energy « Henry Rzepa's blog

Posts Tagged ‘energy’

Imaging normal vibrational modes of a single molecule of CoTPP: a mystery about the nature of the imaged species.

Thursday, April 25th, 2019

Previously, I explored (computationally) the normal vibrational modes of Co(II)-tetraphenylporphyrin (CoTPP) as a “flattened” species on copper or gold surfaces for comparison with those recently imaged[1]. The initial intent was to estimate the “flattening” energy. There are six electronic possibilities for this molecule on a metal surface. Respectively positively, or negatively charged and a neutral species, each in either a low or a high-spin electronic state. I reported five of these earlier, finding each had quite high barriers for “flattening” the molecule. For the final 6th possibility, the triplet anion, the SCF (self-consistent-field) had failed to converge, but for which I can now report converged results.^†

charge	Spin Multiplicity	ΔG, Twisted Ph, Hartree	ΔG, “flattened”, Hartree	ΔΔG, kcal/mol
-1	Triplet	-3294.68134 (C₂)	-3294.64735 (C_2v)	21.3
			-3294.60006 (C_s)	51.0
			-3294.37012 (D_2h)	195.3
	Singlet	-3294.67713 (S₄)	-3294.39418 (D_4h)	175.6
			-3294.39321 (D_2h)	178.2
			-3294.56652 (D₂)	69.4
FAIR data at DOI: 10.14469/hpc/5486

I am exploring the so-called “flattened” mode, induced by the voltage applied at the tip of the STM (scanning-tunnelling microscope) probe and which causes the phenyl rings to rotate as per above. This rotation in turn causes the hydrogen atom-pair encircled above to approach each other very closely.^‡ To avoid these repulsions, the molecule buckles into one of two modes. The first causes the phenyl rings to stack up/down/up/down. The second involves an all-up stacking, as shown below. Although these are in fact 4th-order saddle points as isolated molecules, the STM voltage can inject sufficient energy to convert these into apparently stable minima on the metal surface.

All syn mode, Triplet anion

The up/down/up/down “flattened” form (below) shows a much more modest planarisation energy than all the other charged/neutral states reported in the previous post, whereas the all-up isomer (which on the face of it looks a far easier proposition to come into close contact with a metal surface) is far higher in free energy.

The caption to Figure 3 in the original article[1] does not explicitly mention the nature of the metal surface on which the vibrations were recorded, but we do get “The intensity in the upper right corner of the 320-cm⁻¹ map is from a neighbouring Cu–CO stretch” which suggests it is in fact a copper surface. Coupled with the other observation that in “contrast to gold, the Kondo resonance of cobalt disappears on Cu(100), suggesting that it acquires nearly a full electron from the metal (see Extended Data Fig. 2),” the model below of a triplet-state anion on the Cu surface seems the most appropriate.

Syn/anti mode, Triplet anion with C2v symmetry

There is one final remark made in the article worth repeating here: “This suggests that the vibronic functions are complex-valued in this state, as expected for Jahn–Teller active degenerate orbitals of the planar porphyrin.²⁶” Orbital degeneracy can only occur if the molecule has e.g. D_4h point group symmetry, whereas the triplet anion stationary-point shown in the figure above has only C_2v symmetry for which no orbital degeneracies (E) are expected. Enforcing D_4h symmetry on Co(II) tetraphenylporphyrin results in eight pairs of H…H contacts of 1.34Å,^‡ which is an impossibly short distance (the shortest known is ~1.5Å). Moreover this geometry has an equally impossible free energy 176 kcal/mol above the relaxed free molecule. Visually from Figure 3, the H…H contact distance looks even shorter (below, circled in red)! A D_2h form (with no E-type orbitals) can also be located.

Singlet, Calculated with D_4h symmetry. Click for vibrations.	Singlet, Calculated with D_2h symmetry. Click for vibrations.
Taken from Figure 3 (Ref 1).

These totally flat species are calculated to be at 13 or 12th-order saddle points, with the eight most negative force constants having vectors which correspond to up/down avoidance motions of the proximate hydrogen pairs encircled above and the remaining being buckling modes of the entire ring.

So to the mystery, being the nature of the “flattened” CoTPP on the copper metal surface, as represented in Figure 3 of the article.[1] Is it truly flat, as implied by the article? If so, the energy of such a species would be beyond the limits of what is normally considered feasible. Moreover, it would represent a species with truly mind-blowing short H…H contacts. Or could it be a saddle-shaped geometry, where the phenyl rings are not lying flat in contact with the metal but interacting via the phenyl para-hydrogens? That geometry has not only a much more reasonable energy above the unflattened free molecule, but also acceptable H…H contacts (~2.0.Å) However, would such a shape correspond to the visualised vibrational modes also shown in Figure 3? I have a feeling that there must be more to this story.

^†These convergence problems were solved by improving the basis set via adding “diffuse” functions, as in (u)ωB97XD/6-311+G(d,p). ^‡If the crystal structure for these species is flattened without geometry optimisation, the H-H distance is around 0.8Å

References

J. Lee, K.T. Crampton, N. Tallarida, and V.A. Apkarian, "Visualizing vibrational normal modes of a single molecule with atomically confined light", Nature, vol. 568, pp. 78-82, 2019. https://doi.org/10.1038/s41586-019-1059-9

Tags:019-1059-9, 10.1038, Biomolecules, Chelating agents, chemical bonding, Chemical compounds, Chemistry, Coordination chemistry, Coordination complex, Copper, copper metal surface, Cu–CO, E-type, energy, free energy, higher energy, impossible free energy, Inorganic chemistry, Jahn–Teller effect, lowest energy electronic state, Metabolism, metal, metal surface, modest planarisation energy, Molecule, Natural sciences, Physical sciences, planarisation, Porphyrin, reasonable energy, Resonance, Solid-state chemistry, sufficient energy, Teller, Tetraphenylporphyrin
Posted in Interesting chemistry | 1 Comment »

Imaging vibrational normal modes of a single molecule.

Thursday, April 18th, 2019

The topic of this post originates from a recent article which is attracting much attention.[1] The technique uses confined light to both increase the spatial resolution by around three orders of magnitude and also to amplify the signal from individual molecules to the point it can be recorded. To me, Figure 3 in this article summarises it nicely (caption: visualization of vibrational normal modes). Here I intend to show selected modes as animated and rotatable 3D models with the help of their calculation using density functional theory (a mode of presentation that the confinement of Figure 3 to the pages of a conventional journal article does not enable).

