position, Évariste Galois, George Andrew Olah, George Olah, great chemist, Jahn-Teller, minimum symmetric energy, Olah, Physical organic chemistry, Saul Winstein, symmetric energy potentials
Posted in Interesting chemistry | No Comments »

George Olah and the norbornyl cation.

March 10th, 2017

George Olah passed away on March 8th. He was part of the generation of scientists in the post-war 1950s who had access to chemical instrumentation that truly revolutionised chemistry. In particular he showed how the then newly available NMR spectroscopy illuminated structures of cations in solvents such “Magic acid“. The obituaries will probably mention his famous “feud” with H. C. Brown over the structure of the norbornyl cation (X=CH₂⁺), implicated in the mechanism of many a solvolysis reaction that characterised the golden period of physical organic chemistry just before and after WWII.

The dispute between Olah and Brown was not played on a pitch using quite the same goal posts. Olah did much of his work in magic acid and Brown did his in aqueous solutions. I was involved in a tiny way when the discussion about the precise character of the norbornyl cation was reaching its peak in the mid 1970s. At the time, I was working with Michael Dewar, who was himself not shy in joining in the fun and sometimes very acrimonious disputes at conferences. We contributed by calculating the so-called core-electron carbon ESCA spectrum.[1] History records that we came down on the wrong side,^‡ by suggesting that this form of spectroscopy supported Brown rather than Winstein/Olah on the basis of a 6:1 spectral deconvolution (classical) rather than 5:2 (non-classical). More recently of course the crystal structure of the parent cation itself has been shown to be non-classical[2] (there are other crystal structures which differ in respect to having one or more additional methyl groups[3]). For a 3D model of norbornyl cation, see DOI: 10.5517/CCZ21LN. This still leaves the issue (very slightly) open for the structure of the solvated cation when formed in water!

When I started to teach a course in molecular modelling, I touched briefly on how modelling could contribute and whilst updating the notes in the 1990s, wondered why the boron analogue had never been so studied (X=BH₂). Unlike the crystallographically difficult norbornyl ion-pair, the iso-electronic boron species would be neutral and not need a counter-ion. Perhaps it might be a more manageable molecule? Checking the Cambridge structural database, such a species has never been reported!^† So here as my homage to Olah, I report its calculated structure (b2plypd3/Def2-TZVPP, DOI: 10.14469/hpc/2236).

The norbornyl cation has symmetrical C-C bridging distances of ~1.80±0.02Å and a basal C-C distance of ~1.39±0.02Å. The calculated values for the boron equivalent are 2.16Å and 1.36Å respectively, with all positive force constants. B-C bonds are normally 1.66-1.72Å, significantly longer than C-C bonds, which makes the longer B-C lengths in this example unsurprising. More interestingly, the species has one vibrational normal mode (ν 203 cm^-1) which corresponds to the [1,2] shift of the BH₂group across the basal C-C. For a classical species, this vibrational motion would correspond to a transition state (an imaginary vibration) but for a non-classical species it is of course real. In this sense it is analogous to the so-called real Kekulé mode in non-classical benzene, which “equilibrates” the two classical Kekulé structures. The corresponding calculated vibration for the norbornyl cation itself is ν 194 cm^-1 (DOI: 10.14469/hpc/2238).

Of course, the entire controversy over the structure of this species is littered with comparisons between not quite similar systems, differing in a methyl group more or less. So morphing a C⁺ to a B might be seen as quite a large change. But perhaps if it had been crystallised in say the 1960s, would the subsequent debates have taken a different turn?

^‡ We were also wrong about the symmetry of the Diels-Alder cyclisation, which is nowadays accepted to be synchronous rather than asynchronous for simple Diels-Alder reactions. But that is another story.

