Coming on the heels of the very nice combined computational/experimental study of the enantioselective Strecker reaction by Jacobsen (see this post), there’s this JACS communication that really disappoints in its use of computational chemistry. Cobb uses yet another chiral thiourea to produce the enantioselective intramolecular Michael addition of nitronoates (Reaction1).¹ The reaction goes with excellent diastereoselectivity and eneatioselectivity, and can even be done with a substrate to produce three chiral centers. This is very nice synthetic chemistry.

The lack of reactivity of the Z ester suggested that the thiourea must associate with both the nitro group and the ester carbonyl. The authors provide a B3LYP/3-21G complex of thiourea with a simple nitroester (once again without providing coordinates in the supporting materials!) to demonstrate this sort of association. But this single structure, at this very low computational level, with these simplified reagents, and lacking solvent (see Rzepa’s comment) really makes one wonder just what value this computation provides. It also goes to demonstrate just how much effort Jacobsen went through to provide substantive computational support for his proposed mechanism of action.

References

(1) Nodes, W. J.; Nutt, D. R.; Chippindale, A. M.; Cobb, A. J. A., "Enantioselective Intramolecular Michael Addition of Nitronates onto Conjugated Esters: Access to Cyclic γ-Amino Acids with up to Three Stereocenters," J. Am. Chem. Soc. 2009, 131, 16016-16017, DOI: 10.1021/ja9070915

The competition between Bergman cyclization and Myers-Saito cyclization of ene-ynes and related species is discussed in Chapter 3.3 of my book and also in these posts. Yet another variation, the Garratt-Braverman cyclization^1-3 has now been examined in terms of competition with the Myers-Saito cyclization for 1 using both experiments and computations.⁴ Subjecting 1 to base should cause the rearrangement to either GB1 or MS2. These can undergo either the Garratt-Braverman cyclization to give GB2 or the Myers-Saito cyclization to MS2.

B3LYP/6-31G(d) predicts that GB1 is only slightly higher in energy than MS1 (by 0.7 kcal mol^-1). The transition states (GB1toGB2 or MS1toMS2 – see Figure 1) each lie 24.4 kcal mol^-1 above their respective reactants. However, the diradical GB2 is 7.2 kcal mol^-1 below GB1 but MS2 is only 0.3 kcal mol^-1 below MS1. So while the two reactions are of similar kinetic probability, having identical activation barriers, the GB route leads to the more thermodynamically stable intermediate. Furthermore, the GB route ultimately results in GBP, via an intramolecular cyclization of the diradical, while the MS route, which ends with MSP, requires intermolecular abstraction of 4 hydrogens. Thus, the unimolecularity of the GB path further favors the GB route over the MS pathway. In fact, experimental studies of 1 and related compounds all give rise to the GB product only.

GB1	GB1toGB2
GB2
MS1	MS1toMS2
MS2

Figure 1. B3LYP/6-31G(d) optimized structures.⁴

References

(1) Braverman, S.; Segev, D., "Novel cyclization of diallenic sulfones," J. Am. Chem. Soc. 2002, 96, 1245-1247, DOI: 10.1021/ja00811a060

(2) Garratt, P. J.; Neoh, S. B., "Strained heterocycles. Properties of five-membered heterocycles fused to four-, six-, and eight-membered rings prepared by base-catalyzed rearrangement of 4-heterohepta-1,6-diynes," J. Org. Chem. 2002, 44, 2667-2674, DOI: 10.1021/jo01329a016

(3) Zafrani, Y.; Gottlieb, H. E.; Sprecher, M.; Braverman, S., "Sequential Intermediates in the Base-Catalyzed Conversion of Bis(π-conjugated propargyl) Sulfones to 1,3-Dihydrobenzo- and Naphtho[c]thiophene-2,2-dioxides," J. Org. Chem. 2005, 70, 10166-10168, DOI: 10.1021/jo051692i

(4) Basak, A.; Das, S.; Mallick, D.; Jemmis, E. D., "Which One Is Preferred: Myers-Saito Cyclization of Ene-Yne-Allene or Garratt-Braverman Cyclization of Conjugated Bisallenic Sulfone? A Theoretical and Experimental Study," J. Am. Chem. Soc. 2009, 131, 15695-15704, DOI: 10.1021/ja9023644

The longstanding unknown oxyallyl diradical (1) singlet-triplet gap has now been addressed with a very nice photoelectron spectroscopy study by Lineberger with interpretation greatly aided by computations provided by Hrovat and Borden.¹

The photoelectron detachment spectrum of oxyallyl radical anion shows 5 major peaks, one at 1.942 eV and a series of four peaks starting at 1.997 eV separated by 405 cm^-1.