I should start by quoting some pertinent aspects obtained from the article itself. The caption to Figure 3 includes assignments, which I presume were done with the help of Gaussian calculations. Thus in the Methods section, we find … The geometry of a free CoTPP molecule is optimized under tight convergence criteria using Gaussian 09 (ref. 33). The orientationally averaged Raman spectrum and vibrational normal modes are calculated with the geometry of a free molecule … All the calculations mentioned above are performed at the B3LYP/6-31G* level with the effective core potential at the cobalt centre. Armed with this information, I looked at the data included with the article (the data supporting the findings of this study are available within the paper. Experimental source data for Figs. 1–4 are provided with the paper) but did not spot any data specifically relating to those Gaussian 09 calculations; in particular any data that would allow me to animate some vibrational normal modes for display here. No matter, it is easy to re-calculate, although I had to obtain the basic 3D coordinates from the Cambridge crystal data base (e.g. entry IKUDOH, DOI: 10.5517/cc6hj4b) since they were unavailable from the article itself. At this point some decisions about molecular symmetry needed to be made (the symmetry is not mentioned in the article), since it is useful to attach the irreducible representations (IR) of each mode as a label^♥ (lacking in Figure 3). The crystal structure I picked has idealised S₄ symmetry, but it could be higher at D_2d or lower at C₂.

The next issue to be solved is how many electrons to associate with the molecule. Tetraphenylporphyrin has 347 electrons and the free molecule would be expected to be a doublet spin state (with the quartet as an excited state). Were the vibrational modes calculated for this state? Perhaps not since I then found this statement: The physisorbed CoTPP is positively charged on gold, as demonstrated through TERS measurements using CO-terminated tips²⁴ and through the Smoluchowski effect²⁹…. In contrast to gold, the Kondo resonance of cobalt disappears on Cu(100), suggesting that it acquires nearly a full electron from the metal (see Extended Data Fig. 2). So it seems worth calculating both the cation and the anion singlets as well as the neutral doublet. But at this stage we do not know for certain what spin state the Gaussian 09 assignments in Figure 3 were done for, since there is no data associated with the article to tell us, only that they were done for the free molecule (nominally a doublet).

There is one more remark made in the article we need to take into account: After lowering the sample bias to approach the molecule and scanning at close range, the molecule flattens. Its phenyl rings, which in the free molecule assume a dihedral angle of 72°, rotate to become coplanar (see Extended Data Fig. 1b). Evidently, the binding energy of the phenyl groups to copper overcomes the steric hindrance in the planar geometry. So it might be useful to calculate this “flattened” form to see how much steric repulsion energy needs to be overcome by that binding of the phenyl groups to the surface of the metal.

Finally, I decided to not try to replicate exactly the reported calculations (B3LYP/6-31G(d)) since this type of DFT mode does not include any dispersion attraction terms; moreover by today’s standards the basis set is also rather small. So here you have an ωB97Xd/6-311G(d,p) calculation, with tight convergence criteria (integral accuracy 10^-14 and SCF 10^-9; again we do not know what values were used for the article). To ensure that my data is as FAIR as possible, here is its DOI: 10.14469/hpc/5461

charge	Multiplicity	ΔG, Twisted Ph Hartree	ΔG, Co-planar Ph Hartree	ΔΔG, kcal/mol
0	Doublet	-3294.58693	-3294.48867	61.7
0	Quartet	-3294.58777	-3294.51985	42.6
+1	Singlet	-3294.35473	-3294.24973	65.9
+1	Triplet	-3294.40821	-3294.33092	48.5
-1	Singlet	-3294.67713	-3294.56652	69.4

Starting with a singlet cation as a model, the intent is to compare the “free molecule” energy with that of a flattened version where the dihedral angles of the phenyl rings relative to the porphyrin ring are constrained to ~0° rather than ~72°. This emerges as a 4th order saddle point (a stationary point with four negative roots for the force constant matrix). Such a property means that each co-planar phenyl group is independently a transition state for rotation. The calculated geometry overall is far from planar, having S₄ symmetry. The image below in (a) shows how non-planar the molecule still is; (b) an attempt to orient it into the same position as is displayed in Figure 3 of the article.[1]

Singlet cation. Click on the image to get a rotatable model.

The free energy ΔG is 65.9 kcal/mol higher than the twisted form, which means that according to the model proposed, the binding energy of the phenyl groups to copper must recover at least this much energy. If we consider a cationic porphyrin interacting with an anionic metal surface as an ion-pair, then this is perhaps feasible. It is difficult however to see how more than two of the phenyl rings can simultaneously interact with a flat metal surface.

Next, the triplet state of the cation, again a 4th-order saddle point with a rotational barrier of ΔG^‡48.5 kcal/mol; the triplet being 33.6 kcal/mol lower than the singlet using this functional (singlet-triplet separations can be quite sensitive to the DFT functional used).

Triplet cation. Click on the image to get a rotatable model.

Next, the neutral doublet, another 4th-order saddle point and below it the quartet state, which this time is just a 2nd-order saddle point (an interesting observation in itself).

Neutral Doublet

Neutral Quartet

Finally, the “flattened” singlet anion, which also emerges as a 4th-order saddle point (~~the triplet state has SCF convergence issues which I am still grappling with~~).

Singlet anion

To inspect the vibrational modes of any of these species, click on the appropriate image to open a JSmol display. Then right-click in the molecule window, navigate to the 3rd menu down from the top (Model – 48/226), where the frames/vibrations are ordered in sets of 25. Open the appropriate set and select the vibration you want from the list of wavenumbers shown. The preselected normal mode is the one identified in Figure 3 as 388 cm^-1, the symmetric N-Co stretch (I note the figure 3 caption refers to them as vibrational frequencies; they are of course vibrational wavenumbers!). You can also inspect the four modes shown as negative numbers (correctly as imaginary numbers) to see how the phenyl groups rotate. If you want to analyze the vibrational modes using other tools (the free Avogadro program is a good one), then download the appropriate log or checkpoint file from the FAIR data archives at 10.14469/hpc/5461.

