Category: Hypervalency

Dealing with unusual valencies beyond the Lewis model

Contriving aromaticity from S≡C Triple bonds

In the previous post, the molecule F₃S-C≡SF₃ was found to exhibit a valence bond isomerism, one of the S-C bonds being single, the other triple, and with a large barrier (~31 kcal/mol, ν 284i cm^-1) to interconversion of the two valence-bond forms. So an interesting extension of this phenomenon is shown below:

A cyclic form of the SCS Motif. Click for 3D
If the same type of valence bond isomerism were to occur, we would now have three C≡S triple bonds swapping places with three CS single bonds, a sort of super version of the notation normally shown for benzene itself. If the barrier to this swapping is finite, then the interconversion shown above would be a proper equilibrium (the top arrows), but if there is no barrier, then the interconversion would be a proper resonance (the bottom double-headed arrow). Another way of posing the question is whether the so-called Kekulé vibrational mode (which in effect represents the motions implied above) has a negative force constant or a positive one respectively for the two sets of arrows shown.

A B3LYP/cc-pVTZ calculation (DOI: 10042/to-3646) reveals that the optimized geometry exhibits six equal SC bonds, all 1.616Å long. Typically, a single SC bond is around 1.82Å, a double 1.65Å and a triple is about 1.5Å at the same level of theory, so this C=S bond is clearly at least a double one. A NICS(0) calculation at the centroid has the value of -14.6 ppm, which indicates aromaticity. We conclude the appropriate arrow above is the bottom resonance one, rather than the top equilibrium one. This is confirmed by finding that the Kekulé vibrational mode has a strongly positive force constant (ν 1083 cm^-1, animated in 3D model above), which contrasts with the negative value (ν 284i cm^-1) found for bond shifting in F₃S-C≡SF₃ itself. Again, comparison indicates that a C≡S triple bond has a frequency of around 1400 cm^-1 and a double around 1200 cm^-1 (the degenerate C=S non–Kekulé vibrational mode for this system is indeed calculated at around 1225 cm^-1). So to summarise; a single F₃S-C≡SF₃ unit reveals very strong bond alternation, and negative force constant (transition state) for interconversion of the two bond forms, but a cyclic form reveals the opposite behaviour, with no alternation and instead strong aromaticity.

In part this difference in behaviour must be due to the constraints on the geometry of the cyclic form. F₃S-C≡SF₃ interconverts via a highly twisted geometry with C₂ symmetry, and this twisting is not exactly possible if you create a cyclic equivalent. In part it is also due to the aromatic stabilisation energies. In the resonance above, you should be able to count a total of 12 electrons involved! Nominally, if you try to apply the 4n+2 aromaticity rule, it does not fit, until you realise that in fact you must be dealing with two sets of 6 electrons. The system in fact is a classic double-aromatic, in which six electrons circulate in the plane of the molecule (the σ-set) and six above and below (the π-set; the MOs for the molecule confirm exactly this interpretation). Notice how this itself contrasts with a similarly aromatic system, the atom swapping in three nitrosonium cations, where the Kekulé mode force constant was strongly negative.

ELF Analysis for F6S3C3. Click for 3D
To complete the analysis, the ELF basins (above) reveal the six SC regions to each contain 2.7 electrons, together with three carbon carbene monosynaptic basins. For comparison, a system with a high degree of SC triple character (HCS⁺) has around 3.8 in the SC region. Perhaps a better model is TfOSCH (for which the carbon also has a carbene lone pair), which has 2.6e in the CS region. The carbene lone “pair” for the present molecule integrates to 2.6e each, which totals to a nice octet of electrons around each carbon and to around 7 for each S, confirming that whilst the S is hypervalent, its valence octet is not expanded!). This ELF picture does rather tend to confirm the original resonance structure representation shown at the top.

All that is needed is is for someone to make this molecule to confirm its properties. Perhaps by trimerising F₂SC, itself formed by cheletropic elimination? It is worth noting that the iso-electronic P/N (e.g. of S/C) analogues are very well known.

Phosphonitrilic compounds

January 1, 2010
Ménage à deux: Non-classical SC bonds.

