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Henry Rzepa (10 unread)

• February 21, 2010
• 2:59

  The structure of the hydrogen ion in water.

   » ‎ Henry Rzepa
  

  Stoyanov, Stoyanova and Reed recently published on the structure of the hydrogen ion in water. Their model was H(H2O)n⁺, where n=6 (DOI: 10.1021/ja9101826). This suggestion was picked up by Steve Bachrach on his blog, where he added a further three structures to the proposed list, and noted of course that with this type of system there must be a fair chance that the true structure consists of a well-distributed Boltzmann population of a number of almost iso-energetic forms.

  

  The proposed structure of the hydrated proton in water

  The evidence for the structure above comes from IR spectra. These operate on a fast enough scale to freeze-out individual forms, and therefore represent the instantaneous species rather than time averaged environments. A lively debate started on Steve’s blog, starting with Steve’s observation that the original article had reported only experimental results and no theoretical modelling of the proposed structure. It emerged that one way of modelling such species was within a cavity surrounded bv a continuum field modelling the bulk solvent (water in this case), and in particular one must properly optimize the structure and calculate the force constants within this field. When this is done, one significant difference between a simple gas-phase model of the structure above and its continuum-field structure emerges. In the former, the central O…H…O motif is symmetric (indeed the entire molecule is C2-symmetric). When the solvent field is applied, this unit desymmetrizes, ending up with one short (1.118Å) and one long (1.295Å) bond. I have transferred discussion of this from Steve’s blog to this one so that the resulting vibrations of this species can be shown here in animated form (its not possible to post animations in the comment field of a blog).

  Firstly, the model. It is a PBE1PBE/aug-cc-pVTZ (the DFT method being the same as Steve used in his modelling, the basis set being rather better) and the continuum field applied was as SCRF(CPCM,solvent=water). The complete calculation can be inspected at DOI: 10042/to-4261. It is also important to remember that the force constants are harmonic. The resulting vibrations with the highest calculated intensities are tabled below.

  Obs	1H freq	Intensity	2H freq
  -	338	481	?
  654	476	429	438
  1202	1242	3837	942
  1746	1749	599	1284
  2816	3065	2829	2268
  -	3127	913	2253
  3134	3341	2018	2462
  3134	3347	668	2424

  One might note that the vibrations in the range 3100-3300 always tend to be over-estimated using theory, in part because of incomplete basis sets, and in part because the harmonic frequencies are always 200 or more wavenumbers higher than the observed anharmonic values. The match for the mid range vibrations (1746, 1202) seems remarkably good. Only the low range value (654) is significantly out, and this may be another anharmonic effect. Added for good measure are the closest matches to each vibration when the system is fully substituted with deuterium (because of mode mixing, the modes do not always map exactly; thus the mode at 338 appears to have no exact deuteriated analogue).

  The displacement vectors are shown below (click on each picture to obtain an animation).

  Normal mode 476 cm-1.	Normal mode 1242.
  Normal mode 1749	Normal mode 3065
  Normal mode 3341	Normal mode 3347

  

  Calculated IR spectrum for H(H2O)6 +

  

  Calculated IR spectrum for D(D2O)6 +

  The overall conclusion does seem to be that the structure shown above for the solvated proton does seem to match the observed IR peaks rather well, and that further more accurate modelling of this species might be a worthwhile endeavour.

• February 20, 2010
• 11:14

  Quintuple bonds: part 2

   » ‎ Henry Rzepa
  

  In the previous post, I ruminated about how chemists set themselves targets. Thus, having settled on describing regions between two (and sometimes three) atoms as bonds, they added a property of that bond called its order. The race was then on to find molecules which exhibit the highest order between any particular pair of atoms. The record is thus far five (six has been mooted but its a little less certain) for the molecule below

  

  A molecule with a Quintuple-bond

  There are many ways of describing the electronic behaviour in that region called a bond, one being the ELF (Electron localization function) technique, which certainly sounds as if it is describing a bond! The ELF function for the molecule above however was distinctly odd, and this was attributed to the Cr-Cr bond being not so much a covalent bond, but another (much less recognized type) known as a charge-shift bond. In particular, two of the ELF basin centroids did not occupy the central region between the two atoms, but had in effect fled that region, and in the process had also each split into two. Other ELF basins did not much look like bonds, but retained much of their core-electron (i.e. non bonding) character. The issue now becomes whether the ELF method is sensible, or simply an artefact. In other words, it needs calibrating against other (homonuclear) molecules which might exhibit charge-shift behaviour.

  Three such molecules are in fact the halogens, F2, Cl2, Br2 as discussed by Shaik, Hiberty and co (DOI: 10.1002/chem.200500265). So lets take a look at what an ELF analysis shows for these, and how it compares with the chromium quintuple bond.

  ELF analysis for F2
  ELF analysis for Cl2	ELF analysis for Br2

  At the B3LYP/6-311G(d) level, the ELF function shows the (valence) electrons located in two regions. Firstly, what we might call the lone pairs are located in a torus surrounding each halogen atom (i.e. the molecule must be axially symmetric). The remaining electrons are in basins with centroids along the axis of each bond. The Br2 centroid is a single conventional disynaptic basin, with an integration of 0.77 electrons. With Cl2 however, something odd happens (and the effect was described in DOI: 10.1002/chem.200500265 ); the disynaptic basin splits into a close pair, each integrating to 0.33 electrons, and looking as if the two parts want to run away from one another. This was interpreted as indicating that the purely covalent description of the halogen bond is in fact repulsive and not attractive! The effect is enhanced for F2, with two very much split basins, each integrating to 0.08 electrons. This serves to remind us of how odd a bond the F-F one truly is (and how easily it is homolyzed)!

  Now that we have our calibration, does it match to the Cr-Cr quintuple bond? Very much so! Again, the valence basins show very low integrations (compared to the nominal bond order), and again they appear to have split and run away from each other. Most of the valence electrons in that species prefer instead to masquerade as core-electrons. So we can conclude that by the ELF criterion, the Cr-Cr bond is not quintuple, and not covalent but charge shifted. Of course, this does seem at odds with the Cr-Cr internuclear distance, which is indeed very short! This shortening probably arises from electrostatic attractions in the charge-shifted valence bond forms. It simply goes to show that what the nuclei get up to and what the electrons do may not be one and the same thing!