I conclude by noting that the aspect of this article which I presume reports the Gaussian normal vibrational mode calculations (Figure 3, caption Bottom, assigned vibrational normal modes), has been a challenging one to analyse.^† Neither the charge state nor the spin state of these calculations is clearly indicated in the article (unless I missed it somewhere). The barriers to flattening out the molecule by twisting all four phenyl groups are unreported in the article, but emerge as substantial from the calculations here. The various species I calculated (summarised in the table and figures above) are all predicted to be non-planar. In the absence of provided coordinates with the article, the visual appearances (bottom row, Figure 3) are the only information available. These certainly appear flat and rather different from my projections shown above or below.

All of which amounts to a plea for more data and especially FAIR data to be submitted, providing information such as the charge and spin states used for the calculations, along with a full listing of all the normal mode vectors and wavenumbers. The article is only a letter at this stage; perhaps this information will appear in due course!

^†As noted above I have not attempted a direct replication, not least because there is no reported data to which any replication could be compared. ^♥The IRs of each vibrational mode are displayed along with the wavenumber when the 3D JSmol display is shown with a right-mouse-click.

References

J. Lee, K.T. Crampton, N. Tallarida, and V.A. Apkarian, "Visualizing vibrational normal modes of a single molecule with atomically confined light", Nature, vol. 568, pp. 78-82, 2019. https://doi.org/10.1038/s41586-019-1059-9

Tags:anionic metal surface, Cambridge, chemical bonding, Chemistry, dihedral, energy, flat metal surface, metal, Natural sciences, Neutral Quartet, Physical sciences, Raman scattering, Raman spectroscopy, Resonance, spectroscopy, steric repulsion energy
Posted in Interesting chemistry | No Comments »

Smoke and mirrors. All is not what it seems with this Sn2 reaction!

Thursday, April 4th, 2019

Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2′ displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1. The reason for posing this question is that as an Sn1 reaction, simply ionizing off the chlorine to form a diazacyclopropenium cation might be a very easy process. Why? Because the resulting cation is analogous to the cyclopropenium cation, famously proposed by Breslow as the first example of a 4n+2 aromatic ring for which the value of n is zero and not 1 as for benzene.[1] Another example of a famous “Sn1” reaction is the solvolysis of t-butyl chloride to form the very stable tertiary carbocation and chloride anion (except in fact that it is not an Sn1 reaction but an Sn2 one!)

Here is the located transition state for the above, using Na⁺.6H₂O as the counter-ion to the chloride. The calculated free energy of this transition state is 3.2 kcal/mol lower than the previous Sn2′ version (FAIR data collection, 10.14469/hpc/5045), with an overall barrier to reaction of 26.5 kcal/mol. This compares to ~24.5 kcal/mol obtained by Breslow for solvolysis of the cyclopropenyl tosylate. Given the relatively simple solvation model I used in the calculation (only six waters to solvate all the ions, and a continuum solvent field for water), the agreement is not too bad.

The animation above is of a normal vibrational mode known as the transition mode (click on the image above to get a 3D rotatable animated model). The calculated vectors for this mode (its energy being an eigenvalue of the force constant matrix) are regularly used to “characterise” a transition state. I will digress with a quick bit of history here, starting in 1972 when another famous article appeared.[2] The key aspect of this study was the derivation of the first derivatives of the energy of a molecule with respect to the (3N) geometrical coordinates of the atoms, using a relatively simply quantum mechanical method (MINDO/2) to obtain that energy. Analytical first derivatives of the MINDO/2 Hamiltonian were then used to both locate the transition state for a simple reaction and then to evaluate the second derivatives (the force constant matrix) using a finite difference method. That force constant matrix, when diagonalized, reveals one negative root (eigenvalue) which is characteristic of a transition state. The vectors reveal how the atoms displace along the vibration, and should of course approximate to the path to either reactant or product.

Since that time, it has been a more or less mandatory requirement for any study reporting transition state models to characterise them using the vectors of the negative eigenvalue. The eigenvalue invariably expressed as a wavenumber. Because this comes from the square root of the mass-weighted negative force constant, it is often called the imaginary mode. Thus in this example, 115i cm^-1, the i indicating it is an imaginary number. The vectors are derived from quadratic force constants, which is a parabolic potential surface for the molecule. Since most potential surfaces are not quadratic, it is recognized as an approximation, but nonetheless good enough to serve to characterise the transition state as the one connecting the assumed reactant and product. Thousands of published studies in the literature have used this approach.

So now to the animation above. If you look closely you will see that it is a nitrogen and not a carbon that is oscillating between two chlorines (here it is the lighter atoms that move most). The vectors confirm that, with a large one at N and only a small one at C. So it is Sn2 displacement at nitrogen that we have located?

Not so fast. This is a reminder that we have to explore a larger region of the potential energy surface, beyond the quadratic region of the transition state from which the vectors above are derived. This is done using an IRC (intrinsic reaction coordinate). Here it is, and you see something remarkable.

The Cl…N…Cl motions seen above in the transition state mode change very strongly in regions away from the transition state. On one side of the transition state, it forms a Cl…C bond, on the other side a Cl…N.

It is also reasonable to ask why the paths either side of the transition state are not the same? That may be because with only six explicit water molecules, three of which solvate the sodium ion, there are not enough to solvate equally the chloride anions either side of the transition state. As a result one chlorine does not behave in quite the same way as the other. The addition of an extra water molecule or two may well change the resulting reaction coordinate significantly.

The overall message is that there are two ways to characterise a computed reaction path. One involves looking at the motions of all the atoms just in the narrow region of the transition state. Most reported literature studies do only this. When the full path is explored with an IRC, a different picture can emerge, as here. The Cl…N…Cl Sn2 mode is replaced by a Cl…C/N…Cl mode. This example however is probably rare, with most reactions the transition state vibration and the IRC do actually agree!