A previous post posed the question; during the transformation of one molecule to another, what is the maximum number of electron pairs that can simultaneously move either to or from any one atom-pair bond as part of the reaction? A rather artificial example (atom-swapping between three nitrosonium cations) was used to illustrate the concept, in which three electron pairs would all move from a triple bond to a region not previously containing any electrons to form new triple bonds and destroy the old. Here is a slightly more realistic example of the phenomenon, illustrated by the (narcisistic) reaction below of a bis(sulfur trifluoride) carbene. Close relatives of this molecule are actually known, with either one SF₃ of the units replaced by a CF₃ group or a SF₅ replacing the SF₃ (DOI: 10.1021/ja00290a038 ).

F3SCSF3 and the nature of its S-C bonds

The two C-S bonds in this molecule are not the same (and similarly for the CF₃ analogue), one being long (single), the other short (assumed triple), and the angle subtended at the central carbon is around 150° (B3LYP/cc-pVTZ calculation, DOI: 10042/to-3643). The transition state for interconverting one form to the other would presumably correspond to the concerted movement of two pairs of electrons from one CS region to the other as shown above, not so much a Ménage à trois, as a Ménage à deux! The transition state itself (DOI: 10042/to-3644) has C₂ symmetry, with a calculated free energy barrier of 31 kcal/mol and ν 284i cm^-1 for the bond shifting process.

Transition state for bond equalisation. Click for animation

The molecule above does have a further point of interest; one of the sulfur atoms (the triply bonded one) is approximately tetrahedral in coordination, whilst the other has a “T-shape”. An inorganic chemist would describe one sulfur as tetravalent (oxidation state IV), the other as hexavalent (oxidation state VI) and the equilibrium between them a dismutation of the two oxidation states. Does this have any reality? The ELF method has been mentioned a number of times in these posts, and it is applied here to seek an answer. The ELF basin centroids are shown below.

ELF basins for F3SCSF3. Click for 3D

The integrations are as follows: 14 = 2.24 (a single C-S bond), 30=1.66 (an incipient carbene forming, as implied above), 13+15+16 = 4.34 (a reasonably persuasive triple bond, comprising, unusually, three separated basins). The fluorines 2, 3 and 6 all exhibit bonding basins to the S (respectively 2.17, 2.17 and 2.09), but fluorines 1,5 and 4 do not! Sulfur 8 additionally has a lone pair, 29=2.31, but sulfur 9 does not. One aspect of this analysis is the nature of the triple bond between S9-C7. Because the three basins are separate, does that mean that the bond cannot rotate about its axis?

AIM Analysis of F3SCSF3

An alternative AIM analysis is shown above. Now, the CS triple bond is reduced to a single bond critical point (BCP), labelled 10. AIM allows a property known as bond ellipticity to be computed at that BCP. Typically, single and triple bonds have ellipticities close to zero, whilst double bonds have a value of around 0.4 to 0.5. That for point 10 is 0.18, which seems to support the ELF analysis above. Pretty unsual bonding it would have to be agreed!

ELF centroids for transition state for dismutation.

But what of the original question posed at the start in the diagram; do two pairs of electrons move away together from one triple bond to form another. A further ELF analysis at the transition state for this process reveals that in effect the two pairs do different things. One localizes onto the carbon, to form a proper carbene, the other becomes a sulfur lone pair. So the valence dismutation involves three pairs of electrons, not two as shown at the start, with each pair doing its own thing.

Six-electron model for valence isomerism in F3SCSF3

December 30, 2009
The nature of the C≡S triple bond: part 3.

In the previous two posts, a strategy for tuning the nature of the CS bond in the molecule HO-S≡C-H was developed, based largely on the lone pair of electrons identified on the carbon atom. By replacing the HO group by one with greater σ-electron withdrawing propensity, the stereo-electronic effect between the O-S bond and the carbon lone pair was enhanced, and in the process, the SC bond was strengthened. It is time to do a control experiment in the other direction. Now, the HO-S group is replaced by a H2B-S group. The B-S bond, boron being very much less electronegative than oxygen, should be a very poor σ-acceptor. In addition, whereas oxygen was a π-electron donor (acting to strengthen the S=C region), boron is a π-acceptor, and will also act in the opposite direction. So now, this group should serve to weaken the S-C bond.