• February 16, 2010
• 11:48

  Quintuple bonds

   » ‎ Henry Rzepa
  

  Climbers scale Mt. Everest, because its there, and chemists have their own version of this. Ever since G. N. Lewis introduced the concept of the electron-pair bond in 1916, the idea of a bond as having a formal bond-order has been seen as a useful way of thinking about molecules. The initial menagerie of single, double and triple formal bond orders (with a few half sizes) was extended in the 1960s to four, and in 2005 to five. Since then, something of a race has developed to produce the compound with the shortest quintuple bond. One of the candidates for this honour is shown below (2008, DOI: 10.1002/anie.200803859) which is a crystalline species (a few diatomics which exist in the gas phase are also candidates; for other reviews of the topic see 10.1038/nchem.359, 10.1021/ja905035f and 10.1246/cl.2009.1122).

  

  A molecule with a Quintuple-bond

  (OK, its shown as a quadruple bond, but Chemdraw cannot handle five!). The Cr…Cr length is 1.74Å (R=aryl). It was also reported that DFT calculations (BP86/triple-ζ) reproduce this length well. The five highest occupied molecular orbitals are all centred around the Cr-Cr region, and the bonding is formally described as five pairs of electrons filling 1σ, 2π, and 2δ type molecular orbitals.

  So the electron pair bond, approaching its 100th birthday, is alive and well? But it does seem worth asking if those ten electrons really do cram together to occupy the region between the two Cr atoms. The stalwarts in these blog posts, AIM and ELF will be deployed to see if they too verify this simple concept. Firstly, AIM (calculated at the BP86/6-311G(d) level, DOI: 10042/to-4181 for a model system with R=H).

  

  Quintuple bond complex, AIM analysis. Click for 3D

  The Cr…Cr region has the requisite bond critical point, and the value of ρ(r) at this point has the large value (for Cr) of 0.313 au, indeed hinting at a large bond order. The Laplacian ∇²ρ(r) has the more extraordinary value of +1.45 at this point, which makes it the strongest charge-shift bond ever noted (typically, ∇²ρ(r) is ~+0.5 for other examples of homonuclear charge-shift bonds, see DOI: 10.1038/nchem.327).

  This charge-shift character perhaps hints that this quintuple bond is no ordinary bond. Charge-shift bonds are characterized by valence bond structures where the covalent form may actually be repulsive, and the bond is stabilized instead by resonance with charge-shifted ionic valence bond forms. So given this, the ELF perhaps comes as no surprise.

  

  Quintuple bond. ELF analysis

  This diagram needs some explanation. The colour code is as follows: purple spheres represent the centroids of conventional disynaptic ELF basins. The only interesting ones are the four connecting the nitrogens to the Cr (21-24) which integrate to 3.35 electrons each. The cyan spheres (shown as 3,4 above) are the inner core-electrons of the Cr atoms (10.2 electrons of a neon core) and surrounding them are five further basins for each Cr integrating to 12 electrons per Cr. These include 8 of the outer-core (3s,3p) and four of the valence (3d, 4s) electrons, leaving ~2 valence Cr electrons not accounted for. Some of these final electrons are to be found in the basins represented by red spheres. The very diffuse (39, 40) basins far from the centre have a tiny electron integration (~0.003) and more missing Cr valence electrons are found in the bridging basins (32,36; 0.56 and 0.25 electrons each). Added to the 2*3.35 electrons found in the Cr-N bond, this suggests the 3d/4s shell of the Cr is occupied by ~11.5 electrons. The 3d-shell is thus full, and the system is indeed an 18-electron (8+10) system with some occupancy of the 4s shell as well. An alternative view of the ELF surface can be seen below, showing the unusual environment surrounding the Cr pair.

  

  Quintuple bond, showing ELF isosurface. Click for 3D

  It seems that AIM (the topology of the electron density) and ELF (the topology of the electron localization function) are giving us quite different pictures of the quintuple bond. The latter does seem to indicate that the conventional covalent shared electron pair picture of this bond is not really what is going on, and that the idea of a quintuple bond as sharing five electron pairs in the bonding region between the two Cr atoms is not really realistic. It may be of course that the ELF concept also is not really applicable for such bonds (it is after all essentially an empirical function, the deeper significance of which is debatable).  Nonetheless, the quintuple bond clearly has some surprises for us, and it would itself be no surprise to find out that controversy about the meaning of such a bond continues apace.

• February 14, 2010
• 6:03

  Conformational analysis of cyclotriborazane

   » ‎ Henry Rzepa
  

  In an earlier post, I re-visited the conformational analysis of cyclohexane by looking at the vibrations of the entirely planar form (of D6h symmetry). The method also gave interesting results for the larger cyclo-octane ring. How about a larger leap into the unknown?

  Let us proceed as follows. One fun game to play in chemistry is to invoke iso-electronic substitutions. In this case, we can subtitute a nitrogen and a boron atom for a pair of carbons. Thrice invoked, it leads to a molecule known as cyclotriborazane.

  

  Cyclotriborazane.

  This species is in fact very well known, and a crystal-structure was determined some time ago (DOI: 10.1021/ja00786a022). It is worth considering some of its properties.

  1. The species is crystalline, and sublimes rather than melts. Contrast this with the iso-electronic cyclohexane, which melts at around 6C (itself a surprisingly high value).
  2. The parent H3BNH3 also has a very high melting point of > 100C, which is attributed to an extensive array of so-called dihydrogen bonds in the crystal lattice, in which a positively charged hydrogen deriving from an NH is attracted to a negatively charged hydrogen deriving from a BH. Such dihydrogen bonds have been shown to be quite strong due to this electrostatic interaction, and are responsible for the extraordinary elevation of the melting point compared to the iso-electronic ethane.
  3. The chair form of cyclotriborazane aligns the three hydrogens shown in either blue or red in the axial positions. The three red hydrogens might be expected to be all negatively charged, and the three blue ones positively charged. So in the chair conformation, might we expected the electrostatic repulsions between either the blue or the red hydrogens to destabilize these axial positions, and hence perhaps even destabilize the chair conformation itself?

  The crystal structure however shows clearly that the chair is still the favoured conformation. Equally intriguing, one might expect the three blue hydrogens to stack up to attract electrostatically to the three red hydrogens. But you can see from the crystal packing if you activate the model below that this does not happen!

  

  Cyclotriborazane Crystal structure. Click for 3D

  What of the vibrational analysis, conducted as it was for cyclohexane itself (DOI: 10042/to-4170). Well, just as before, for the planar geometry, three imaginary modes are calculated (A2“, E”) and just as before, they distort the geometry in the direction of a chair (Cs symmetry), a C2-disymmetric twist boat (with a predicted optical rotation of -54°) and a boat respectively (the latter, as before, being a transition state connecting the two C2-enantiomers).