^†GAXLIA is perhaps the closest analogue.[4],

References

M.J.S. Dewar, R.C. Haddon, A. Komornicki, and H. Rzepa, "Ground states of molecules. 34. MINDO/3 calculations for nonclassical ions", Journal of the American Chemical Society, vol. 99, pp. 377-385, 1977. https://doi.org/10.1021/ja00444a012
F. Scholz, D. Himmel, F.W. Heinemann, P.V.R. Schleyer, K. Meyer, and I. Krossing, "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation", Science, vol. 341, pp. 62-64, 2013. http://dx.doi.org/10.1126/science.1238849
T. Laube, "Redetermination of the Crystal Structure of the 1,2,4,7‐anti‐tetramethylbicyclo[2.2.1]heptan‐2‐yl cation at 110 K", Helvetica Chimica Acta, vol. 77, pp. 943-956, 1994. https://doi.org/10.1002/hlca.19940770407
P.J. Fagan, E.G. Burns, and J.C. Calabrese, "Synthesis of boroles and their use in low-temperature Diels-Alder reactions with unactivated alkenes", Journal of the American Chemical Society, vol. 110, pp. 2979-2981, 1988. https://doi.org/10.1021/ja00217a053

Tags: 2-Norbornyl cation, aqueous solutions, Chemical bond, chemical instrumentation, Chemistry, George Andrew Olah, George Olah, Ion association, Magic acid, Michael Dewar, Molecule, Nature, Physical organic chemistry, Reactive intermediates, spectroscopy
Posted in Interesting chemistry | 18 Comments »

Ammonium tetraphenylborate and the mystery of its π-facial hydrogen bonding.

March 10th, 2017

A few years back, I did a post about the Pirkle reagent[1] and the unusual π-facial hydrogen bonding structure[2] it exhibits. For the Pirkle reagent, this bonding manifests as a close contact between the acidic OH hydrogen and the edge of a phenyl ring; the hydrogen bond is off-centre from the middle of the aryl ring. Here I update the topic, with a new search of the CSD (Cambridge structure database), but this time looking at the positional preference of that bond and whether it is on or off-centre.

The search (February 2017 database, DOI:10.14469/hpc/2233) is shown above, QA = N, O, F, Cl and other constraints are R < 0.01, no errors, no disorder. Two distances are plotted, one (DIST1) is from the H to the ring centroid and the second (DIST2) from the H to an edge carbon atom. The colour code relates to ANG1, the angle subtended at the centroid. A value of 90° would indicate the H is orthogonal to the plane of the aromatic ring.

You can see from the above that the yellow dots correspond to ~90° and that by and large the H…centroid distances are shorter than the H…C distances.

The above is another representation of this search, again showing that the preferred angle is 90°, although there is a fair bit of scatter. The extreme outliers may be crystallographic errors, but one point caught my eye and is circled in red above; ammonium tetrafluoroborate (3D model DOI: 10.5517/CC4V6TZ). This has a very short distance from the H to the centroid (2.07Å), shorter than the Pirkle reagent that we looked at all those years back. The authors[3] note that “The N-H…Ph distances, H…M 2.067Å … are exceptionally short (M = aromatic midpoint)” but also that “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system.” This implies that such bonds are largely agnostic about whether they bind to the centroid of the ring or to its edge and that the most probable position might arise simply because of crystal packing. An interesting variation on this molecule is a crystal that includes a further 5NH₃ in addition to ammonium tetraphenylborate (3D model DOI: 10.5517/cc7bly2). Here an ammonia intervenes between the ammonium cation and a phenyl ring, resulting in a binding of the ammonia with two NHs closer to the edge of the ring and one NH interacting in parallel mode.

Time therefore for a calculation, using B3LYP+GD3BJ/Def2-TZVPP, the functional being chosen because the dispersion contribution is not built in, but uses what is currently thought to be the best representation of these attractions. The issue now is what molecular unit to use? This is an ionic structure and so a periodic boundary model is most appropriate, but given its size I reduced this to two models comprising smaller discrete fragments.

A unit just comprising the simple ion pair. This leaves two of the four N-H bonds devoid of hydrogen bonding (DOI:10.14469/hpc/2234). The optimisation adopts a pose where two NH groups are directed towards a carbon atom rather than the ring centroid. How much of this is due to the smallness of this model?
A unit comprising a double ion pair, which allows one ammonium group to participate with all four NH groups across four phenyl rings and exhibiting six NH interactions in total with six rings (DOI: 10.14469/hpc/2235). The NH hydrogen vectors all interact with ring carbons rather than the ring centroid.