References

R. Breslow, "SYNTHESIS OF THE s-TRIPHENYLCYCLOPROPENYL CATION", Journal of the American Chemical Society, vol. 79, pp. 5318-5318, 1957. https://doi.org/10.1021/ja01576a067
J.W. McIver, and A. Komornicki, "Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method", Journal of the American Chemical Society, vol. 94, pp. 2625-2633, 1972. https://doi.org/10.1021/ja00763a011

Tags:animation, Carbenium ion, Cations, Chemical elements, chemical reaction, Chemistry, Chlorine, computational chemistry, Cyclopropenium ion, Diazirine, energy, energy profile, free energy, Halogens, Natural sciences, Nucleophilic aromatic substitution, Oxidizing agents, Physical sciences, potential energy surface, SN1 reaction, Substitution reactions
Posted in reaction mechanism | No Comments »

The Graham reaction: Deciding upon a reasonable mechanism and curly arrow representation.

Monday, February 18th, 2019

Students learning organic chemistry are often asked in examinations and tutorials to devise the mechanisms (as represented by curly arrows) for the core corpus of important reactions, with the purpose of learning skills that allow them to go on to improvise mechanisms for new reactions. A common question asked by students is how should such mechanisms be presented in an exam in order to gain full credit? Alternatively, is there a single correct mechanism for any given reaction? To which the lecturer or tutor will often respond that any reasonable mechanism will receive such credit. The implication is that a mechanism is “reasonable” if it “follows the rules”. The rules are rarely declared fully, but seem to be part of the absorbed but often mysterious skill acquired in learning the subject. These rules also include those governing how the curly arrows should be drawn.^† Here I explore this topic using the Graham reaction.[1]^‡

I start by noting the year in which the Graham procedure was published, 1965. Although the routine representation of mechanism using curly arrows had been established for about 5-10 years by then, the quality of such representations in many articles was patchy. Thus, this one (the publisher will need payment for me to reproduce the diagram here, so I leave you to get it yourself) needs some modern tidying up. In the scheme below, I have also made a small change, using water itself as a base to remove a NH proton, rather than hydroxide anion as used in the article (I will return to the anion later). The immediate reason is that water is a much simpler molecule to use at the start of our investigation than solvated sodium hydroxide. You might want to start with comparing the mechanism above with the literature version[1] to discover any differences.

The next stage is to compute all of this using quantum mechanics, which will tell us about the energy of the system as it evolves and also identify the free energy of the transition states for the reaction. I am not going to go into any detail of how these energies are obtained, suffice to say that all the calculations can be found at the following DOI: 10.14469/hpc/5045 The results of this exercise are represented by the following alternative mechanism.^♥

How was this new scheme obtained? The key step is locating a transition state in the energy surface, a point where the first derivatives of the energy with respect to all the 3N-6 coordinates defining the geometry (the derivative vector) are zero and where the second derivative matrix has just one negative eigenvalue (check up on your Maths for what these terms mean). Each located transition state (which is an energy maximum in just one of the 3N-6 coordinates) can be followed downhill in energy to two energy minima, one of which is declared the reactant of the reaction and the other the product, using a process known as an IRC (intrinsic reaction coordinate). The coordinates of these minima are then inspected so they can be mapped to the conventional representations shown above. New bonds in the formalism above are shown with dashed lines and have an arrow-head ending at their mid-point; breaking bonds (more generally, bonds reducing their bond order) have an arrow starting from their mid-point. The change in geometry along the IRC for TS1 can then be shown as an animation of the reaction coordinate, which you can see below.

Don’t worry too much about when bonds appear to connect or disconnect, the animation program simply uses a simple bond length rule to do this. The major difference with the original mechanism is that it is the chlorine on the nitrogen also bearing a proton that gets removed. Also, the N-N bond is formed as part of the same concerted process, rather than as a separate step.

Shown above is the computed energy along the reaction path. Here a “reality check” can be carried out. The activation free energy (the difference between the transition state and the reactant) emerges as a rather unsavoury ΔG^‡=40.8 kcal/mol. Why is this unsavoury? Well, according to transition state theory, the rate of a (unimolecular) reaction is given by the expression: Ln(k/T) = 23.76 – ΔG^‡/RT where T is temperature (~323K in this example), R = is the gas constant and k is the unimolecular rate constant. When you solve it for ΔG^‡=40.8, it turns out to be a very slow reaction indeed. More typically, a reaction that occurs in a few minutes at this sort of temperature has ΔG^‡= ~15 kcal/mol. So this turns out to be an “unreasonable” mechanism, but based on the quantum mechanically predicted rate and not on the nature of the “curly arrows”. And no, one cannot do this sort of thing in an examination (not even on a mobile phone; there is no app for it, yet!) I must also mention that the “curly arrows” used in the above representation are, like the bonds, based on simple rules of connecting a breaking with a forming bond with such an arrow. There IS a method of computing both their number and their coordinates “realistically”, but I will defer this to a future post. So be patient!

The next thing to note is that the energy plot shows this stage of the reaction as being endothermic. Time to locate TS2, which it turns out corresponds to the N to C migration of the chlorine to complete the Graham reaction. As it happens, TS2 is computed to be 10.6 kcal/mol lower than TS1 in free energy, so it is not “rate limiting”.

To provide insight into the properties of this reaction path, a plot of the calculated dipole moment along the reaction path is shown. At the transition state (IRC value = 0), the dipole moment is a maximum, which suggests it is trying to form an ion-pair, part of which is the diazacylopropenium cation shown in the first scheme above. The ion-pair is however not fully formed, probably because it is not solvated properly.

We can add the two reaction paths together to get the overall reaction energy, which is no longer endothermic but approximately thermoneutral. Things are still not quite “reasonable” because the actual reaction is exothermic.

Time then to move on to hydroxide anion as the catalytic base, in the form of sodium hydroxide. To do this, we need to include lots of water molecules (here six), primarily to solvate the Na⁺(shown in purple below) but also any liberated Cl^–. You can see the water molecules moving around a lot as the reaction proceeds, via again TS1 to end at a similar point as before.

The energy plot is now rather different. The activation energy is now lower than the 15 kcal/mol requirement for a fast reaction; in fact ΔG^‡= 9.5 kcal/mol and overall it is already showing exothermicity. What a difference replacing a proton (from water) by a sodium cation makes!

Take a look also at this dipole moment plot as the reaction proceeds! TS1 is almost entirely non-ionic!

To complete the reaction, the chlorines have to rearrange. This time a rather different mode is adopted, as shown below, termed an Sn2′ reaction. The energy of TS2′ is again lower than TS1, by 9.2 kcal/mol. Again no explicit diazacylopropenium cation-anion pair (an aromatic 4n+2, n=0 Hückel system) is formed.