  

  Planar cyclotriborazane distorting to chair.

  But here we get a surprise! According to the B3LYP/6-311G(d,p) model, the final resting energy for the chair is almost the same (indeed 0.2 kcal/mol higher in free energy) as the twist-boat. Perhaps that blue/red repulsion did have an effect after all! If you look at the calculated structure, you can indeed see that the blue/red hydrogens are splayed-out, avoiding each other!

  

  Calculated geometry of the chair form of cyclotriborazane

  This is one of those molecules where one might have expected surprises. In the end, it is surprising at how similar cyclotriborazane is to its iso-electronic cousin cyclohexane.

• February 09, 2010
• 9:38

  Protected: To blog or to publish. That is the question.

   » ‎ Henry Rzepa
  

  This post is password protected. To view it please enter your password below:

  Password:
  
  

• January 31, 2010
• 4:01

  The conformational analysis of cyclo-octane

   » ‎ Henry Rzepa
  

  In the previous post, I suggested that inspecting the imaginary modes of planar cyclohexane might be a fruitful and systematic way in which at least parts of the conformational surface of this ring might be probed. Here, the same process is conducted for cyclo-octane. The ring starts with planar D8h symmetry, and at this geometry (B3LYP/6-311G(d,p), DOI: 10042/to-3742) five negative force constants (corresponding to imaginary modes) are calculated. The most negative is non-degenerate, and gives directly the crown conformation of D4d symmetry (DOI: 10042/to-3738). The remaining four modes comprise two degenerate pairs. Following either of the E2u eigenvectors downhill leads to another conformation, D2d (DOI: 10042/to-3741), with a geometry which is noteworthy for exhibiting a pair of unusually close non-bonded H…H contacts (1.908Å). This value is about  0.3Å shorter than the sum of the Wan der Waals radii (DOI: 10.1021/jp8111556). We can debate whether such a close approach or inter-penetration of two hydrogens is a bond or not (an AIM analysis appears at the bottom of this post).

  D8h, +82.8 kcal/mol
  Follow B2u 467i	Follow E3g 404i	Follow E2u 230i
  to D4d +0.8	to Ci 131i (Au), +7.5	to D2d +3.6
  B2u	E3g	E2u
  Cs 0.0	C2 +1.6	-

  Following the remaining E3g mode leads to a stationary point of Ci symmetry (DOI: 10042/to-3743). This is a valley-ridge potential, since this point turns out to be a transition state itself, and following the Au imaginary mode at this point results in another, this time stable conformation, of chiral C2 symmetry (DOI: 10042/to-3744). This has a calculated optical rotation [α]D of 72° (at 589nm in chloroform).

  Are these three conformations all there are? Well, a thorough analysis of the conformational space has in fact identified six minima (DOI: 10.1002/(SICI)1096-987X(19980415)19:5<524::AID-JCC5>3.0.CO;2-O), of which the most stable has Cs symmetry (the so-called chair-boat conformation, and the one most frequently found in crystal structures of cyclo-octanes). Where is that one in the above analysis? It arrives by a distortion of the D4d form (DOI: 10042/to-3747) via a transition state of no symmetry (DOI: 10042/to-3752)

  Whilst the full potential surface clearly has many more features, following the modes of the planar conformation of cyclo-octane is a simple and rapid way of establishing four of the six limiting stable conformations (the two remaining forms have  D2 and S4 symmetry, see DOI 10.1016/0166-1280(88)80008-3).

  

  AIM analysis of D2d cyclo-octane.

  Finally as promised, the AIM analysis of the D2d conformer (above). The ρ(r) value at the interesting H…H critical point is 0.015, which is pretty high in comparison to most normal hydrogen bonds, and would be conventionally taken to indicate attraction. The Laplacian ∇²ρ(r) is +0.05. The “bond” ellipticity ε has a value of 0.29. Single bonds are close to zero, and C=C double bonds are ~0.4, so this is pretty high (see also DOI: 10.1002/anie.200805751).

  The two highest C-H stretching vibrations for this conformation are well separated from all the others (ν 3095, 3103 cm^-1 for the symmetric A1 and antisymmetric B2 combinations, below for animations). These vibrations serve to both decrease and increase the H…H distances as part of the atomic (harmonic) displacements, and clearly doing so takes more energy than vibrating any of the other C-H bonds. It seems unlikely that the C-H bonds are themselves stronger, so does that mean that the H…H interaction is attractive or is it repulsive? In this context, it is worth noting that the symmetric vibration (both H…H distances decrease/increase at the same time) is lower in wavenumber than the mode which decreases one and increases the other.

  A1

  B2

• January 28, 2010
• 4:49

  The conformation of cyclohexane

   » ‎ Henry Rzepa
  

  Like benzene, its fully saturated version cyclohexane represents an icon of organic chemistry. By 1890, the structure of planar benzene was pretty much understood, but organic chemistry was still struggling somewhat to fully embrace three rather than two dimensions. A grand-old-man of organic chemistry at the time, Adolf von Baeyer, believed that cyclohexane too was flat, and what he said went. So when a young upstart named Hermann Sachse suggested it was not flat, and furthermore could exist in two forms, which we now call chair and boat, no-one believed him. His was a trigonometric proof, deriving from the tetrahedral angle of 109.47 at carbon, and producing what he termed strainless rings.

  Whilst the chair form of cyclohexane now delights all generations of chemistry students, the boat is rather more mysterious. Perhaps due to Sachse, it is still often referred to as a higher energy form of the chair (Barton, in the 1956 review that effectively won him the Nobel prize, clearly states that the boat is one of only two conformations free of angle strain, DOI: 10.1039/QR9561000044). Over the last 30 years or so, and especially with the advent of molecular modelling programs, the complexity of the conformations of cyclohexane has become realised. A nice recent illustration of that complexity is by Jonathan Goodman using commercial software. Here a slightly different take on that is presented.

  The starting point is the flat Baeyer model for cyclohexane. Like benzene, it has D6h symmetry. When subjected to a full force constant analysis using a modern program (in this instance Gaussian 09), this geometry is revealed (DOI: 10042/to-3708) to have three negative force constants, which in simple terms means it has three distortions which will reduce its energy. The eigenvectors of these force constants are shown below, and each set of vectors acts to reduce the symmetry of the species. Such symmetry-reduction is a well known aspect of group theory, and its analysis in the Lie symmetry groups is used in many areas of physics and mathematics, but it is a less used in chemistry.