The H2BSCH molecule. Click for 3D.

At the B3LYP/cc-pVTZ level (DOI: 10042/to-3189), the S-C bond now emerges as 1.834Å compared to 1.544Å for the HO-substituted version and the S-C stretch is reduced to 803 cm-1. The NBO interaction term between LP(1)C2 and BD*(1) S1-B3 is indeed quite small (6.9 kcal/mol). The basin integration for point 10 increases to 2.22e, whilst point 9 decreases to 1.90e, and 8 is again up at 2.11. The SC bond is now merely a single bond!

So what have we proved? Well, we find that our hypothesis works in both directions, to either strengthen or weaken the CS region. Indeed, variation of the S-substituent (HO, OTf, BH2) has quite a dramatic effect on the nature of the CS bond, evolving it all the way from a single bond at one extreme to one with significantly triple character at the other.

December 6, 2009
The nature of the C≡S Triple bond: Part 2

In my first post on this theme, an ELF (Electron localization function) analysis of the bonding in the molecule HO-S≡C-H (DOI: 10.1002/anie.200903969) was presented. This analysis identified a lone pair of electrons localized on the carbon (integrating in fact to almost exactly 2.0) in addition to electrons in the CC region. This picture seems to indicate that the triple bond splits into two well defined regions of electron density (synaptic basins). In a comment to this post, I also pointed out that an NBO analysis showed a large interaction energy between the carbon lone pair and the S-O σ^* orbital, characteristic of anomeric effects (in eg sugars). This latter observation gives us a handle on possibly tweaking the effect. Thus if the S-O σ* orbital can be made a better electron acceptor, then its interaction with the lone pair could be enhanced.

Accordingly, the analysis has been repeated for H-C≡S-OTf (OTf = triflate = trifluoromethane sulfonate), since the triflate would be expected to increase significantly the electron accepting properties of the S-O bond.

ELF analysis for H-C≡S-OTf. Click for 3D model
One dramatic change has indeed occurred. Previously, a well-defined ELF disynaptic basin had been identified in the S-O region, with an integration of 1.12e. If the OH group is replaced by OTf, this disynaptic basin can no longer be located. The electrons have instead moved into sulfur lone pairs, and the S-CF₃ bond, which is an expected consequence of the greater electronegativity of the triflate group. Point 15 (the S=C region) integrates to 2.56e (compared with 2.36 for the OH analogue), and the carbon lone pair decreases from 2.01 to 1.86e.

Taken as a whole, these changes suggest that the CS bond has gotten stronger, resulting from transfer of electron density from the non-bonding carbon lone pair, to the CS bond itself. Indeed, its length is now 1.492Å, a significant shrinkage compared to 1.544Å for the OH parent (B3LYP/cc-pVTZ). Likewise, the C-S vibrational stretch of 1381 cm^-1 for the OTf derivative is an increase over 1215 cm^-1 for the OH system and 1304 cm^-1 for diatomic CS itself (B3LYP/cc-pVTZ).

These results suggest that the ELF procedure, combined with the insight from the NBO analysis, can be used as a tool to rationally design a variation to the original molecule which does appear to enhance the triple bond character of the CS region, and to fulfil further the ambition of the original article by Schreiner and co-workers. As a triflate, it may even be susceptible to a simple preparation from the alcohol parent! Anyone up for it?

It is also worth noting that the above system is headed off towards HC≡S⁺, the thioacylium cation (although crystal structures of the acylium ion are known, none have been reported for the thioacylium ion). Both N≡N and C≡O contract their bond lengths when protonated, so it should be no great surprise to find that CS does so as well (1.476Å, ν 1543 cm^-1).

December 5, 2009
The nature of the C≡S triple bond

Steve Bachrach has just blogged on a recent article (DOI: 10.1002/anie.200903969) claiming the isolation of a compound with a C≡S triple bond;

A compound with a C≡S triple bond

Steve notes that Schreiner and co claim a “structure with a rather strong CS double bond or a weak triple bond”. With this size of molecule, the proverbial kitchen sink can be thrown at the analysis of the bonding. But one technique that was NOT applied is ELF (see the earlier post using ELF to analyze the bonding in MgPh₂). So here is such an analysis, computed for the CCSD/cc-pVTZ wavefunction at the geometry reported in the publication (see also DOI: 10042/to-2980). The (centroids of the) synaptic basins are the small purple spheres.

