Tag: Chemical bond

The “hydrogen bond”; its early history.
My holiday reading has been Derek Lowe’s excellent Chemistry Book setting out 250 milestones in chemistry, organised by year. An entry for 1920 entitled hydrogen bonding seemed worth exploring in more detail here.

As with many historical concepts, it can often take a few years to coalesce into something we would readily recognise today, and hydrogen bonds are no exception. Wikipedia is another source of the history and it cites a 1912 article as the origin of the term in relation to the solvation of amines[cite]10.1039/CT9120101635[/cite] but also notes that the better known setting of water occurs later in 1920.[cite]10.1021/ja01452a015[/cite] Here I try to capture the essence of the concept with a few diagrams taken from these two articles.

Firstly “The state of amines in aqueous solution“[cite]10.1039/CT9120101635[/cite] which is mostly concerned with the measurement of ionization constants of primary, secondary and tertiary amines. It boils down to the below:

and the connection to ionization is laid out as:

Since in 1912, Lewis’ electron pair theory of the covalent bond had not yet emerged, the authors use the terms “strong union” and “weak union”, and of course it is the “weak union” that we now know of as the hydrogen bond. Some other comments about this seminal diagram:
1. The article contains the very explicit and modern term stereochemical, which is used in a manner that suggests it was already common.^‡ But there is only a hint at most that the nitrogen atoms might be tetrahedral, or that the “weak union” between (what we now think of as the lone pair on) the nitrogen and the hydrogen of the water is directional.
2. The second weak union between the tetramethyl ammonium (which we now describe as a cation) and the hydroxide (now described as an anion; both terms are however implied by the description strong electrolyte) is probably not what we would now call a hydrogen bond, more an intimate ion-pair.
The second article in 1920 on water itself[cite]10.1021/ja01452a015[/cite] is post-Lewis, but perhaps applied in a manner which we would not entirely agree with nowadays. Thus dinitrogen, N≡N is shown as below with just a single connecting bond.

Then we get the interaction between ammonia and water,^† analogous to the example shown above:

and for water itself:^♠

which in each case shows the central hydrogen having what we now call a valence shell of four electrons,^♣ and hence more equivalent to the “strong unions” above. This shows that in 1920 chemists were rapidly adopting Lewis’ representations, but not always entirely successfully.

On balance, I think the 1912 article sets out the modern concept of a hydrogen bond representing a weak union to a hydrogen rather better than the Latimer and Rodebush attempt (at least diagrammatically).

^‡Stereochemical notation is discussed in this post, and it dates from the 1930s.

^†The modern take is explored here, in which the equilibrium set up between a “weak union” between ammonia and water (the weak electrolyte) and an isomeric “strong union” which represents ionization into an ammonium hydroxide ion-pair (the strong electrolyte) is favoured for the former by ΔG ~6 kcal/mol.

^♠The equilibrium between a “weak union” of two water molecules and the fully ionized strong union of hydronium hydroxide favours the former by ΔG ~23 kcal/mol.

^♣ This 1920 representation does imply symmetry for the hydrogen, being ~equally disposed between the two oxygens. We now know that such symmetric hydrogen bonding is not unusual (see this post for how to fine-tune a hydrogen bond into this situation) but rather than requiring four electrons as implied in the diagram above, it is now better described as a three-centre-two-electron bond instead.

This post has DOI: 10.14469/hpc/10732
December 31, 2016
Long C=C bonds.

Following on from a search for long C-C bonds, here is the same repeated for C=C double bonds.

The query restricts the search to each carbon having just two non-metallic substituents. To avoid conjugation with these, they each are 4-coordinated; the carbons themselves are three-coordinated. Further constraints are the usual no disorder, no errors and R < 0.1 and the C=C distance > 1.4Å (the standard value is ~1.32-1.34Å). The search query is deposited as DOI: 10.14469/hpc/1959[cite]10.14469/hpc/1959[/cite]

The apparent longest example is LIRVEN, DOI: 10.5517/CC4R2MK[cite]10.5517/CC4R2MK[/cite] with a value of 1.589Å, longer than most C-C single bonds! Closer inspection reveals the presence of lithium cations, and so the molecule bearing the C=C bond must sustain two negative charges. So this apparent C=C bond is in fact anionic, with one electron going into each of the π* orbitals, thus lengthening the CC bond.^‡ Not a true example of a neutral C=C bond[cite]10.1016/S1387-7003(99)00136-7[/cite] but it now becomes interesting for what its spin state might be. Is it a biradical or a triplet for example? One to be investigated further I fancy! Another example of this type is QUKCEE[cite]10.1246/bcsj.73.1461[/cite]