  348i cm-1 (B2g)	244i (E2u)	244i (E2u)
  D6h to C2h for cyclohexane. Click for animation.	D6h to D2. Click for animation.	D6h to C2v. Click for animation.

  The first of these symmetry-reducing vibrations (the B2g mode) converts the geometry immediately to the chair conformation of cyclohexane. So in some ways, this use of symmetry is a modern equivalent of the trigonometry used by Sachse to prove his point.

  The next two modes are degenerate in energy, and the first of these reduces the symmetry to D2. The result is what we now call the twist-boat. It is interesting, because the D2 group is one of the (relatively few) chiral groups, and the twist-boat exhibits disymmetric symmetry. In other words, following the vibrational eigenvectors in one direction leads to one enantiomer of the twist boat, and in the other direction to the other enantiomer. So (in theory only), one might actually be able to produce chiral cyclohexane (the experiment and resolution would have to be done at very low temperatures!). It is also interesting that theory nowadays could quite reliably calculate the optical rotation of this species (and its circular dichroism spectrum), so we certainly would know what to look out for.

  The second component of the degenerate E imaginary mode leads directly to a species of C2v symmetry, which we recognize as Sachse’s second possible form of cyclohexane. The symmetry-reductions of D6h to C2h, D2 and C2v all have paths on the grand diagram of the 32 crystallographic point groups and their sub groups, and is an interesting application of group theory to a mainstream topic in organic chemistry.

  But the story is not quite complete yet. The C2v boat is not the final outcome of the last distortion! It too is a transition state, connecting again the two D2 forms. So the path from D6h to C2v is NOT a minimum energy reaction path, but a rather different type of path known as a valley-ridge inflection path. An example of such a surface can be seen for the dimerisation of cyclopentadiene (DOI: 10.1021/ja016622h) and effectively it connects one transition state to a second transition state, without involving any intermediates on the pathway. At some stage, the dynamics of the system takes over, and the symmetry breaks without the system ever actually reaching the second transition structure. This final aspect of the potential energy surface of cyclohexane was not discussed by Jonathan Goodman in his own article on the topic.

  So symmetry-breaking is the topic of this blog, and its connection to physics and mathematics. And, I might add that the same approach can be taken for looking at the conformations of cyclobutane, pentane, heptane and octane. But that will be left for another post.

• January 23, 2010
• 12:37

  Blisteringly bent (quadruple) bonds

   » ‎ Henry Rzepa
  

  So ingrained is the habit to think of a bond as a simple straight line connecting two atoms, that we rarely ask ourselves if they are bent, and if so, by how much (and indeed, does it matter?). Well Hursthouse, Malik, and Sales, as long ago as 1978, asked just such a question about the unlikeliest of bonds, a quadruple Cr-Cr bond, found in the compound di-μ-trimethylsilylmethyl-bis-[(tri-methylphosphine) (trimethylsilylmethyI)chromium(II) (DOI: 10.1039/dt9780001314). They arrived at this conclusion by looking very carefully at how the overlaps with the Cr d-orbitals might be achieved.

  

  A system with a bent Cr-Cr quadruple bond. Click for 3D

  One would indeed instinctively think that whilst the relatively weak single bond (about which rotation is easily possible) might be bendable, it seems less intuitive to imagine that something as apparently strong as a quadruple bond could be so. What might the measurable consequences be? Well, Girolami et al 16 years later (DOI: 10.1021/om00017a023) pointed out that such compounds exhibit restricted rotation about the Cr-CH2 bonds in the system, with quite significant barriers. This, it was felt, was due to an agostic CH…Cr interaction,  which might in turn have induced bending of the Cr-Cr bond itself. There the story sort of peters out; no-one else has discussed bent quadruple bonds, or indeed exactly how bent they actually are.

  Well, another 16 years has passed, and now we have a rather better set of tools with which to answer such questions, yes you guessed (if you have read my earlier posts), AIM and ELF. Lets start with AIM, shown below (B3LYP/6-311G(d) calculation, for a somewhat reduced model compared to the real system).

  

  AIM analysis. Click for 3D

  The bond critical point labelled 1 is the Cr-Cr interaction. It has a ρ(r) of 0.142, really very modest for a purportedly quadruple bond. The ∇²ρ(r) is +0.39, which is the wrong sign for a simple covalent bond, and indeed matches the criteria for the (homonuclear) charge shift category popularized by Shaik and Hibberty. Point 2 is the Cr-CH2(si) bond (of calculated length 2.157Å), ρ(r) 0.078 and with an ellipticity ε of 0.34. This latter value compares to e.g. a value of 0.0 expected for a single (rotatable) bond and ~0.4 for a double bond, and seems to match very well with the observation of restricted rotation about this bond. So far, so good! Surprising however is the absence of any BCP in the region marked with a ?, given that the Cr-C length in this region is 2.257Å (only slightly longer than than that for point 2 and surely a good candidate for some sort of Cr-C bond!). There is no sign of any bending of the Cr-Cr bond in this type of analysis (i.e. point 1 lies along the Cr-Cr axis), or indeed of any evidence for α CH…Cr agostic bonding.

  Time then for ELF (below). Well, in one regard, a similar picture to the earlier AIM is obtained. Points 1 and 2 sort of match, and again, no point is found in the region marked with a ?. However, there the similarities end.

  

  ELF basin centroids for Cr-Cr system. Click for 3D

  Thus, point 1 (the apparent quadruple bond) integrates to only 1.04 electrons! But wait for it, it lies well off the straight line connecting the two chromium atoms. Wow! So the bond really is bent! And, because it is contains only 1.04 electrons, that might explain why it can bend so easily! Well, if the Cr-Cr bond does not contain the electrons, where have they gone? The mystery is solved when point 2 is inspected (there are of course two of them, the molecule having C2 symmetry). These each correspond to 1.92 electrons. The ELF analysis furthermore tells us that point 2 is actually trisynaptic, covering both chromium atoms and the carbon. We have found 4.88 electrons associated with the Cr-Cr bond after all (and this is not bad, since one rarely finds the full quota directly in such regions using ELF). To indicate this, point 2 above is actually shown connected to three atoms.

  So to summarise, our Cr-Cr quadruple bond in the ELF analysis occupies three different synaptic basins, arranged in a triangle around the C-Cr axis (as shown below), and with the straight line between the Cr-Cr not entertaining any basin. That certainly is bent!