ELF analysis of the bonding in HOS≡CH. Click for 3D
The key (disynaptic) basin is labelled 10, and it integrates to 2.36 electrons, rather far from the 6 electrons which might be expected for a triple bond! Its centroid is also significantly off-centre from the S-C bond. Basin 11 integrates to 2.01 electrons; it resembles a lone pair on the carbon, although the ELF analysis actually labels it a S-C disynaptic basin. It approximately maps to the HOMO orbital. Monosynaptic basin 9 encompases the two formal lone pairs on the sulfur, and it integrates to 3.59e (quite often, what we regard as separate, rabbit-ear, lone pairs on an atom manifest only as a single monosynaptic basin). Completing the analysis are two further monosynaptic basins 6 and 7, which represent lone pairs on the oxygen (2.45e each) and the disynaptic basin 8 (1.1e).

Bonding, much like the Humpty-Dumpty meaning, is very much what you want it to be! But in this case, one has to ask whether the description of the bonding in the C≡S region really is best described as a weak triple bond, or even a strong double bond, or whether the nominal six electrons of the triple bond split into two regions, one clearly bonding, the other more non-bonding.

December 1, 2009
Multi-centre bonding in the Grignard Reagent

The Grignard reaction is encountered early on in most chemistry courses, and most labs include the preparation of this reagent, typically by the following reaction:

2PhBr + 2Mg → 2PhMgBr ↔ MgBr₂ + Ph₂Mg

The reagent itself exists as part of an equilibrium, named after Schlenk, in which a significant concentration of a dialkyl or diarylmagnesium species is formed. The topic of this blog entry is to analyse the structure and bonding in this latter species.

First, the structure is shown below (for 2,6-diethylphenyl magnesium). This reveals a dimeric structure with a four membered ring core, comprising two Mg atoms connected by two bridging aryl groups.

The crystal structure of a di-aryl magnesium. Click to view 3D
The question to be addressed here is the nature of the aryl groups. Put simply, it seems as if their bridging role means that one of the six carbons involved in the benzene ring has become sp³ hybridized. This would in turn mean that the cyclic conjugation of the benzene ring is interrupted, and a species akin to the Wheland intermediate is formed in which the aromaticity of two of the benzene rings is no longer sustained. This situation could be depicted thus;

A Simple bonding representation in Ph2Mg dimer

Is this really the best way of depicting the bonding in this species? A more subtle analysis of the bonding can be achieved using a technique known as ELF (involving analysis of the electron localization function). This reveals bonds as so-called synaptic basins, which come in two varieties; disynaptic basins corresponding to two-centre bonds, and trisynaptic basins which reveal three-centre bonds (there is also a monosynaptic basin which corresponds to electron lone pairs). Such an ELF analysis (based on a B3LYP/6-311G(d,p) computed wavefunction for Ph₂Mg dimer) is shown below;

ELF analysis of the bonding in Ph2Mg dimer. Click for 3D model
The small purple dots represent synaptic basins. Several of these are circled. The ones circled in orange are conventional disynaptic forms, and the basins can be integrated to to 2.48 electrons each. The red basin however is clearly revealed as a trisynaptic form (covering both metal centres and the carbon) and integrating to 2.7 electrons. The three basins surrounding each Mg atom integrate to 7.91 electrons, which reveal the metal to have a conventional octet of electrons in its valence shell. The bonding in the central region could therefore be described as comprising two three-centre-three-electron bonds. The key aspect of this is that the two bridging phenyl groups do not break their aromaticity, ie all four phenyl/aryl groups largely retain their aromaticity! Thus the disynaptic basins for the normal non-bridging phenyl group and circled in green integrates to 2.6 electrons and the blue to 2.8 (an ideal aromatic bond would of course integrate to 3.0 electrons), whereas the equivalent basins for the bridging phenyl (brown and purple, 2.5 and 2.8) are virtually the same.