This next FAZWIM has a C=C length of 1.546Å. It is an old structure (1986), and comes without attached hydrogen atoms. Although drawn with no hydrogens on the central C=C bond, the length suggests this molecule is simply mis-assigned.^†

The final example I will highlight is pretty ordinary looking and published in 2016 as a private communication; ALOVOO, DOI: 10.5517/CCDC.CSD.CC1LJSWS[cite]10.5517/CCDC.CSD.CC1LJSWS[/cite] with a C=C length of 1.443Å. Again no obvious reason for the bond to be longer than normal.^‡†

In hunting for such unusual deviations from the norm, the most obvious explanation is normally some anomaly in the crystallographic analysis. Although the CSD (crystal structure database) is a very heavily curated resource, it seems unlikely that each deposition would be carefully inspected for its chemistry, and this must be our task here. But such anomalies can themselves point to interesting or unusual chemistry, which in turn can be subjected to quantum computation to see if either the unusual value can be replicated or other reasons identified. In this case, this exercise can been conducted by a human, but one can easily envisage the entire process being automated on a far larger scale. The future?

^‡ In fact the stoichiometry shows each “double bond” is actually a di-anion, with two electrons entering each of the the π* orbitals.

^†A calculation on the singlet state for the structure as drawn (ωB97XD/Def2-TZVPP, DOI: 10.14469/hpc/1960) gives a bond length of 1.342Å, i.e. that expected for a double bond. The triplet state is similar in energy, but with a much longer central bond length of 1.476Å, DOI: 10.14469/hpc/1962 but the geometry at the carbons is planar and not bent as shown above. The quintet state is 1.45Å and is again planar, doi 10.14469/hpc/1963. So calculations on FAZWIM strongly suggest the structure as shown is an error.

^‡†The computed value is 1.324Å, perfectly normal. DOI: 10.14469/hpc/1966[cite]10.14469/hpc/1966[/cite]

December 1, 2016
Long C-C bonds.

In an earlier post, I searched for small C-C-C angles, finding one example that was also accompanied by an apparently exceptionally long C-C bond (2.18Å). But this arose from highly unusual bonding giving rise not to a single bond order but one closer to one half! How long can a “normal” (i.e single) C-C bond get, a question which has long fascinated chemists.

A naive search of the CSD is not as straightforward as it seems. Using the simple sub-structure R₃C-CR₃ as the search query gives LIRPEI, DOI: 10.5517/CCQ043Y[cite]10.5517/CCQ043Y[/cite] an apparently unexceptional molecule with a very exceptional C-C distance of 1.87Å. With long bonds one has to be ultra-careful to look at the crystallographic analysis before drawing any conclusions. One class of molecule where this has been done by many groups is the system shown below (red = long bond), with 47 entries and for which the longest C-C bond emerges with the value of 1.79Å[cite]10.1016/j.tetlet.2009.03.202[/cite]

You can view this structure at DOI: 10.5517/CCS0R6Q[cite]10.5517/CCS0R6Q[/cite] and the authors go to some pains to assure us that it is still a closed shell single bond, and not a biradical. That does seem to be the current record holder, but of course we are only talking here about molecules whose crystal structure has been determined.

I will end with an open question; how SHORT could a “single” C-C bond get? Here, a search of the CSD is entirely dominated by crystallographic artefacts, and I am not sure what the value might be.

November 30, 2016
A periodic table for anomeric centres, this time with quantified interactions.
The previous post contained an exploration of the anomeric effect as it occurs at an atom centre X for which the effect is manifest in crystal structures. Here I quantify the effect, by selecting the test molecule MeO-X-OMe, where X is of two types:
1. A two-coordinate atom across the series B-O and Al-S, and carrying the appropriate molecular charge such that X carries two lone pairs of electrons (thus the charge is 0 for O, but -3 for B).
2. A four-coordinate atom across the series B-O and Al-S, with X-H bonds replacing the lone pairs on this centre in the previous example, and again with appropriate molecule charges (e.g. +2 for SH₂).
The donor in the anomeric interaction always originates on the oxygen of the MeO group attached to X. The acceptor is always the X-O σ* empty orbital. The results (table below, ωB97XD/Def2-TZVPP calculation, NBO E(2) in kcal/mol) confirm that as X gets more electronegative, the X-O σ* empty orbital becomes a better acceptor, and so the NBO E(2) interaction energy which quantifies the anomeric interaction gets larger. Eventually (with X=OH₂) the donation of electrons into the X-O σ* empty orbital becomes so effective that the X-O bond (in this case O-O) dissociates fully and the NBO perturbation cannot be computed. Also for reference, a “normal” anomeric interaction (such as is found in e.g. sugars) is around 18 kcal/mol. Anything larger than this could be considered especially strong, and anything less than ~10 kcal/mol would be regarded as weak.