  

  View showing the three synaptic basins comprising the Cr-Cr bond

  ELF of course gives only one interpretation of the bonding; there are others. But this interpretation certainly seems to give an interesting and unusual insight into this remarkable (and largely ignored) phenomenon.

• January 17, 2010
• 3:35

  Semantic Blogs

   » ‎ Henry Rzepa
  

  A Semantic blog is one in which the system at least in part understands about (some of the) concepts and topics that are in the content. The idea is that this content can be more intelligently (is that the correct word?) and importantly, automatically searched, harvested, and connected to the same or similar concepts found elsewhere in other blogs and the Web as whole. I am writing this blog using Firefox, having added a Firefox extension called Zemanta. As I write, the system offers suggestions for similar themes elsewhere that I could choose to link to the blog (and obviously the more one writes, or the more specific the terms one uses, the more sensible the suggestions become. At this precise moment, it is still offering fairly generic suggestions, one of which I have just chosen to add). My purpose in this particular post is to explore how the very process of writing a blog might be affected by such a product. I am also inferring (but cannot add detail at the moment) that all the (semantic) connections or links to other materials will be expressed in this blog using some form of formal declaration, such as e.g. RDF or RDFa.

  Thus this blog has a WordPress plugin called wp-RDFa as part of its library. This gathers meta-data in two forms, FOAF and Dublin-Core, and expresses it using the RDFa formalism. This is really just a standard way of letting any software that might visit the blog know that this meta-data is available for harvesting. FOAF is something we discussed a year or so back; it is a formal way of expressing information about yourself in RDF (see an ACS talk on the topic), and in particular indicating what you are interested in (as a chemist in my case), who you collaborate with, where you visit (information of course that you do wish to make public, you do not have to include any private details). Nowadays, a variety of social networking tools have become semantically enabled. This blog is, a flavour of Wikis (SemediaWiki, and its potential as a format for science journals), Second Life and many others. At the moment, there is little apparent added value emerging from such enrichment (I have just noted another two Zemanta articles flagged, which I will add at this instant) and certainly little in chemistry.

  But what could one aspire to? For example, Steve Bachrach on his blog routinely adds InChI identifiers and keys to uniquely identify all molecules mentioned on his site. Just imagine a situation where one is describing a molecule in one’s own blog, and e.g. Zemanta instantly flags up any other article out there which has tagged the same molecule. That article and your blog can now be semantically identified as talking about the same system. A harvester could collect the information about this molecule, and create a superset of information about it (hey, we chemists already have such a system, it is called Chemical Abstracts! But of course its not quite the same, and I had better reserve a comparison with CAS for another post), which in turn enriches resources such as Zemanta. Its a sort of positive feed-back loop!

  Well, the Semantic Web has been a long time coming (see DOI: [dx.doi.org] or 10.1087/095315101750240421 which were both written in 2001), and since it has not yet changed the Web, some tend to write it off as a lost cause. Perhaps the semantification of blogs will make a difference?

  Related articles by Zemanta

  • More on Zemanta (thwaits.wordpress.com)
  • Google, RDFa, and Reusing Vocabularies (go-to-hellman.blogspot.com)
  • The end of Search? Linked Data, Semantic Web & thoughts. (webr3.org)

  
• January 11, 2010
• 8:48

  Chemical intimacy: Ion pairs in carbocations

   » ‎ Henry Rzepa
  

  The scheme below illustrates one of the iconic reactions in organic chemistry. It is a modern representation of Meerwein’s famous experiment from which he inferred a carbocation intermediate, deduced from studying the rate of enantiomerization of isobornyl chloride when treated with the Lewis acid SnCl4.

  

  The isomerisation of iso-bornyl chloride

  Meerwein himself suggested (in effect, since he lacked the modern terminology used here) that the reaction proceeded via a hydride shift 3, which was acting as the mirror in reflecting 1 onto 1‘. A few years later, isotopic labelling studies demonstrated that another pathway occurs, at more or less the same rate. This alternative proceeds via a series of [1,2] carbon shifts, with the mirror now being 8 rather than 3. I have documented the story in detail in an article that will shortly appear in the J. Chemical Education (DOI: 10.1021/ed800058c). There, calculations reveal that the two transition states, 3 and 8 (which the experiments above suggest should be almost equal in energy) in fact differed by ~8 kcal/mol in favour of the latter for a gas-phase model which does not include the counterion. These calculations were done at a level (B3LYP/cc-pVQZ) which indicates that 8 kcal/mol represents a real discrepancy not so much in the calculation as in the model used for that calculation. I suggested that perhaps the discrepancy might be due to tunneling effects in the hydride transfer reaction, accelerating that pathway compared to methyl transfer.

  What was missing from that particular model was the counter-ion, which is supposed to form an intimate ion-pair with the carbocation in moderately polar solvents. How much does the presence of such an object perturb the transition states?  To find out, we need calculate such systems (which by definition have very large dipole moments) with inclusion of solvation corrections. Now that new algorithms for computing transition states with solvation have made this a routine calculation, I can report an update to these results. This was done at the B3LYP/cc-pVTZ (aug-cc-pVTZ-pp for the Sn) level, using dichloromethane as a continuum solvent. Without the SnCl5 counterion, 3 and 8 differ by 5.4 kcal/mol in free energy (this difference now includes all the solvation free energy terms), and in the presence of the counter-ion this remains unchanged at 5.4 kcal/mol (see DOIs 10042/to-3668 and 10042/to-3667 without SnCl5 and 10042/to-3670 and 10042/to-3665 with). The free energy of activation with SnCl5 (see DOI: 10042/to-3695 for starting material) is 16.6 kcal/mol (for the [2,6] H shift) and 11.2 kcal/mol (for the  [1,2] Me shift), which indicates a facile room temperature reaction (as indeed is the case).

  TS H-transfer. Click for animation

  TS 1,2 Methyl shift. Click for animation

  What are the implications for this result?