This brief computational exploration has covered only one method (the B3LYP DFT procedure), albeit with what is thought to be a good dispersion attraction term added and a reasonable basis set. It does seem to show that hydrogen bonds interacting with the centroid of a phenyl ring are not the preferred mode, which is instead an interaction with the edge of the ring. The quote above, “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system” suggests that whilst the average position might be the centroid, a true hydrogen bond to the centroid might be rarer than thought. Although most of the crystallographic examples located in the searches above deem to show a preference for the ring centroid, this might be more apparent than real.

References

H.S. Rzepa, M.L. Webb, A.M.Z. Slawin, and D.J. Williams, "? Facial hydrogen bonding in the chiral resolving agent (S)-2,2,2-trifluoro-1-(9-anthryl)ethanol and its racemic modification", Journal of the Chemical Society, Chemical Communications, pp. 765, 1991. https://doi.org/10.1039/c39910000765
H.S. Rzepa, M.H. Smith, and M.L. Webb, "A crystallographic AM1 and PM3 SCF-MO investigation of strong OH ⋯π-alkene and alkyne hydrogen bonding interactions", J. Chem. Soc., Perkin Trans. 2, pp. 703-707, 1994. https://doi.org/10.1039/p29940000703
T. Steiner, and S.A. Mason, "Short N+—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318

Tags: Ammonia, Ammonium, aromaticity, Cations, Centroid, chemical bonding, Chemistry, Hydrogen bond, Phenyl group
Posted in crystal_structure_mining | No Comments »

A nice example of open data (in London).

March 5th, 2017

Living in London, travelling using public transport is often the best way to get around. Before setting out on a journey one checks the status of the network. Doing so today I came across this page: our open data from Transport for London.

I learnt that by making TFL travel data openly available, some 11,000 developers (sic!) have registered for access, out of which some 600 travel apps have emerged.
The data is in XML, which makes it readily inter-operable.[1]
This encourages crowd-sourced innovation.
They have taken the trouble to produce an API (application programmable interface) which allows rich access to the data and information about e.g. AccidentStats, AirQuality, BikePoint, Journey, Line, Mode, Occupancy, Place, Road, Search, StopPoint Vehicle.

Chemists could learn some lessons here! Of course, there are quite a few chemical databases with APIs that are examples of open data, but the “ESI” (electronic supporting information) sources which almost all published articles rely upon to disseminate data are clearly struggling to cope. Take for example this recent article[2], where much of the data has been dropped into the inevitable PDF “coffin” and which is a breathtaking 907 pages long. To give the authors their due, they also provide 20 CIF files which ARE good sources of data. Rarely commented on, but clearly missing from the information associated with this (indeed most) articles is the metadata about the data. Thus the metadata for these CIF files amounts to just e.g. 229. To find out the context, one has to scour the article (or the 907 pages of the ESI) to identify compound 229 (I strongly suspect it’s a molecule because of the implied semantics of the term, not because its been explicitly declared). You will not find the metadata at e.g. data.datacite.org which is one open aggregator and global search engine based on deposited metadata.

I have commented elsewhere on this blog that other types of data could also be enhanced in the manner that CIF crystallographic files represent. For example the Mpublish NMR project,^‡ examples of which are shown here, and for which typical data AND its metadata can be seen at DOI: 10.14469/hpc/1053. I fancy that if this method had been adopted,[2] those 907 pages might have shrunk somewhat, although of course not entirely. But my hope is that gradually the innovative chemistry community will find ways of exhuming more and more data from the PDF coffin and in the process reducing the paginated lengths of the PDF-based ESI further, perchance eventually even to zero?

If you are yourself preparing an article and sweating over the ESI at this very moment, do please take a look at the Mpublish method and how perhaps it can help make your NMR data at least more useful to others.