Combing both stages of the reaction as before. The discontinuity in the centre is due to further solvent reorganisation not picked up at the ends of the two individual IRCs which were joined to make this plot. Note also that the reaction is now appropriately exothermic overall.

So what have we learnt?

That a “reasonable” mechanism as shown in a journal article, and perhaps reproduced in a text-book, lecture or tutorial notes or even an examination, can be subjected in a non-arbitrary manner to a reality check using modern quantum mechanical calculations.
For the Graham reaction, this results in a somewhat different pathway for the reaction compared to the original suggestion.
1. In particular, the removal of chlorine occurs from the same nitrogen as the initial deprotonation
2. This process does not result in an intermediate nitrene being formed, rather the chlorine removal is concerted with N-N bond formation.
3. The resulting 1-chloro-1H-diazirine does not directly ionize to form a diazacyclopropenium cation-chloride anion ion pair, but instead can undertake an Sn2′ reaction to form the final 3-chloro-3-methyl-3H-diazirine.
A simple change in the conditions, such as replacing water as a catalytic agent with Na⁺OH^–(5H₂O) can have a large impact on the energetics and indeed pathways involved. In this case, the reaction is conducted in NaOCl or NaOBr solutions, for which the pH is ~13.5,^♣ indicating [OH^–] is ~0.3M.
The curly arrows here are “reasonable” for the computed pathway, but are determined by some simple formalisms which I have adopted (such as terminating an arrow-head at the mid-point of a newly forming bond). As I hinted above, these curly arrows can also be subjected to quantum mechanical scrutiny and I hope to illustrate this process in a future post.

But do not think I am suggesting here that this is the “correct” mechanism, it is merely one mechanism for which the relative energies of the various postulated species involved have been calculated relatively accurately. It does not preclude that other, perhaps different, routes could be identified in the future where the energetics of the process are even lower.

^†This blog is inspired by the two students who recently asked such questions. ^‡In fact, you also have to acquire this completely unrelated article[2] for reasons I leave you to discover yourself. ^♥You might want to consider the merits or demerits of an alternative way of showing the curly arrows. Is this representation “more reasonable”? ^♣I thank Ed Smith for measuring this value for NaOBr and for suggesting the Graham reaction in the first place as an interesting one to model.

References

W.H. Graham, "The Halogenation of Amidines. I. Synthesis of 3-Halo- and Other Negatively Substituted Diazirines1", Journal of the American Chemical Society, vol. 87, pp. 4396-4397, 1965. https://doi.org/10.1021/ja00947a040
E.W. Abel, B.C. Crosse, and D.B. Brady, "Trimeric Alkylthiotricarbonyls of Manganese and Rhenium", Journal of the American Chemical Society, vol. 87, pp. 4397-4398, 1965. https://doi.org/10.1021/ja00947a041

Tags:/RT, activation energy, activation free energy, animation, arrow pushing, arrow-head, cellular telephone, Chemical kinetics, chemical reaction, Chemistry, computed energy, Ed Smith, energy, energy maximum, energy minima, energy plot, energy profile, energy surface, free energy, lecturer, mechanism, Natural sciences, Organic chemistry, overall reaction energy, Physical sciences, Reaction rate constant, Resonance, Transition state, Transition state theory, tutor, Tutorial
Posted in Curly arrows, Interesting chemistry | No Comments »

Dispersion-induced triplet aromatisation?

Thursday, January 3rd, 2019

There is emerging interest in cyclic conjugated molecules that happen to have triplet spin states and which might be expected to follow a 4n rule for aromaticity.[1] The simplest such system would be the triplet state of cyclobutadiene, for which a non or anti-aromatic singlet state is always found to be lower in energy. Here I explore some crystal structures containing this motif for possible insights.

My search query is shown below, and the search is constrained so that the four substituents are Si, C or H.

The results show three clusters. The top left and bottom right have one long bond length ~1.6Å and the other much shorter at ~1.35Å (Δ_r ~0.25Å) The central region contains two examples, 2 where the difference between the two lengths is rather smaller and 1 where they are equal.

The first example 1[2] is in fact the di-anion of cyclobutadiene and as a 6π aromatic, one indeed expects the C-C bonds to be equal in length. The second 2 is tetra t-butylcyclobutadiene as reported in 1983.[3] At room temperature the two C-C bond lengths are 1.464 and 1.483Å, at -30°C, 1.466 and 1.492Å and at -150°C 1.441 and 1.526Å (Δ_r 0.085Å). These results led to the conclusion that this species was not intrinsically square but rectangular, as expected of singlet cyclobutadiene. The equalisation was attributed to equal populations of two disordered rectangular orientations averaging to an approximately square shape at higher temperatures.

But why is the behaviour of this particular cyclobutadiene different from the others in the plot above? Perhaps the answer lies these in the results of the Schreiner group[4], in which the dispersion attractions of substituents such as t-butyl can have substantial and often unexpected effects on the structures of molecules. So it is reasonable to pose the question; could the room temperature bond length differences of 2 be smaller compared with the other more extreme examples as a result of dispersion effects?

Here I have computed the singlet geometry of tetra t-butylcyclobutadiene at the B3LYP+D3BJ/Def2-TZVPP level (i.e. using the D3BJ dispersion correction, FAIR data DOI: 10.14469/hpc/4924). Δ_r for this singlet state is 0.264Å, larger than apparently from the crystal structure, but in agreement with the other crystal results as seen above.

The origins of the measured structure of 2 must be in the barrier to the automerisation of the singlet state. For normal cyclobutadienes, this must be relatively high since the transition state is presumably anti-aromatic. High enough that the averaging of the two rectangular structures is slow enough that it manifests as two different bond lengths. But in 2, as the temperature of the crystal increases, the bonds become more equal, suggesting a lower barrier to the equalisation than the other examples. This is also supported by the apparent identification of a triplet square state for the tetra-TMS analogue of tetra-tert-butyl cyclobutadiene derivative [5] which again suggests that dispersion might favour a square form over the rectangular one.