  1. Modelling an (intimate) ion-pair is different from that of covalent compounds in one respect. Whereas the geometry at covalent atoms is very well established and largely predictable, ion-pairs are potentially much more flexible. In other words, it is nowhere near as obvious where to place the counter-ion. In the above diagrams, the SnCl5 is located at a reasonable position, but there are other positions where it could be. Although what is shown is an energy optimized structure, a full search of all the possible positions that the SnCl5 could adopt has not been undertaken, and the possibility must remain that another pose of the ion might be lower in energy, for either of the two transition states. Indeed, if it turns out there are many positions for the ion of very similar in energy, then the entropy of the system would have to be corrected for these microstates.
  2. Nevertheless, one can draw insight from the two structures shown above (click to animate the transition mode). The counter-ion for the hydride transfer does approach the transferring hydrogen quite closely, and does appear to establish a H-bond between two hydrogens and one chlorine. This would stabilize that structure relative to the methyl shift transition state, where such hydrogen bonds do not appear to form. In this case  however, these interactions do not change the relative stabilties.
  3. These ion-pairs do have very large dipole moments (~23D for 3, ~27D for 8), which suggests that the result might in fact be sensitive to the nature of the solvent (and presumably the counter-ion itself).

  Many reactions do take place in which intimate ion-pairs are formed (including a fair number of catalytic systems involving metals). We cannot generalise from the result above, but it may well be that the perturbation induced by such counter-ion may play significant roles in deciding selectivities. I would venture to suggest that increasingly modelling such as reported here will play a significant role in establishing mechanisms accounting for the selectivity of catalytic reactions.

• January 09, 2010
• 16:39

  How long will a blog last? ArchivePress

   » ‎ Henry Rzepa

  After around 40 posts here, I decided to take a look at the whole effort and ask some questions. For example

  1. Should (scientific) blogs be used to report new science, or merely opinion on existing science (see this blog also)?
  2. If the former, should they be abstracted in the manner of regular articles (e.g. by CAS etc).
  3. Unlike e.g. a journal, a blog is often (and certainly in this case) the effort of an individual. Journals on the other hand can last for centuries (see for example this link to the ToC of the world’s oldest scientific journal that has been in continuous publication for 355 years!). So how long should/can a blog last?
  4. The last question leads on to whether blogs should be archived or curated in a larger sense?

  The last question leads directly to projects such as ArchivePress which has just started up a few months ago. I will quote two of their objectives

  • Methodology and guidance for the effective capture and management of blog posts.
  • Scripts/plugins to enable WordPress to be used as a blog aggregator and archiving engine.

  Of course, this will have to be a fairly generic solution, and certainly one aspect of my blog presents another challenge, namely how to preserve the molecules mentioned here (many of the posts include 3D coordinates lurking under the images). But one step at a time!

  I will post on another solution to the preservation issues, which should enter the public domain in a month or so. Meanwhile, let’s see what the ArchivePress project can offer!

• January 01, 2010
• 5:44

  Contriving aromaticity from S≡C Triple bonds

   » ‎ Henry Rzepa

  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

   

• December 30, 2009
• 15:45

  Ménage à deux: Non-classical SC bonds.

   » ‎ Henry Rzepa

  A previous post posed the question; during the transformation of one molecule to another, what is the maximum number of electron pairs 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 09, 2009
• 1:54

  Clar islands in a π Cloud

   » ‎ Henry Rzepa

  Clar islands are found not so much in an ocean, but in a type of molecule known as polycyclic aromatic hydrocarbons (PAH). One member of this class, graphene, is attracting a lot of attention recently as a potential material for use in computer chips. Clar coined the term in 1972 to explain the properties of PAHs, and the background is covered in a recent article by Fowler and co-workers (DOI: 10.1039/b604769f). The concept is illustrated by the following hydrocarbon:

  

  Clar islands in a polybenzenoid hydrocarbon

  The Clar islands are shown in red, and represent in effect the resonance form of this species which maximises the number of aromatic electronic sextets possible to achieve via a cyclohexatriene resonance form. It encapsulates the concept that maximum stabilization is achieved when the π-electrons in the molecule cluster together (or localize) in cyclic groups of six (rather than eg other allowed values as predicted by the 4n+2 rule of aromaticity). As a historical note, although Clar popularized the concept in the 1970s, the (C) representation had in fact been introduced almost one hundred years earlier, by Henry Armstrong (DOI: 10.1039/PL8900600095). Many demonstrations that Clar islands are reasonably based in quantum mechanical reality have been made; a very graphical and convincing one is that by Fowler and coworkers in the reference noted above, using the calculated magnetic response property known as π current densities (although this shows that the six outer islands tend merge into a single continuous outer periphery).

  Current density maps showing Clar islands for the molecule above (taken from DOI: 10.1039/b604769f)

  Previous posts on this blog have mentioned the application of another computed quantum mechanical property known as ELF, the electron localization function introduced by Becke and Edgecombe in 1990 (DOI: 10.1063/1.458517 ) and subsequently adapted for use with DFT-based wavefunctions. ELF is normally applied to help analyze the bonding in a molecule; the value of the function is normalized to lie between 1.0 (a simple interpretation is that this is the value associated with a perfectly localized electron pair) and 0.0. ELF has no association with magnetic response (the latter being an excitation phenomenon), but since the Clar islands can also be considered a localizing property of the π electrons, it is tempting to ask whether the ELF function can also reveal their characteristics (this question was first posed in DOI: 10.1039/b810147g).

  

  The ELF function, as isosurfaces contoured at various thresholds. Click for 3D

  The diagram above shows the ELF function computed for the π-electrons of the molecule above (B3LYP/6-31G(d), as isosurfaces contoured at various values. At the value of 1.0, no features are discernible, but at 0.95 features which resemble basins associated with each atom centre have appeared, in the region of the 2p-valence atomic orbital on each carbon atom we regard as contributing the π-electron to the system. As the ELF threshold is reduced, these objects start to merge into what are called valence basins associated with bonds in the molecule. The outer periphery is the first to start coalescing. By a value of 0.75 (click on the diagram above to see a 3D model) the basins have merged to form seven clear-cut rings which happen to coincide exactly with the Clar islands. This feature persists down to a threshold of 0.55. Below this value, the seven individual basins merge into a single basin contiguous across the top (and bottom) surfaces of the molecule. One can also conceptualize the journey in the other direction. At low ELF values, the function is continuous, but as the threshold increases, it starts to bifurcate into separated basins. The first clear-cut bifurcation is indeed into the Clar islands, and this persists across a relatively wide range of ELF values, which suggests it is a significant feature. What is somewhat surprising is the close apparent correspondence of this way of analysing the electronic properties of the π electrons with their magnetic response computed via current densities. But association with aromaticity has previously been made (DOI: 10.1063/1.1635799). Thus Santos and co-workers have shown that the value of the ELF function at the point where it bifurcates from a ring into discrete valence or atomic basins can be related to other metrics of aromaticity. Here, that value is around 0.75 for the Clar basins, which is also within the range of values that Santos et al associate with prominent aromaticity (benzene itself has a value around  0.95).