^‡I understand an article describing this project is in preparation. If you cannot wait, this recent application of the Mpublish project has some details.[3]

References

P. Murray-Rust, and H.S. Rzepa, "Chemical Markup, XML, and the Worldwide Web. 1. Basic Principles", Journal of Chemical Information and Computer Sciences, vol. 39, pp. 928-942, 1999. https://doi.org/10.1021/ci990052b
J.M. Lopchuk, K. Fjelbye, Y. Kawamata, L.R. Malins, C. Pan, R. Gianatassio, J. Wang, L. Prieto, J. Bradow, T.A. Brandt, M.R. Collins, J. Elleraas, J. Ewanicki, W. Farrell, O.O. Fadeyi, G.M. Gallego, J.J. Mousseau, R. Oliver, N.W. Sach, J.K. Smith, J.E. Spangler, H. Zhu, J. Zhu, and P.S. Baran, "Strain-Release Heteroatom Functionalization: Development, Scope, and Stereospecificity", Journal of the American Chemical Society, vol. 139, pp. 3209-3226, 2017. https://doi.org/10.1021/jacs.6b13229
M.J. Harvey, A. McLean, and H.S. Rzepa, "A metadata-driven approach to data repository design", Journal of Cheminformatics, vol. 9, 2017. https://doi.org/10.1186/s13321-017-0190-6

Tags: API, chemical databases, City: London, Company: TfL, Government, Greater London, Local government in London, London, Passenger Transportation Ground & Sea - NEC, PDF, Public transport, Route planning software, search engine, Sustainable transport, Technology/Internet, Transport, Transport for London, travel apps, travel data, XML
Posted in Chemical IT | No Comments »

Stable "unstable" molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

March 5th, 2017

Cyclobutadiene is one of those small iconic molecules, the transience and instability of which was explained theoretically long before it was actually detected in 1965.[1] Given that instability, I was intrigued as to how many crystal structures might have been reported for this ring system, along with the rather more stable congener cyclo-octatetraene. Here is what I found.

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified).

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

The three clusters deserve explanations. The orange cluster reveals a long C-C bond (rather longer than normal C-C bonds), accompanied by short C=C bonds, as indicated by the valence bond form shown below. Take particular note that the arrow connecting the two forms is NOT a resonance arrow but an equilibrium arrow. The “bond shifting” is not fast but slow, allowing long and short bonds to be measured in a crystal structure.

The rather larger blue cluster exhibits much more equal bonds. These arise from the presence of “push-pull” substituents on the ring which serve to delocalise the unfavourable cyclobutadiene ring and hence decrease the unfavourable anti-aromaticity. A typical example is shown below (EACBUT):

The small red cluster shows a long C=C bond and a short C-C bond! I have commented previously on apparently abnormally long C=C bonds, which in fact all turned out to be errors, and I suspect the same is true here. The bond orders in the indexing in the CSD data base have probably been mis-assigned, as per below for GANBII;

The Conquest search query is shown (with no disorder, no errors and R < 0.1 specified) for the 8-ring, which further specifies a torsion angle about a C-C bond to determine how planar the ring might be.

The “normal” cluster in the top left exhibits long C-C bonds and short C=C bonds. The colour code indicates how planar the ring is (red-blue spectrum = twisted ⇒ planar). The majority of examples are twisted about the C-C bond(s), but there are a few interesting examples that are not, as shown by the blue dots. There are only a few “bond-equalised” examples in the centre; perhaps “push-pull” induced equalisation is more difficult or perhaps few examples have been made?

The members of the red cluster in the bottom right all reveal short “C-C” bonds and long “C=C” bonds. Intriguingly they all also have low values of the torsion about one C-C bond (although not always about all four C-C bonds). A typical example (BAQVUK, DOI: 10.5517/CC4GWWB ) is shown below. These all need careful inspection and possibly reversal of the C-C and C=C indexing.

It was interesting to discover how many crystalline examples of this archetypal “unstable” cyclobutadiene motif have been made, and the means by which some of them at least have been stabilized. In the more abundant cyclo-octatetraene system, I learnt that one has to be cautious about blindly accepting the bond order designations in the database. Perhaps we might learn here that some of these have indeed been re-assigned in the next release of the database.

References

L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

Tags: antiaromaticity, Chemistry, cyclobutadiene, Instability, Nature, Physical organic chemistry, Physics, search query
Posted in crystal_structure_mining | 4 Comments »

Stable “unstable” molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

March 5th, 2017

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified).

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

References

L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

Tags: antiaromaticity, Chemistry, cyclobutadiene, Instability, Nature, Physical organic chemistry, Physics, search query
Posted in crystal_structure_mining | 4 Comments »

More tetrahedral fun. Spherical aromaticity (and other oddities) in N4 and C4 systems?