X[cite]10.14469/hpc/1221[/cite]*

BH₂ CH₂ NH₂ OH₂

12.5 17.7 18.5 dissociates

AlH₂ SiH₂ PH₂ SH₂

6.9 12.9 21.9 31.3

B C N O

8.3 11.7 12.9 14.2

Al Si P S

4.8 6.6 11.2 18.2

For the entry X=S, the E(2) term is actually larger than for the oxygen. I should note that the Me group itself is not passive in this process. The C-H bonds can also act as significant electron donors, but here I am not going to analyse this additional complexity.

This table reveals that there is nothing special about carbon as an anomeric centre, and here also the normal intimate association with the term anomeric and heterocyclohexanes such as found in sugars.

* Here I introduce a refinement to my normal process of citing the data produced for any specific calculation. Rather than including 16 individual citations for each cell in the table, I have gathered all these calculations into a collection and cite here only the DOI of that collection. When resolved, the individual members of that collection can then be inspected for the actual data.
August 8, 2016
A periodic table for anomeric centres.

In the last few posts, I have explored the anomeric effect as it occurs at an atom centre X. Here I try to summarise the atoms for which the effect is manifest in crystal structures.

The effect is defined by X bearing two substituents, one of which Z is a centre bearing a “lone pair” of electrons (or two electrons in a π-bond), and another Y in which the X-Y bond has a low-lying acceptor or σ* empty orbital into which the lone pair can be donated. This donation will only occur if the Z-lone pair and the X-Y bond vectors align antiperiplanar. Here is the summary so far.

X Blog entry

B 16601

C 14508,8898

N this one

O 16646

Si 16601

P 16601

S this one

As required of a good periodic table, it has gaps that need completing, in this case X=N and X=S. Firstly N, for which the small molecule below is known (FUHFAP).

A ωB97XD/Def2-TZVPP calculation[cite]10.14469/ch/195294[/cite] yields an electron density distribution, which can be collected into monosynaptic basins using the ELF technique. There are two oxygen lone pairs (17 and 20) that are close to antiperiplanar to the adjacent N-O bond, having E(2) interaction energies obtained using the NBO method of 15.1 and 15.8 kcal/mol, typical of the anomeric range. The basin labelled 13 on X=N1 below is also perfectly aligned antiperiplanar with the adjacent O3-C2 bond, but its E(2) interaction energy is only 7.3 kcal/mol. Thus a strong anomeric interaction on the anomeric atom itself does not seem to occur. The same effect was noted for X=O in the previous post; the explanation remains unidentified.

With the X=S gap, we have lots of opportunity with polysulfide compounds, a good example of which is the C₂-symmetric and helical S₈ dianion TEGWAF[cite]10.5517/CCYKJ88[/cite]

Each of the 8 sulfur atoms exhibits antiperiplanar orientation of an S lone pair with an adjacent S-S acceptor σ* orbital;
1:2-3=23.7 kcal/mol;
2:3-4=18.5;
3:4-8=11.7, 3:2-1=7.4;
4:8-7=11.4, 4:3-2=9.2.

This just surveys the central main group elements, and it is possible that this little mini-periodic table may yet grow.

August 6, 2016
A wider look at π-complex metal-alkene (and alkyne) compounds.

Previously, I looked at the historic origins of the so-called π-complex theory of metal-alkene complexes. Here I follow this up with some data mining of the crystal structure database for such structures.