  

  A C114 PAH

  The ELF function for the 114-carbon unit shown above again reveals prominent Clar islands, the inner heptet being very similar to the picture painted using current densities.

  

  Clar islands in the ELF function for a C114 carbon PAH

  The final example involves diboranyl isophlorin (DOI: 10.1002/chem.200700046), a 20 π-electron antiaromatic system. Such systems are particularly prone to forming locally aromatic Clar islands as an alternative to global antiaromaticity (DOI: 10.1039/b810147g).

  

  A Diboranyl isophlorin.

  The ELF function is shown for both the neutral diboranyl system and its (supposedly more aromatic) dication. Here a mystery forms. No Clar islands are seen, and instead it is the periphery that bifurcates, at ELF thresholds of 0.5 for the neutral and 0.7 for the dication. The latter value clearly is that of an aromatic species, but the former is somewhat in no-man’s land, but certainly less aromatic that the dication. One for further study I fancy!

  

  ELF Function for diboranyl molecules (red=neutral, green=dication). Click for 3D

  Does the ELF function have any possible advantage over the use of current density methods for analysing aromaticity? Well, the latter is normally applied to flat systems with planes of symmetry defining the π-system, and with respect to which an applied magnetic field is oriented. How to orient this magnetic field is not so obvious for prominently non-planar or helical molecules. Since the ELF function does not depend on the orientation of an applied magnetic field, it may be a useful adjunct for studying the properties of π-electrons in non-planar systems.

• December 06, 2009
• 4:56

  The nature of the C≡S triple bond: part 3.

   » ‎ Henry Rzepa

  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 05, 2009
• 7:11

  The nature of the C≡S Triple bond: Part 2

   » ‎ Henry Rzepa

  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 01, 2009
• 5:55

  The nature of the C≡S triple bond

   » ‎ Henry Rzepa

  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(T)/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.

• 3:58

  Multi-centre bonding in the Grignard Reagent

   » ‎ Henry Rzepa

  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.

• November 29, 2009
• 3:20

  The Fine-tuned principle in chemistry

   » ‎ Henry Rzepa

  The  so-called  Fine tuned model of the universe asserts that any small change in several of the dimensionless fundamental physical constants would make the universe radically different (and hence one in which life as we know it could not exist). I suggest here that there may be molecules which epitomize the same principle in chemistry. Consider for example dimethyl formamide. The NMR spectra of this molecule reveal that at room temperature, the two methyl groups are inequivalent, indicating that the rate constant for rotation about the C-N bond has a very particular range of values at the temperatures at which most living organisms exist on our planet.

  

  Dimethyl formamide

  The half-restricted room-temperature rotation about the C-N bond arises from exactly the right amount of resonance contribution from the ionic form shown on the right, and this in turn depends on the relative energies of the nitrogen pair and the π system of the carbonyl group having the correct relationship. It is probably also true that the environment that this grouping finds itself in will alter the contribution (i.e. stabilize the ionic form over the neutral one).   A little less contribution and the C-N bond would rotate much more easily, a little more and it would be much more rigid. Since this peptide bond is an essential and repeated feature of the structure of most biological proteins and enzymes, one might speculate that if that bond could rotate more easily, most enzymes would be much floppier than they are, and may not be easily induced to fold in a repeatable manner into the conformations that enable all the metabolic processes and make them the efficient catalysts they are. If the bond rotated less easily, it might be that the same enzymes would end up being too rigid, and this may prevent them from flexing sufficiently to allow key metabolites to enter or leave the active site.

  Nowadays, the flexing of proteins is commonly studied using techniques of molecular dynamics,  the driving forces for which are specified using molecule mechanics force fields. Here, the rotation about the C-N bond is defined by simple mechanical force constants or torsional barriers. I ask here how sensitive the dynamics of protein folding and catalysis are to the C-N rotational barrier? Is this truly a fine-tuned molecule, or might it be that the existence of life as we know it has a wide tolerance to the strength of the C-N bond?

• November 18, 2009
• 7:16

  Mechanistic Ménage à trois

   » ‎ Henry Rzepa

  Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography of the electronic dance (the order in which the steps take place). The basic grammar of describing that choreography tends to be the full-headed curly arrow for closed shell systems and its half-barbed equivalent for open shell systems. An effectively unstated and hence implicit rule for closed shell systems is that only one curly arrow is used per breaking or forming bond, i.e. electrons move around bonds in pairs. So consider the following reaction (inspired by a posting on  Steve Bachrach’s blog)

  

  This is very much a hypothetical mechanism, or a thought-experiment if you will. Three nitrosonium cations decide to get together to swap their partners. Each diatomic molecule swaps e.g. one oxygen for another during this exchange reaction (it could easily be studied experimentally of course using isotopic substitution). Three sets of three curly arrows have been used, shown in different colours above.  One set of these arrows at least has plenty of analogy in the real world; representing a π2s+π2s+π2s cycloaddition reaction. The other two sets represents rotation of the  in-plane π-set and the in-plane σ-set. What about the choreography? Can all three sets move at the same time? If so, they would provide an exception to the rule above; three bonds would concurrently change their order from 3 to 0; the other three the reverse of 0 to 3.

  What does quantum mechanics say about this? Well, a well defined, synchronous concerted transition state can indeed be found (B3LYP/6-31G(d), DOI:  10042/to-2905) It has one imaginary frequency (click on the above diagram to view the animation) which does indeed perform the bond transposition function required! It has the form of the so-called Kekule mode (deriving from a mode found in benzene which involves shortening of the lengths of three bonds, and lengthening of the other three, much in the manner of the resonance named after  Kekule; see e.g. DOI: 10.1039/B911817A for more details). Of course, describing it as a change in the bond orders 3 → 0/0 → 3 is simplistic; the bond order in the nitrosonium cation itself is almost certainly somewhat less than three.  But clearly, the implicit rule that  mechanistic arrow pushing should not involve more than one arrow departing from or arriving at any one bond can be broken. I will leave it to the reader of this blog to see what happens when you try to rearrange the choreography of the above reaction. Try pushing first one set of three arrows, then another and a final third. What do you get? (the why of the dance is almost certainly due to electrostatic repulsions between the three nitrosonium cations).