It is interesting how a veritable mainstay of most taught chemistry courses, the Grignard reagent, can have such subtle aspects of the bonding surrounding both the metal atom and the aromatic groups, and how rarely this bonding is actually dissected in most text books.

December 1, 2009
Hypervalency: a reality check

We have seen in the series of posts on the topic of hypervalency how the first row main group elements such as Be, B, C and N can sustain apparent hypercoordination and arguably hypervalency. The latter is defined not so much by expanding the total valence shell of electrons surrounding the hypervalent atom beyond eight, but in having more than four well defined bonds to it, as quantified by AIM and ELF analysis. The previous post made the suggestion of how a compound involving hypervalent boron could also sustain a genuine bond to the rare gas helium. It is surely time to seek evidence that this type of bonding can be sustained in reality. Fortunately, a crystal structure of a reasonably analogous compound IS available (DOI: 10.1016/0022-328X(94)05089-T).

YOCVIV: Crystal structure of hexacoordinate boron. Click for 3D

AIM analysis for YOCVIV

The AIM analysis shows five bond critical points in the B-C regions and one in the B-Br region. with ρ(r) values of 0.121 and 0.146 respectively. The corresponding ∇²ρ values were -0.07 and -0.22. These BCPs are matched by equally well defined disynaptic basins in the ELF analysis with electron populations of respectively 0.67 and 2.1 electrons. This compares with ρ(r) values of 0.157 and 0.069, and ELF integrations of 1.22 and 2.0 calculated for the structurally similar proposed B-He compound.

ELF analysis for YOCVIV. Click for 3D

The analogy is sufficiently similar to suggest that (in this case boron) hypervalency for such first row main group elements can be reflected in real systems.

October 5, 2009

Uncompressed Monovalent Helium

Quite a few threads have developed in this series of posts, and following each leads in rather different directions. In this previous post the comment was made that coordinating a carbon dication to the face of a cyclopentadienyl anion resulted in a monocation which had a remarkably high proton affinity. So it is a simple progression to ask whether these systems may in turn harbour a large affinity for binding not so much a H⁺ as the next homologue He²⁺?

This possibility is explored with the series X=Be, B, C (tetramethyl substituted, resulting in neutral, +1 and +2 systems overall). The first two emerge as stable in terms of having all positive force constants for C_4v symmetry; the last emerges as a transition state and is not discussed further. The specific system X=B has a B-He bond length of 1.317Å/B3LYP/6-311G(d,p), 1.305Å/B3LYP/Def2-QZVPP and 1.290Å/double-hybrid RI-B2GP-B2PLYP/TZVPP, which does seem as if it might be typical of a single bond between these two elements. The ρ(r)_B-He AIM value (B3LYP/6-311G(d,p) is 0.069 au, and ν_B-He of 713 cm^-1 (727 for Def2-QZVPP basis) makes it about one third the strength of a C-H bond. The disynaptic basin for the B-He region integrates to 1.99 electrons, whilst the four B-C basins correspond to 1.22 electrons each.

X	Charge	ρ(r) X-He	C-B ELF integration	ν_X-He, cm^-1	Repository
Be	0	0.031	1.10	484	10042/to-2443
B	1	0.069	1.22	713	10042/to-2444 10042/to-2446 10042/to-2453
C	2	0.026	–	136	10042/to-2445

B-He vibrational stretching mode — B-He stretching mode. Click to vibrate

We can conclude that for X=B, this species exhibits not only a pentavalent boron atom, but a monovalent helium atom. The latter bond may indeed be amongst the strongest ever proposed for this element in a ground state, and indeed perhaps is even viable as a solid crystalline compound rather than merely existing in the gas phase. The Cambridge crystal database contains no entries for He or Ne, not even as an encapsulated clathrate (although crystal structures of such complexes for Kr and Ar are known). Theoretical studies of the rare gases in endohedral fullerene-like cages (DOI: 10.1002/chem.200801399) predict that under these compressed circumstances e.g. two helium atoms can approach each other to 1.265Å or less (see also DOI: 10.1002/chem.200700467) but these close approaches were not considered to be chemical bonds as we think of them. Perhaps Merino, Frenking, Krapp and co’s search for the chemistry of helium (they had found it earlier in the gas phase excited states of their molecules, DOI: 10.1021/ja00254a005) might be realised for the ground state of the system described here.