To finish, I show the crystal structure search for the 8-ring homologue of cyclobutadiene, plotted for the two adjacent C-C lengths and (in colour) the dihedral angle associated with the three atoms involved and the fourth along the ring. Cluster 1 represents various boat-shaped derivatives with very different C-C bond lengths. Cluster 2 are all ionic, and as per above represent a planar 10π-electron ring. Cluster 3 are mostly “tethered” molecules in which additional rings enforce planarity.

COT

Unfortunately, none of these derivatives include tert-butyl or TMS derivatives in adjacent positions around the central ring. Perhaps octa(t-Bu)cyclo-octatetraene or its TMS analogue would be interesting molecules to try to synthesize!

References

A. Kostenko, B. Tumanskii, Y. Kobayashi, M. Nakamoto, A. Sekiguchi, and Y. Apeloig, "Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene", Angewandte Chemie International Edition, vol. 56, pp. 10183-10187, 2017. https://doi.org/10.1002/anie.201705228
T. Matsuo, T. Mizue, and A. Sekiguchi, "Synthesis and Molecular Structure of a Dilithium Salt of the cis-Diphenylcyclobutadiene Dianion", Chemistry Letters, vol. 29, pp. 896-897, 2000. https://doi.org/10.1246/cl.2000.896
H. Irngartinger, and M. Nixdorf, "Bonding Electron Density Distribution in Tetra‐tert‐butylcyclobutadiene— A Molecule with an Obviously Non‐Square Four‐Membered ring", Angewandte Chemie International Edition in English, vol. 22, pp. 403-404, 1983. https://doi.org/10.1002/anie.198304031
S. Rösel, H. Quanz, C. Logemann, J. Becker, E. Mossou, L. Cañadillas-Delgado, E. Caldeweyher, S. Grimme, and P.R. Schreiner, "London Dispersion Enables the Shortest Intermolecular Hydrocarbon H···H Contact", Journal of the American Chemical Society, vol. 139, pp. 7428-7431, 2017. https://doi.org/10.1021/jacs.7b01879

Tags:antiaromaticity, aromaticity, Baird's rule, Conjugated system, crystal structure search, energy, Hückel's rule, Nature, Physical organic chemistry, Physical sciences, search query, Triplet state
Posted in Interesting chemistry | 1 Comment »

The “White City Trio” – The formation of an amide from an acid and an amine in non-polar solution (updated).

Wednesday, August 8th, 2018

White City is a small area in west london created as an exhibition site in 1908, morphing over the years into an Olympic games venue, a greyhound track, the home nearby of the BBC (British Broadcasting Corporation) and most recently the new western campus for Imperial College London.^♣ The first Imperial department to move into the MSRH (Molecular Sciences Research Hub) building is chemistry. As a personal celebration of this occasion, I here dedicate three transition states located during my first week of occupancy there, naming them the White City trio following earlier inspiration by a string trio and their own instruments.

The chemistry revisits the mechanism of amide formation from an acid and an amine, which I first described on this blog about four years ago. I had constructed a model of one amine and one carboxylic acid, to which I added a further acid in recognition that proton transfers are a key aspect of the mechanism. When the model is quantified using quantum calculations (ωB97XD/6-311G(d,p)/SCRF=p-toluene) it resulted in a free energy barrier ΔG₂₉₈^‡ of about 22 kcal/mol. Re-reading what I wrote, I see I did rather gloss over this value, which implies a decently rapid reaction! In fact, the reaction occurs relatively slowly at the temperature of refluxing toluene. Perhaps some alarm bells should have been tinkling at this stage (although the sluggish reaction might for example instead be due to poor solubility) and so here I have a rethink of the model used to see if that modest barrier really is correct.

The new premise is to test if the required proton transfers can instead be mediated using a second molecule of amine instead of acid; thus two molecules of carboxylic acid are now accompanied by two of amine, one of which will be used to transfer protons. The second acid is retained to facilitate comparison. As before, the mechanism is characterised by three transition states and two tetrahedral intermediates. The new mechanism is summarised below, with TS1-3 being the White City Trio.

The free energies are summarised in the table below. TS3, the rate limiting step, is slightly lower in energy if the amine is used for the proton transfer than via carboxylic acid. This is the wrong direction; we really want the barrier to increase to explain the relative difficulty of the reaction as observed in refluxing toluene! Fear not however, the new barrier is indeed a much more sluggish 28.6 kcal/mol (30.5 using a larger basis set).

Species (FAIR Data DOI 10.14469/hpc/4598)	ΔG₂₉₈ (ΔG₂₉₈^‡) kcal/mol	Structure
Ionic reactants	-649.737562^♥ (0.0)
TS1 (N-C bond formation via acid PT)	-649.702436 (22.0)
TS1 (N-C bond formation via amine PT), the “White City”	-649.702307 (22.1)
TI1 from TS1	-649.709938 (17.3)
TS2 (PT from N to O via acid PT)	-649.713027 (15.4)
TS2 (PT from N to O via amine PT), the “White City”	-649.706042
TI2 from TS2	-649.711481 (16.4)
TS3 (O-C bond cleavage via amine PT), the “White City”	-649.691918 (28.6) [30.5]^‡
TS3 (O-C bond cleavage via acid PT)	-649.689910 (29.9)
Non-ionic product from TS3	-649.732417 (+3.2)
Ionic product after PT	-649.741246 (-2.3)

How did this happen? It’s the reactants! The original reactant model was based on the known structure of acetic acid dimer, with an amine weakly hydrogen bonded. Adding an extra amine now allows an entirely new motif to form, in which the amine disrupts the acetic dimer to form a cyclic system with a pair of very strong (-)O-H-N(+)-H-O(-) hydrogen bond units.† The original model did not have sufficient components to fully allow this to happen.

So the White City Trio achieve a performance which helps explain why a reaction is sluggish rather than facile (normally one strives to show the opposite). Perhaps however it should be the White City quartet, in recognition that the reactant also had a role to play?

^♣A photograph of the building under construction can be seen here. ^‡Def2-TZVPPD basis set. ^†There does not appear to be a recorded structure for methylammonium acetate. We hope to obtain one to check what the extended structure actually is. ^♥I will elaborate an interesting new use of this value in a separate post.