Alkene-metal "π-complexes" have what might be called a representational problem; they do not happily fit into the standard Lewis model of using lines connecting atoms to represent electron pairs. Structure 1 was the original representation used by Dewar intending the meaning of partial back donation from a filled metal orbital to the empty π* of the alkene. At the other extreme these compounds can be called metallacyclopropanes (2) in which only single bonds feature (these can be thought of as representing full back bonding from metal to alkene and full forward bonding from alkene to metal). Representations 3 and 4 are a more fuzzy blend of these, implying some sort of partial bond order for the metal-carbon bonds. Taken together, they imply that the formal bond order of the C-C bond might vary between single to double. Structures 1 and 2 in particular imply that there might be two distinct ways in arranging the bonding and that π-complexes and metallacyclopropanes might therefore be distinct valence-bond isomers, each potentially capable of separate existence.

Why do these representations matter? Well, I am going to mine the crystal structure database for these species to try to see if there is any evidence for a bimodal distribution in the C-C lengths, perhaps indicating evidence of the isomerism suggested above. Such a structural database is indexed against atom-pair connectivity in the first instance and then bond type; one can specify the following types of bond connecting any two atoms: single, double, triple, quadruple, polymeric, delocalised, pi and any. It is not entirely obvious which if any of these types apply to structure 1 (it is not possible to draw a bond ending at the mid-point of another bond using the Conquest structure editor); the dashed lines in structures 3 and 4 could be classed as delocalised, pi, or most generally any. The search query can be constructed thus, where the two carbons carry R which can be either H or C and all four C-R bonds are specified as acyclic (to try to avoid complications by excluding compounds such as cyclic metallacenes). Because representation 1 cannot be constructed in the editor, I am going to specify that each carbon carries four bonds of any type in the first instance. The torsion specified is defined as R-C-C-M and the full queries can be found deposited here.[cite]10.14469/hpc/642[/cite]

If the metallacyclopropane representation 2 is defined with explicit single bonds, one gets only 22 hits (no errors, no disorder, R < 0.1). The distribution of C-C bond lengths is shown below. Already one sees a representational problem emerging. A true metallacyclopropane might be expected to show a C-C single bond length, say > ~1.5Å. But only one or two of these examples actually have this value, the most probable value being ~1.4Å.

Using representation 3, one gets 1861 hits, but as before one sees a maximum at ~1.4Å with a tail reaching to both single and double bond values for the C-C distance.^‡

If the C-C bond is also specified as "any", the hits increase to 3948, but the bond length distribution is still very similar, with no sign of any bimodal distribution.

Such a distribution is however found if the torsions between the R-C bond vector and the C-M bond vector are plotted (for all types of bond). A large number of the complexes have a torsion <90°, which suggests that in fact the substituent R is probably interacting with the metal (even though this would lead to formal cyclicity, specifying R-C as acyclic does not detect this interaction). Could this be masking a bimodal distribution in the C-C lengths?

If the previous search is repeated, but this time specifying that all four torsions must lie in the range 90-180° (the range expected for a "classical" alkene-metal complex and selecting only the top right hand side cluster in the plot above) the reduced value of 1051 hits are obtained, but the monomodal distribution remains.

For this last set, here is a plot of the two C-metal bond length, with colour indicating the C-C bond length, indicating the two C-metal bonds are clearly linearly correlated.

One final variation; the atom on either C can only be H or a 4-coordinate (sp³) carbon; 645 hits. Again, a monomodal distribution centered at 1.4Å.

So this foray through metal alkene complexes suggests that there is a continuum between the formal metallacyclopropane with a C-C single bond and the only slightly perturbed alkene-metal complex with a C=C double bond. Whilst this would not prevent any one of these compounds existing as two distinctly different valence-bond isomers, it makes it very unlikely. I had noted in an earlier post that for molecules of the type RX≡XR (X=Si, Ge, Sn, Pb) that there was indeed a clear bimodal distribution of the X-X lengths evident in the crystal structures (for a relatively small sample number). The structures 1-4 shown at the start of this post are all simply just variations in a continuum and not distinct isomers.

POSTSCRIPT: I noted above the bimodel distribution in compounds involving formal triple bonds. So I repeated the search above for π-complex metal-alkyne complexes. Specifying an acyclic C-R bond, and any for the CC bond type, one gets the following.

There is now a tantalizing suggestion of two clusters, one at 1.3 and another at 1.4Å. The torsional distribution shows that the latter distance appears to be associated with much smaller torsions, whereas the top right cluster is associated with shorter lengths.

If the torsions are restricted to the range 90-180, then the histogram looses the smaller cluster, and perhaps gains a second cluster at 1.22Å? As I said, all quite tantalizing!