B3LYP/6-311++G(d,p) computations indicate that the energy for electron detachment from the radical anion to triplet oxyallyl diradical is 1.979 eV. (The structure of triplet 1 is shown in Figure 1.) Further, the computed vibrational frequency of the C-C-C bend is 408 cm^-1. These computations suggest that the four peak sequence represents a vibrational progression in the C-C-C bend of the triplet oxyallyl diradical.

1A1

3B2

Figure 1. Structures of the singlet and triplet oxyallyl diradical 1.¹

CASPT2 computations on singlet oxyallayl diradical indicate that it lies in a very shallow well, lower than the zero-point energy. (This structure is shown in Figure 1.) In fact, the singlet diradical can collapse without a barrier to cyclopropanone. Interestingly, the C-O stretching frequency of 1 is computed to be 1731 cm^-1, and close inspection of the photoelectron spectrum does show a progression of this magnitude originating from peak A. Therefore, both the singlet and triplet states of 1 are identified and their gap is extraordinarily small – the singlet is only 0.055 eV lower in energy than the triplet.

References

(1) Ichino, T.; Villano, S. M.; Gianola, A. J.; Goebbert, D. J.; Velarde, L.; Sanov, A.; Blanksby, S. J.; Zhou, X.; Hrovat, D. A.; Borden, W. T.; Lineberger, W. C., "The Lowest Singlet and Triplet States of the Oxyallyl Diradical," Angew. Chem. Int. Ed., 2009, 48, 8509-8511, DOI: 10.1002/anie.200904417

Does the Carbon-Sulfur triple bond exist? There’s probably little doubt it does in the CS molecule. But now Schreiner and Mloston have offered up the H-C≡S-OH species as a possibility.¹ Obtained by flash photolysis of 1, giving 2, and upon irradiation at 254 nm, H-C≡S-OH 3 is the observed species and not the expected carbene HO-C-SH 4. 3 is confirmed by excellent agreement between the observed and computationally predicted IR spectra.

The CCSD(T)/cc-pVTZ structures of 3 and 4 are shown in Figure 1. It is interesting that the carbene is not observed, even though it is 26.6 kcal mol^-1 more stable than 3.

3

4

Figure 1. CCSD(T)/cc-PVTZ optimized structures of 3 and 4.¹

So is there a triple bond? The short C-S distance (1.547 Å) is very similar to that in CS (1.545 Å). NBO analysis indicates a triple bond. But the MOs indicate significant lone pair build-up on both C and S, consistent with the strongly non-linear angles about these two atoms. The authors conclude that 3 is a “structure with a rather strong CS double bond or a weak triple bond”.

References

(1) Schreiner, P. R.; Reisenauer, H. P.; Romanski, J.; Mloston, G., "A Formal Carbon-Sulfur Triple Bond: H-C≡S-O-H," Angew. Chem. Int. Ed., 2009, 48, 8133-8136, DOI: 10.1002/anie.200903969

A nice follow-up to some of my own work points out again the possible dramatic role of dynamic effects. Way back when, Jack Gilbert discovered that the reaction of cyclopentyne with alkenes gives the cyclobutene product with stereoretention (Reaction 1),¹ seemingly in violation of the Woodward-Hoffmann rules.

Jack and I proposed an intermediate spirocyclopropyl carbene which could then open to product, and this would follow a stereoretention path.^2,3 In a subsequent paper,⁴ we noted that a diradical pathway is also possible, and conjectured that dynamics might account for the stereoretention – that formation of the diradical leads directly to the carbene, leaving a very short lifetime of the diradical (Scheme 1). The consequence of the short lived diradical is that there little opportunity to rotate about the C-C bond and scramble the stereochemistry.