October 3, 2009

Pentavalent nitrogen and boron

The previous posts have seen how a molecule containing a hypervalent carbon atom can be designed by making a series of logical chemical connections. Another logical step is to investigate whether the adjacent atoms in the periodic table may exhibit similar effects (C²⁺ ≡ B⁺ ≡ N³⁺ ≡ Be ≡ O⁴⁺). So here are reported some results (B3LYP/6-311G(d,p) ) for boron, beryllium and nitrogen, for the general tetramethyl substituted system shown below

X	Charge	X-C length, Å	ρ(r) C-X	ELF integration	ν-Trampoline, cm^-1	ν X-H, cm^-1	Repository
N	2	1.616	.172	1.14	883	3417	10042/to-2439
C	1	1.580	.195	1.10	970	3291	10042/to-2438
B	0	1.649	.136	1.06	949	2746	10042/to-2440
Be	-1	1.817	.064	0.98	797	1887	10042/to-2441

The systems H, C and B are stable in the sense that the C_4v-symmetric calculated geometry has only positive calculated force constants (Be has a small negative frequency). All show bond critical points in the X-C region (although these bonds are clearly bent) and X-H region, and significant integrations for the X-C disynaptic basins in the ELF analysis. The boron analogue is also of interest as being a neutral rather than a charged molecule, and therefore may be a worthy target for synthetic effort.

October 3, 2009

Full circle with carbon hypervalencies

The previous post talked about making links or connections. And part of the purpose for presenting this chemistry as a blog is to expose how these connections are made, or or less as it happens in real time (and not the chronologically sanitized version of discovery that most research papers are). So each post represents an evolution or mutation from the previous one. To recapitulate, we have seen how the idea of cyclopentadienyl anion as a ligand for a dipositive carbon atom has evolved. Let us move in yet another direction; the cyclobutadienyl dianion. This ligand has recently been shown to bind Mg²⁺ (DOI: 10.1002/ejic.200800066), so why not He²⁺? And picking up again the previous theme, we will then protonate the bound complex. The result now is a monocation, and it has the C_4v-symmetric structure shown below (DOI: 10042/to-2438). This bears some resemblance to pyramidane, a neutral C₅H₄ compound with hemispherical carbon reported in 2001 (DOI: 10.1021/jp011642r) which is also a stable minimum in the potential energy surface.

C4-symmetric pentavalent carbon

Now, the apical C-C bonds have shrunk to 1.58Å, the trampoline mode is increased to 970 cm^-1 and the apical C-H frequency to 3291 cm^-1. The apical C-C value for the AIM bond critical point ρ(r) is up 0.195 au and the disynaptic basin integration in that region is now 1.1 electrons. Replacing the apical C-H by C-F further strengthens the system (DOI: 10042/to-2447); the apical C-C bonds contract slightly to 1.57Å, the bouncing castle/trampoline mode shoots up to ν 1595 cm^-1, ρ(r) reaches 0.201 au and the disynaptic basins 1.25 electrons. With this latter system, the C-F disynaptic basin contains only 1.08 electrons, suggesting it is similar in nature to the other four bonds surrounding the apical carbon, i.e. this carbon is surrounded by five more or less equivalent bonds. The pseudo-halogen CN can also replace the F (DOI: 10042/to-2449) to similar effect (ρ(r)_C-C 0.190, ρ(r)_C-CN 0.290).

AIM Analysis

ELF Basin centroids. Click for 3D

We are back to pentavalent, pentacoordinate carbon again, but we have gradually optimized the properties of the system for five short C-C bonds surrounding one carbon atom, and the largest electron density and disynaptic basin integration. Whilst the sentiments expressed by Hoffmann, Schleyer and Schaefer (DOI: 10.1002/anie.200801206) for more realism in predicting molecules must not be ignored, it is to be hoped that the original suggestions made here will lead to the discovery of realistic and makeable molecules exhibiting true C-C hypervalency.

October 2, 2009