^‡The tail in all the histograms extends into the 1.1-1.3Å region, which seems unreasonable for a carbon where four bonds are specified. This region probably represents errors in the crystallographic analysis or reporting. But who knows, perhaps some very unusual compounds are lurking there!

June 13, 2016

X[cite]10.14469/hpc/1221[/cite]*
BH₂	CH₂	NH₂	OH₂
12.5	17.7	18.5	dissociates
AlH₂	SiH₂	PH₂	SH₂
6.9	12.9	21.9	31.3
B	C	N	O
8.3	11.7	12.9	14.2
Al	Si	P	S
4.8	6.6	11.2	18.2

X	Blog entry
B	16601
C	14508,8898
N	this one
O	16646
Si	16601
P	16601
S	this one

Quintuple bonds: resurfaced.

Six years ago, I posted on the nature of a then recently reported[cite]10.1002/anie.200803859[/cite] Cr-Cr quintuple bond. The topic resurfaced as part of the discussion on a more recent post on NSF₃, and a sub-topic on the nature of the higher order bonding in C₂. The comment made a connection between that discussion and the Cr-Cr bond alluded to above. I responded briefly to that comment, but because I want to include 3D rotatable surfaces, I expand the discussion here and not in the comment.^‡

Firstly, a quick update. Since the original post, quite a few Cr-Cr quintuple bonds have been reported. In searching the crystal structure database, I used the text "quintuple" as a text search term (since specifying a quintuple bond as such is not supported) along with a Boolean AND using the sub-structure Cr-Cr (with any type of bond allowed). The result is shown below. It is striking that in fact these "quintuple" bonds cluster into a set with a bond distance of ~1.74Å and another with 1.83Å. Are these valence bond isomers?

Now to the system shown at the top (one of the 1.74Å set). My original post discussed the results of a density functional evaluation of the properties of the electron density in the Cr-Cr region. Most striking was the value of the Laplacian ∇²ρ(r) of this density, the value of +1.45au being the largest ever reported for a pair of identical atoms. I should remind that ∇²ρ(r) is used as one measure of the character of a bond, being the balance between electronic kinetic energy density and potential energy density along a bond. But it is well recognised that the bonding between such transition metals has what is called multi-reference character; the wavefunction is not well described by just a single doubly occupied electronic configuration. More electronic configurations have to be included, and hence a MC-SCF (multi-configuration) self-consistent description of the wavefunction is needed. So as a response to the comment noted above, I decided to carry out CASSCF/6-311G(d) calculations, in which an active space of electrons and molecular orbitals is specified, and using the geometry previously obtained at the DFT level. Thus a CASSCF(8,8) calculation takes 8 electrons and evaluates all possible configurations arising from placing them into an active space of eight molecular orbitals. With metals unfortunately the active space is likely to be large, and so I decided to computed (10,10), (12,12) and (14,14) CASSCF as well to see if any convergence might occur. The last is close to the limit offered by the program. The values shown below are at the QTAIM line (bond) critical point along the Cr-Cr axis.

Active space	ρ(r)	∇²ρ(r)	Total energy, Hartree	% of CS config	Calculation DOI
8	.303	1.720	-2383.48049	63	[cite]10.14469/ch/191860[/cite]
10	.308	1.612	-2383.68830	61	[cite]10.14469/ch/191857[/cite]
12	.308	1.612	-2383.70398	60.6	[cite]10.14469/ch/191858[/cite]
14	.308	1.612	-2383.72161	59	[cite]10.14469/ch/191855[/cite]
DFT	.313	1.45	–	100	[cite]10.14469/ch/4156[/cite]

From the trend above, we might safely conclude that the CASSCF active space IS convergent, at least for the density if not for the energy. Also convergent are the properties of the density such as ∇²ρ(r), and noteworthy is that the value of this property is even higher than was obtained using single-configuration DFT theory. So the claim that this system has a record such property does not change. Negative values of the Laplacian are normally taken to indicate a conventionally covalent bond, whereas +ve values show the bond has what is called charge-shift character.[cite]10.1038/nchem.327[/cite] So these Cr-Cr quintuple bonds must be amongst the most charge-shifted exemplars!

I show some surfaces (click on the image to get a rotatable model) computed from the CASSCF(14,14) density. Firstly the electron density ρ(r) itself, contoured at 0.25au, showing the high value between the chromium atoms.