Tags:acetic acid, Acid, Amide, Amine, carboxylic acid, Chemistry, Company: BBC, Company: British Broadcasting Corporation, energy, Ester, exhibition site, free energy barrier, Functional groups, Hydrogen bond, Imperial College, Imperial College London, Ionic product, Newspaper & Magazine Printing Services, Non-ionic product, Olympic games, Organic chemistry, White City Trio
Posted in Interesting chemistry | 6 Comments »

The "White City Trio" – The formation of an amide from an acid and an amine in non-polar solution (updated).

Wednesday, August 8th, 2018

Species (FAIR Data DOI 10.14469/hpc/4598)	ΔG₂₉₈ (ΔG₂₉₈^‡) kcal/mol	Structure
Ionic reactants	-649.737562^♥ (0.0)
TS1 (N-C bond formation via acid PT)	-649.702436 (22.0)
TS1 (N-C bond formation via amine PT), the “White City”	-649.702307 (22.1)
TI1 from TS1	-649.709938 (17.3)
TS2 (PT from N to O via acid PT)	-649.713027 (15.4)
TS2 (PT from N to O via amine PT), the “White City”	-649.706042
TI2 from TS2	-649.711481 (16.4)
TS3 (O-C bond cleavage via amine PT), the “White City”	-649.691918 (28.6) [30.5]^‡
TS3 (O-C bond cleavage via acid PT)	-649.689910 (29.9)
Non-ionic product from TS3	-649.732417 (+3.2)
Ionic product after PT	-649.741246 (-2.3)

Harnessing FAIR data: A suggested useful persistent identifier (PID) for quantum chemical calculations.

Tuesday, August 7th, 2018

Harnessing FAIR data is an event being held in London on September 3rd; no doubt most speakers will espouse its virtues and speculate about how to realize its potential. Admirable aspirations indeed, but capturing hearts and minds also needs lots of real life applications! Whilst assembling a forthcoming post on this blog, I realized I might have one nice application which also pushes the envelope a bit further, in a manner that I describe below.

The post I refer to above is about using quantum chemical calculations to chart possible mechanistic pathways for the reaction between a carboxylic acid and an amine to form an amide. The FAIR data for the entire project is collected at DOI: 10.14469/hpc/4598. Part of what makes it FAIR is the metadata not only collected about this data but also formally registered with the DataCite agency. Registration in turn enables Finding; it is this aspect I want to demonstrate here.

The metadata for the above DOI includes information such as;

The ORCID persistent identifier (PID) for the creator of the data (in this instance myself)
Date stamps for the original creation date and subsequent modifications.
A rights declaration, in this case the CC0 license which describes how the data can be re-used.
Related identifiers, in this case describing members of this collection.

The data itself is held in the members of the collection, each of which is described by a more specific set of metadata in addition to the more general types in the above list (e.g. 10.14469/hpc/4606).

One important additional metadata descriptor is the ORE locator (Object Re-use and Exchange, itself almost a synonym for FAIR). This allows a machine to deduce a direct path to the data file itself, and hence to retrieve it automatically if desired. It is important to note that the DOI itself (i.e. 10.14469/hpc/4606) points only to the “landing page” for the dataset, and does not necessarily describe the direct path to any specific file in the dataset. The ORE path can be used with e.g. software such as JSmol to directly load a molecule based only on its DOI. You can see an example of this here.
Each molecule-based dataset contains additional specific metadata relating to the molecule itself. For example this is how the InChiKey, an identifier specific to that molecule, is expressed in metadata;
<subject subjectScheme="inchikey" schemeURI="http://www.inchi-trust.org/">PVXKWVPAMVWJSQ-UHFFFAOYSA-N</subject>
The advantage of expressing the metadata in this way is that a general search of the type:
https://search.datacite.org/works?query=subjectScheme:inchikey+subject:CZABGBRSHXZJCF-UHFFFAOYSA-N
can be used to track down any molecule with metadata corresponding to the above InChIkey.
Here is more metadata, introduced in this blog. It relates to the (computed) value of the Gibbs energy (the energy unit is in Hartree^†), as returned by the Gaussian program;
<subject subjectScheme="Gibbs_Energy" schemeURI="https://goldbook.iupac.org/html/G/G02629.html" valueURI="http://gaussian.com/thermo/">-649.732417</subject>
I here argue that it represents a unique identifier for a molecule calculation using the quantum mechanical procedures implemented in e.g. Gaussian. This identifier is different from the InChIkey, in that it can be truncated to provide different levels of information.
- At the coarsest level, a search of the type
 https://search.datacite.org/works?query=subjectScheme:Gibbs_energy+subject:-649.*
 should reveal all molecules with the same number of atoms and electrons whose Gibbs energy has been calculated, but not necessarily with the same InChI (i.e. they may be isomers, or transition states, etc). This level might be useful for revealing most (not necessarily all^‡) molecules involved in say a reaction mechanism. It should also be insensitive to the program system used, since most quantum codes will return a value for the Gibbs energy if the same procedures have been used (i.e. DFT method, basis set, solvation model and dispersion correction) accurate to probably 0.01 Hartree.
- The top level of precision however is high enough to almost certainly relate to a specific molecule and probably using a specific program;
 https://search.datacite.org/works?query=subjectScheme:Gibbs_energy+subject:-649.732417
- The searcher can experiment with different levels of precision to narrow or broaden the search.
- I would also address the issue (before someone asks) of why I have used the Gibbs energy rather than the Total energy. Put simply, the Gibbs energy is far more useful in a chemical context. It can be used to relate the relative Gibbs energies of different isomers of the same molecule to e.g. the equilibrium constant that might be measured. Or the difference in Gibbs energies between a reactant and a transition state can be used to derive the free energy activation barrier for a reaction. The total energy is not so useful in such contexts, although of course it too could be added as a subject in the metadata above if a real use for it is found.
The searcher can also use Boolean combinations of metadata, such as specifying both the InChIKey and the Gibbs Energy, along with say the ORCID of the person who may have published the data;
https://search.datacite.org/works?query= subjectScheme:Gibbs_energy+subject:-649.*+ subjectScheme:inchikey+subject:CZABGBRSHXZJCF-UHFFFAOYSA-N+ ORCID:0000-0002-8635-8390^♥

I have tried to show above how FAIR data implies some form of rich (registered) metadata. And how the metadata can be used to Find (the F in FAIR) data with very specific properties, thus Harnessing FAIR data.