• 7:16

  Mechanistic Ménage à trois

   » ‎ Henry Rzepa

  Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations. These have the potential of exposing the underlying choreography of the electronic dance (the order in which the steps take place). The basic grammar of describing that choreography tends to be the full-headed curly arrow for closed shell systems and its half-barbed equivalent for open shell systems. An effectively unstated and hence implicit rule for closed shell systems is that only one curly arrow is used per breaking or forming bond, i.e. electrons move around bonds in pairs. So consider the following reaction (inspired by a posting on  Steve Bachrach’s blog)

  

  This is very much a hypothetical mechanism, or a thought-experiment if you will. Three nitrosonium cations decide to get together to swap their partners. Each diatomic molecule swaps e.g. one oxygen for another during this exchange reaction (it could easily be studied experimentally of course using isotopic substitution). Three sets of three curly arrows have been used, shown in different colours above.  One set of these arrows at least has plenty of analogy in the real world; representing a π2s+π2s+π2s cycloaddition reaction. The other two sets represents rotation of the  in-plane π-set and the in-plane σ-set. What about the choreography? Can all three sets move at the same time? If so, they would provide an exception to the rule above; three bonds would concurrently change their order from 3 to 0; the other three the reverse of 0 to 3.

  What does quantum mechanics say about this? Well, a well defined, synchronous concerted transition state can indeed be found (B3LYP/6-31G(d), DOI:  10042/to-2905) It has one imaginary frequency (click on the above diagram to view the animation) which does indeed perform the bond transposition function required! It has the form of the so-called Kekule mode (deriving from a mode found in benzene which involves shortening of the lengths of three bonds, and lengthening of the other three, much in the manner of the resonance named after  Kekule; see e.g. DOI: 10.1039/B911817A for more details). Of course, describing it as a change in the bond orders 3 → 0/0 → 3 is simplistic; the bond order in the nitrosonium cation itself is almost certainly somewhat less than three.  But clearly, the implicit rule that  mechanistic arrow pushing should not involve more than one arrow departing from or arriving at any one bond can be broken. I will leave it to the reader of this blog to see what happens when you try to rearrange the choreography of the above reaction. Try pushing first one set of three arrows, then another and a final third. What do you get? (the why of the dance is almost certainly due to electrostatic repulsions between the three nitrosonium cations).

• November 11, 2009
• 3:48

  The SN1 Reaction- revisited

   » ‎ Henry Rzepa

  In an earlier post I wrote about the iconic SN1 solvolysis reaction, and presented a model for the transition state involving 13 water molecules. Here, I follow this up with an improved molecule containing 16 water molecules, and how the barrier for this model compares with experiment. This latter is nicely summarized in the following article: Solvolysis of t-butyl chloride in water-rich methanol + water mixtures, which (for pure water) cites the following activation parameters

  • ΔH^†283 = 23.0 kcal/mol
  • ΔG^†283 = 19.7 kcal/mol
  • ΔS^†283 = +11.1 cal/mol/K

  But first, a word about how this new transtion state has been obtained. The DFT treatment used is quite standard (B3LYP/6-31G(d) ), and one can indeed locate a transition state using just this approach (this is how the previous model was obtained). One has to work very hard to orient the starting guess for the geometry so that as many hydrogen bonds between the waters themselves, and to the substrate, are created. The previous model took quite a few guesses and attempts! The solvent in such a model is simulated by the explicit water molecules themselves. Of course, the quality of the solvent then depends on how many water molecules are used. A proper solvent field using explicit water molecules is thought to require 100s of water molecules! But a reasonable approximation/compromise may well be 13.

  So how can the model be improved? Well, in many ways, some of which include treating the dynamics of the system. But I will stick just to two.

  1. Firstly, we assume that the water molecules are used to form a bridge between the incoming nucleophile (another water) and the leaving group (the chloride). In the previous model, two such bridges were constructed using the 13 water molecules. But in fact, there is still space between two of the methyl groups to construct a third bridge. This takes the total solvent molecules to 16.
  2. Solvent can also be modelled as a continuum, in which a cavity which the substrate occupies is surrounded by a field generated by the continuum solvent. The problem with these cavity approaches in the past has been that it is not easy to optimize the geometry of the molecule contained within the cavity. Because the cavity was constructed by tesselation, the first derivatives of the energy of the molecule within the cavity were not regular, and as a result, geometry optimization (and particularly transition state optimization) would frequently meander and fail to converge. Darrin York and Martin Karplus came to the rescue (some time ago, it has to be said, DOI: 10.1021/jp992097l) by formulating a smoothed out solvation cavity where the first (and second derivatives) are stable and well behaved. This new algorithm has now been implemented in Gaussian09, and it now allows really easy transition state location within a solvent cavity

  The result of this optimization is shown below (and can be seen in original form at the following DOI: 10042/to-2894).

  

  Transition state for Sn1 solvolysis of tert-butyl chloride. Click for animation.

  The model has not changed that much compared to before. The reaction (imaginary) mode still clearly shows formation of the C-O bond and cleavage of the C-Cl bond. Also as before, there is a lot of motion of the methyl groups, as the forming cation induces stereo-electronic alignment with the adjacent C-H bonds (and which explains the large secondary deuterium isotope effects measured for this reaction, kH/kD (298) = 2.39, see DOI: 10.1021/ja01080a004). The hydrogen bonding pattern is also retained (despite the surrounding solvent field!). But what of the predicted activation parameters

  • ΔH^†298 = 17.4 kcal/mol
  • ΔG^†298 = 18.7 kcal/mol
  • ΔS^†298 = -4.4 cal/mol/K

  The overall free energy is in great agreement with experiment! But the entropy is the wrong sign!! The calculation is predicting that the transition state is more rigid than the reactant. One can see how this might happen, since the greater ionic character produces very much stronger hydrogen bonds, which strengthen the three solvent bridges. It may be simply that the rigid-rotor-harmonic-oscillator approximation breaks down horribly for the entropy in this calculation. But it is encouraging that the activation barrier is reproducing experiment, which suggests the model cannot be completely wrong!

• October 05, 2009
• 14:26

  Hypervalency: a reality check

   » ‎ Henry Rzepa

  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 03, 2009
• 10:28

  Uncompressed Monovalent Helium

   » ‎ Henry Rzepa

  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⁺?

  

  Inventing the Helium bond

  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 C4v 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 νB-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	νX-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

  AIM for X=B-He. Click for 3D

  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.

• 3:42

  Pentavalent nitrogen and boron

   » ‎ Henry Rzepa

  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

  

  Pentavalency across a series

  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 C4v-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.