Next, ∇²ρ(r) contoured at ±1.5, revealing its high value in the Cr-Cr region (blue = +ve, red = -ve) and then below at ± 0.25 which includes the covalent bonds of the ligands.

Finally, the ELF (electron localisation function) function which tries to gather the electron density into localised ELF basins (numbers are the integration of the electron density in this basin). This looks very similar to that shown previously and is striking because there is no basin in the Cr-Cr region. Instead, the localisation is along the Cr-N bonds. One might describe this as saying that the Cr-Cr region is very highly correlated.

^‡It is a limitation of the WordPress system that such objects cannot be included in comments.

January 31, 2016

VSEPR Theory: A closer look at trifluorothionitrile, NSF3.
The post on applying VSEPR ("valence shell electron pair repulsion") theory to the geometry of ClF₃ has proved perennially popular. So here is a follow-up on another little molecue, F₃SN. As the name implies, it is often represented with an S≡N bond. Here I take a look at the conventional analysis.

This is as follows:
1. Six valence electrons on the central S atom.
2. Three F atoms contribute one electron each.
3. One electron from the N σ-bond.
4. Donate two electrons from S to the two π-bonds.
5. Eight electrons left around central S, ≡ four valence shell electron pairs.
6. Hence a tetrahedral geometry.
7. The bond-bond repulsions however are not all equal. The SN bond repels the three SF bonds more than the S-F bonds repel each-other.
8. Hence the N-S-F angle is greater than the F-S-F angle, a distorted tetrahedron.
Now for a calculation[cite]10.14469/ch/191808[/cite]; ωB97XD/Def2-TZVP, where the wavefunction is analysed using ELF (electron localisation function), which is a useful way of locating the centroids of bonds and lone pairs (click on diagram below to see 3D model).
- At the outset one notes that there are six ELF disynaptic basins surrounding the central S, integrating to a total of 7.05e. The sulfur is NOT hypervalent; it does not exceed the octet rule.
- These six "electron sub-pair" basins are arranged octahedrally around the sulfur. The coordination is NOT tetrahedral, as implied above.
- The three S-N basins have slightly more electrons (1.25e) than the three S-F basins (1.10e), resulting in …
- the angle subtended at the S for the SN basins being 96° (a bit larger than octahedral) whilst the angle subtended at the S for the SF basins being smaller (89.9°). This matches point 7 above, but is achieved in an entirely different manner.
- As a result, the N-S-F angle (122.5°) is larger than the ideal tetrahedral angle and the F-S-F angle (93.9°) is smaller, an alternative way of expressing point 7 above.
- The S≡N triple bond as shown above does have some reality; it is a "banana bond" with three connectors rather than two. Each banana bond however has only 1.25e, so the bond order of this motif is ~four (not six) but nevertheless resulting in a short S-N distance (1.406Å) with multiple character.
So we have achieved the same result as classical VSEPR, but using partial rather than full electron pairs to do so. We got the same result with ClF₃ before. So perhaps this variation could be called "valence shell partial electron pair repulsions" or VSPEPR.
January 16, 2016
A tutorial problem in stereoelectronic control. A Grob alternative to the Tiffeneau-Demjanov rearrangement?

In answering tutorial problems, students often need skills in deciding how much time to spend on explaining what does not happen, as well as what does. Here I explore alternatives to the mechanism outlined in the previous post to see what computation has to say about what does (or might) not happen.

I start with posing the question what does the chloride counter-ion do? If you are aware of the literature on computational reaction mechanisms, you may note that where ionic species are involved, one of the ions is often excluded from the calculations. Here for example, the pertinent reacting species is a diazonium cation, but the anion would likely not be mentioned, and the calculation would be performed as a charged cation (the physically unrealistic charge=1 in the input file!). This is because of an awkward difficulty with ion-pairs. There is no formal bond between the two charged fragments (unless a zwitterion) and so it is not entirely obvious quite where to place the counter-ion. In the diagram above, position 1 is where it was in my first exploration, but with knowledge that it might form a hydrogen bond to an acidic hydrogen, one could also perhaps place it into positions 2 or 3. In 2, as shown by the blue arrows and product above, an entirely different reaction occurs known as the Grob fragmentation.[cite]10.1002/hlca.19550380306[/cite] In fact as a di-carbonyl compound, it can then participate in an acid-catalysed aldol condensation and this can lead to the same product as the original Tiffeneau-Demjanov rearrangement, albeit with loss of stereochemical integrity. So it might be worth effort in explaining whether this alternative is likely (in other words how robust the likely stereochemical integrity of the product is).