^†It is a current limitation of the V4.1 DataCite schema that there appears no way to specify the data type of the subject, including any units. ^‡In theory, a range query of the type:
https://search.datacite.org/works?query= subjectScheme:Gibbs_energy+subject:[-649.1 TO -649.8]
should be more specific, but I have not yet gotten it to work, probably because of the lack of data-typing means it is not recognised as a range of numeric values. ^♥Implicit in this search is the grouping
https://search.datacite.org/works?query=(subjectScheme:Gibbs_energy+subject:-649.*) + (subjectScheme:inchikey+subject:CZABGBRSHXZJCF-UHFFFAOYSA-N) +ORCID:0000-0002-8635-8390
Currently however DataCite do not correctly honour this form of grouping.

Tags:Academic publishing, chemical context, Code, data, DataCite, energy, free energy activation barrier, Identifiers, Information, ISO/IEC 11179, ORCiD, quantum chemical calculations, real life applications, Technical communication
Posted in Interesting chemistry | 9 Comments »

Aromaticity-induced basicity.

Wednesday, April 18th, 2018

The molecules below were discussed in the previous post as examples of highly polar but formally neutral molecules, a property induced by aromatisation of up to three rings. Since e.g. compound 3 is known only in its protonated phenolic form, here I take a look at the basicity of the oxygen in these systems to see if deprotonation of the ionic phenol form to the neutral polar form is viable.

The equilibrium being considered is shown below for compound 2:

The energetics of this equilibrium shown below, computed at the ωB97XD/Def2-TZVPPD/SCRF=water level and for which the FAIR data DOI is 10.14469/hpc/4073

For 1: X=Cl, the energy is shown below as a function of the O….H distance. Proton abstraction from HCl is exothermic by ~25 kcal/mol.

For 2: X=Cl, the exothermicity increases by only ~5 kcal/mol , despite the apparent aromatisation of a further ring. It is also worth noting that this is greater basicity than that of e.g. water, where around 4-5 water molecules acting in concert are required to deprotonate HCl.For 1: X=OH, the proton abstraction from water is mildly endothermic by about 13 kcal/mol; indeed there is no energy minimum for carbonyl protonation and instead a relatively strong hydrogen bond to the water is formed instead.

For 2: X=OH the endothermicity is reduced to ~9 kcal/mol.

For 1: X=CH₃, deprotonation of methane is now strongly endothermic by ~40 kcal/mol.

So the molecules 1 – 2 above are clearly not superbases, which perhaps augers well for being able to deprotonate the ionic phenols into these neutral but highly polar molecules.

Tags:Antiseptics, Aromatization, Chemistry, energy, energy minimum, Hydrogen, Molecule, Neurotoxins, Science
Posted in Interesting chemistry | No Comments »

A record polarity for a neutral compound?

Friday, April 13th, 2018

In several posts a year or so ago I considered various suggestions for the most polar neutral molecules, as measured by the dipole moment. A record had been claimed[1] for a synthesized molecule of ~14.1±0.7D. I pushed this to a calculated 21.7D for an admittedly hypothetical and unsynthesized molecule. Here I propose a new family of compounds which have the potential to extend the dipole moment for a formally neutral molecule up still further.

These molecules derive from a well-known class of molecule known as ortho-quinomethides. If the methide part is substituted with an electron donating substituent such as an amino group in 3, a push-pull opportunity now arises, which is strongly driven by aromatisation of the quinomethide ring. This allows one to design “neutral” molecules such as 1 and 2, which now contain respectively two and three rings that will be aromatised by the process. The aromatisation stabilization energy is balanced of course by an opposing increase in energy resulting from charge separation. You can observe that partially aromatising three independent rings as in 2 can drive a great deal of charge separation. One may indeed wonder how much charge separation can be sustained before a triplet instability occurs, driving the molecule back to being neutral. In the case of 2, the wavefunction is in fact stable to such an open shell state, but higher homologues may not be. An aspect worth investing!

1	2

DM 12.3	DM 31.5
DOI: 10.14469/hpc/4004	DOI: 10.14469/hpc/4059

Molecule 1 does have some precedent in 3[2] but this system exists as a phenol, having abstracted a proton from an acid and leaving behind the acid anion, as per below for 1. Any attempts to deprotonate this phenol with a superstrong base were unreported.

Unsurprisingly therefore, molecules such as 1 and 2 could be regarded as even more highly potent bases than 3, driven again by further aromatisation. The properties of such a potential superbase will be investigated in the next post.

References

J. Wudarczyk, G. Papamokos, V. Margaritis, D. Schollmeyer, F. Hinkel, M. Baumgarten, G. Floudas, and K. Müllen, "Hexasubstituted Benzenes with Ultrastrong Dipole Moments", Angewandte Chemie International Edition, vol. 55, pp. 3220-3223, 2016. https://doi.org/10.1002/anie.201508249
N.R. Candeias, L.F. Veiros, C.A.M. Afonso, and P.M.P. Gois, "Water: A Suitable Medium for the Petasis Borono‐Mannich Reaction", European Journal of Organic Chemistry, vol. 2009, pp. 1859-1863, 2009. https://doi.org/10.1002/ejoc.200900056

Tags:aromatisation stabilization energy, Chemical polarity, chemical properties, Chemistry, Dipole, Electric dipole moment, Electromagnetism, energy, Moment, Nature, Physical quantities, Physics, Potential theory
Posted in Interesting chemistry | 11 Comments »

Henry Rzepa's blog

Posts Tagged ‘energy’

Imaging normal vibrational modes of a single molecule of CoTPP: a mystery about the nature of the imaged species.

References

Imaging vibrational normal modes of a single molecule.

References

Smoke and mirrors. All is not what it seems with this Sn2 reaction!

References

The Graham reaction: Deciding upon a reasonable mechanism and curly arrow representation.

References

Dispersion-induced triplet aromatisation?

References

The “White City Trio” – The formation of an amide from an acid and an amine in non-polar solution (updated).

The "White City Trio" – The formation of an amide from an acid and an amine in non-polar solution (updated).

Harnessing FAIR data: A suggested useful persistent identifier (PID) for quantum chemical calculations.

Aromaticity-induced basicity.

A record polarity for a neutral compound?

References

Recent Posts

Archives

Blogroll

Meta