March 2nd, 2017

The thread thus far. The post about Na₂He introduced the electride anionic counter-ion to Na⁺ as corresponding topologically to a rare feature known as a non-nuclear attractor. This prompted speculation about other systems with such a feature, and the focus shifted to a tetrahedral arrangement of four hydrogen atoms as a dication, sharing a total of two valence electrons. The story now continues here.

What emerged during comments about H₄²⁺ was that a density functional (DFT) derived wavefunction seemed to predict it to be a stable minimum, but that wavefunctions derived from coupled cluster or CASSCF methods predicted it to be a three-fold degenerate transition state instead. So I asked myself if perhaps other similar tetrahedral molecules less susceptible to such method ambiguity might be found. Here I record some of the species I investigated.

N₄ in a tetrahedral allotropic arrangement of the element (ωB97XD/Def2-TZVPP DFT method: 10.14469/hpc/2217 and CCSD(T)/Def2-TZVPP 10.14469/hpc/2216). I found this intriguing, because each nitrogen has a lone pair of electrons and such an arrangement of eight electrons might be spherically aromatic according to the rule: 2(n+1)², where n=1[1]. N₄itself is indeed a true minimum (r_N-N 1.460Å) with all positive force constants at both the DFT (767, 1005 and 1443) and CCSD(T) (726, 940 and 1304 cm^-1) levels, but with a free energy ~185 kcal/mol higher than dinitrogen. The electronic topology is uneventfully classical, with six line (bond) critical points along each N-N axis (magenta), four ring critical points (green) and one cage point (inner blue sphere); there is no non-nuclear attractor present.The NICS value at the centre of the tetrahedron (coincident with the cage critical point) is -73 ppm, which does suggest aromaticity.
C₄ in a tetrahedral allotropic arrangement of this element is also a minimum as closed shell singlet (r_C-C1.646Å) again with positive force constants (ωB97XD/Def2-TZVPP DFT, 10.14469/hpc/2224, 434, 715, 1052 cm^-1) and the same electronic topology as N₄.
The magnetic shielding at the ring centre is -1685 ppm, a value clearly perturbed by core ring currents or other factors; the molecule does not map to the 2(n+1)²spherical aromaticity rule, which only allows values of 2,8,18, 32… electrons. I tried applying the ELF procedure using the computed WFN file (either direct or symmetrised, using both TopMod and MultiWFN) but the results did not have T_d symmetry.^‡
C₄²⁺ with two fewer electrons is also a minimum as a closed shell singlet (r_C-C 1.521Å) tetrahedral species (ωB97XD/Def2-TZVPP: 10.14469/hpc/2218, 1132, 1136, 1448 cm^-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2225 showing rather different normal mode energies of ~330, 592, 1126 cm^-1) which can be thought as mapping to the spherical aromaticity formula 2(n+1)², where n=0. The electronic topology is slightly different from C₄ itself, with four ring points (green) very close to the cage point in the centre.The ELF function now behaves itself in terms of symmetry, and produces a result in fact very similar to the H₄²⁺ molecule which started this topic rolling. There is an ELF basin with 0.14e located in the centroid and six equivalent basins (2.25e) spanning each pair of carbon atoms, although these C-C bonds are hugely banana shaped! That central electron basin closely resembles the one found in H₄²⁺ itself. The magnetic shielding at the centre of 3349 ppm is not meaningful in deciding if the molecule is indeed “aromatic”.
C₄^1- is again a tetrahedral minimum, this time as a quartet ⁴A₁ state (ωB97XD/Def2-TZVPP: 10.14469/hpc/2219, 918, 1024, 1377 cm^-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2237, 824, 895, 1303 cm^-1). The electronic topology is the same as before.Open shell spherical aromaticity[2] is given by the 2N² + 2N + 1 (with S = N + ½) rule. A quartet state has S=3/2, hence N=1 and the formula stipulates 5 delocalizable electrons for aromaticity, which this species has! The isotropic magnetic shielding is 695 ppm, which again is not immediately helpful.The ELF analysis ((above) shows just two types of basin, with four “lone pairs” at each carbon vertex (1.24e) and eight associated with the C-C “bent” bonds (1.95e).

What did I learn?