System Relative TS free energy TS Dipole moment DataDOI

1 0.0 17.7 [cite]10.14469/ch/191653[/cite]

2 1.4 24.2 [cite]10.14469/ch/191654[/cite]

3 3.7 29.3 [cite]10.14469/ch/191655[/cite]

The energies of the three located transition states increase with the dipole moment; as the counter-ion moves further from the positive charge, its position becomes less stable. Still, route 2 is not that much higher in energy. Time for an IRC (intrinsic reaction coordinate) to explore what actually does happen during route 2, the possible Grob rearrangement.

The reaction animation above shows the required Grob characteristic, the green bond breaking. But instead of the OH then de-protonating, the hydrogen stays in place and instead the Tiffeneau-Demjanov migration takes place. This will require removal of a different proton and indeed in the latter stages, the chloride anion starts off in its determined journey to do so.

The variation in dipole moment as the reaction proceeds is fascinating. At IRC -6, it reaches a minimum, but then reverses itself in hunt of a better way of reducing the dipole moment.

What about 3? This is slightly artificial, since the real system has a methoxy group here, which would inhibit this route. One can still learn chemistry though. The hydrogen bond formed from chloride to the OH encourages the anomeric effect to form a partial oxy-anion, which in turn encourages the red bond to break rather than the green one. But in fact no complete proton transfer happens, and the reaction reaches a non-productive cul-de-sac.

So, to conclude, there is no Grob fragmentation! Instead, a slightly confused Tiffeneau-Demjanov migration occurs in a rather more roundabout manner than previously. We have explored here just TWO reaction trajectories. A more statistical exploration of the trajectory landscape will give us a more complete picture, but I rather fancy that would be very well above the call of duty required to answer a stereochemical problem!

November 28, 2015
A visualization of the anomeric effect from crystal structures.
The anomeric effect is best known in sugars, occuring in sub-structures such as RO-C-OR. Its origins relate to how the lone pairs on each oxygen atom align with the adjacent C-O bonds. When the alignment is 180°, one oxygen lone pair can donate into the C-O σ* empty orbital and a stabilisation occurs. Here I explore whether crystal structures reflect this effect.

The torsion angles along each O-C bond are specified, along with the two C-O distances. All the bonds are declared acyclic, and the usual R < 5%, no disorder and no errors specified.
1. You can see from the plot below that the hotspot occurs when both RO-CO torsions are ~65°. From this we will assume that the two (unseen)^‡ lone pairs at any one of the oxygens are distributed approximately tetrahedrally around each oxygen, and if this is true then one of them must by definition be oriented ~ 180° with respect to the same RO-CO bond (the other is therefore oriented -60°). This allows it to be antiperiplanar to the adjacent C-O bond and hence interact with its σ* empty orbital. So the hotspot corresponds to structures where BOTH oxygen atoms have lone pairs which interact with the adjacent O-C anti bond.
2. There is a tiny cluster for which both RO-CO torsions are ~180° and hence neither oxygen has an antiperiplanar lone pair.
3. Only slightly larger are clusters where one torsion is ~65° and the other ~180°, meaning that only one oxygen has an antiperiplanar lone pair.
4. A plot of the two C-O lengths indeed shows an overall hotspot at ~1.40Å for both distances. If the search is filtered to include only torsions in the range 150-180°, the hotspot value increases to 1.415Å for both. If one torsion is restricted to 40-80° and the other to 150-180° the hotspot shows one C-O bond is about 0.012Å shorter than the other.
I also include a further constraint, that the diffraction data must be collected below 140K. The hotspot moves to ~ 55/60° indicating values free of some vibrational noise.

Interestingly, replacing oxygen with nitrogen reveals relatively few examples of the effect (C(NR₂)₄ is an exception). Replacing O by divalent S produces only 13 hits, with the surprising result (below) that in all of them only one S sets up an anomeric interaction. Arguably, the number of examples is too low to draw any firm conclusions from this observation.

^‡Most diffractometers measure low angle scattering of X-rays by high density electrons. These are the core electrons associated with a nucleus rather than the valence electrons associated with lone pairs. Hence very few positions of valence lone pairs have ever been crystallographically measured.

Acknowledgments

This post has been cross-posted in PDF format at Authorea.
August 27, 2015