Firstly, that the (very unstable) tetrahedral allotrope of nitrogen might be a spherical aromatic.
Secondly, that tetrahedral closed-shell singlet C₄ has a very odd wavefunction; this needs further work.
Thirdly that tetrahedral C₄²⁺ closely resembles H₄²⁺ in having a basin of electrons at the very centre, but that unlike H₄²⁺ it does appear to be a stable minimum.
Finally, that the radical anion C₄^– might be perhaps the smallest possible example of an open shell spherical aromatic.

And perhaps also in trying to answer some simple questions, I have also raised several more puzzles. Onwards and occasionally upwards.

^‡This wavefunction is clearly odd, and needs further analysis.

References

A. Hirsch, Z. Chen, and H. Jiao, "Spherical Aromaticity inIh Symmetrical Fullerenes: The 2(N+1)2 Rule", Angewandte Chemie, vol. 39, pp. 3915-3917, 2000. https://doi.org/10.1002/1521-3773(20001103)39:21<3915::aid-anie3915>3.0.co;2-o
J. Poater, and M. Solà, "Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule", Chemical Communications, vol. 47, pp. 11647, 2011. https://doi.org/10.1039/c1cc14958j

Tags: chemical bonding, Chemistry, Electride, free energy, Ion, Nature, Physical chemistry, Valence electron
Posted in Interesting chemistry | 1 Comment »

The H4 (2+) dication and its bonding.

February 15th, 2017

This post arose from a comment attached to the post on Na₂He and relating to peculiar and rare topological features of the electron density in molecules called non-nuclear attractors. This set me thinking about other molecules that might exhibit this and one of these is shown below.

The topology of the electron density is described by just four basic types, designed formally by the notation [3,-3], [3,-1], [3,1] and [3,3] and more colloquially by the terms nuclear attractor (NNA), line (or bond) critical point, a ring critical point and a cage critical point respectively. Mostly, the nuclear critical points coincide exactly with the actual nuclear positions, but more rarely these points are not found centered at a nucleus. It was such an NNA that was suggested as a comment on the post on Na₂He. There I replied that another example of an NNA is to be found in H₃⁺ and so its a short step to take a look at H₄²⁺ in a tetrahedral arrangement (DOI: 10.14469/hpc/2165). Since only two electrons are available for bonding, it is tempting to represent it as below, with dashed partial bonds connnecting the six edges of the tetrahedron and is associated with real normal vibrational modes; ν 416, 1490 and 1861 cm^-1. A brief search on Scifinder, which appears to reference this species as hydrogen, ion (H₄²⁺), does not identify any publications associated with it (there are studies on H₄¹⁺ however); if any reader here knows of any discussion please alert us!

Analysing the density however gives a different result. A NNA is located at the centre of the tetrahedron and a line (bond) critical point connects this to each of the four hydrogen nuclei. This result is similar to the obtained for H₃⁺. It is rather odd that these non-nuclear attractors have not entered into the vocabulary used to describe the bonding in simple molecules, but this picture is certainly different from the more empirical dashed lines between the four nuclei that one is instinctively drawn to use (above).

The ELF analysis (performed using multiWFN) is more interesting. The nuclear basins associated with the hydrogens reveal each has 0.425e, but the central one (green below) has its own basin with 0.301e.

The NICS value associated with the non-nuclear attractor is -27 ppm, which is indicative of strong spherical aromaticity.

All of which goes to show that even the simplest of molecular species may still have properties that are unexpected or certainly not well-known!

Tags: Attractor, brief search, Chemistry, Electron, Electron density, Hydrogen, Molecule, Nature, Physics, Quantum chemistry
Posted in Interesting chemistry | 11 Comments »

Henry Rzepa's blog

How does silane invert (its configuration)?

How does methane invert (its configuration)?

References

Expanding on the curious connection between the norbornyl cation and small-ring aromatics.

References

George Olah and the norbornyl cation.

References

Ammonium tetraphenylborate and the mystery of its π-facial hydrogen bonding.

References

A nice example of open data (in London).

References

Stable "unstable" molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

References

Stable “unstable” molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

References

More tetrahedral fun. Spherical aromaticity (and other oddities) in N4 and C4 systems?

References

The H4 (2+) dication and its bonding.

Recent Posts

Archives

Blogroll

Meta