Scheme 1

Pilling has published a MD study of this system and finds what we predicted.⁵ The short-time trajectories lead to stereoretention product. This is due to both passages over the TS that lead from the diradical to the product (with no scrambling) and over the TS that connects the diradical to the carbine. Longer trajectories do exhibit some stereoscrambling. Carpenter⁶ has argued that short time dynamics are often what one observes for potential energy surfaces like this one. Pilling also argues that in solution, with the actual alkene which bears bulky substituents that the proton (he examined the reaction of cyclopentyne with ethene), rotations will be slower, leading to formation of the carbene with stereoretention.

References

(1) Gilbert, J. C.; Baze, M. E., "Stereochemistry of [2 + 2] cycloadditions of cyclopentyne," J. Am. Chem. Soc. 2002, 106, 1885-1886, DOI: 10.1021/ja00318a081

(2) Laird, D. W.; Gilbert, J. C., "Norbornyne: A Cycloalkyne Reacting Like A Dicarbene," J. Am. Chem. Soc., 2001, 123, 6704-6705, DOI: 10.1021/ja010589h

(3) Bachrach, S. M.; Gilbert, J. C.; Laird, D. W., "DFT Study of the Cycloaddition Reactions of Strained Alkynes," J. Am. Chem. Soc., 2001, 123, 6706-6707, DOI: 10.1021/ja010590g

(4) Bachrach, S. M.; Gilbert, J. C., "The Reaction of Cyclopentyne with Ethene: Concerted vs Stepwise Mechanism?," J. Org. Chem., 2004, 69, 6357-6364, DOI: 10.1021/jo0492970

(5) Glowacki, D. R.; Marsden, S. P.; Pilling, M. J., "Significance of Nonstatistical Dynamics in Organic Reaction Mechanisms: Time-Dependent Stereoselectivity in Cyclopentyne−Alkene Cycloadditions," J. Am. Chem. Soc. 2009, 131, 13896-13897, DOI: 10.1021/ja9043054

(6) Barry, K. C., "Nonexponential decay of reactive intermediates: new challenges for spectroscopic observation, kinetic modeling and mechanistic interpretation," J. Phys. Org. Chem., 2003, 16, 858-868, DOI: 10.1002/poc.672

Though not quite germane to this blog (Computational Organic Chemistry), the recent commentary by Rzepa¹ does deserve mention. Henry takes on, in a nice breezy style (note the title: The importance of being bonded), the nature of bonding in 1, which initially was thought to be of structure 1a but subsequent x-ray structural analysis suggested the presence of an S-S bond, i.e. 1b. Schleyer has applied NICS analysis to suggest that the compound is bishomoaromatic.² Henry utilizes AIM and ELF analysis to discuss the nature of the bonding, including the possibility of H^…H interaction between the methyl groups and trishomoaromatic character. What I liked about the article is that Henry rightly makes the case that exploration of the notion of “bonding” can be quite opaque and often leads to stretching the models we commonly employ. Well worth the read!

References

(1) Rzepa, H. S., "The importance of being bonded," Nat. Chem., 2009, 1, 510-512, DOI: 10.1038/nchem.373.

(2) Zhang, Q.; Yue, S.; Lu, X.; Chen, Z.; Huang, R.; Zheng, L.; Schleyer, P. v. R., "Homoconjugation/Homoaromaticity in Main Group Inorganic Molecules," J. Am. Chem. Soc., 2009, 131, 9789-9799, DOI: 10.1021/ja9029285

Another benchmark study of the performance of different functionals – this time looking at the conformations of small alkanes.¹ Martin first establishes high level benchmarks: the difference between the trans and gauche conformers of butane: CCSD(T)/cc-pVQZ, 0.606 kcal mol^-1 and W1h-val, 0.611 kcal mol^-1; and the energy differences of the conformers of pentane, especially the TT and TG gap: 0.586 kcal mol^-1 at CCSD(T)/cc-pVTZ and 0.614 kcal mol^-1 at W1h-val.

They then examine the relative conformational energies of butane, pentane, hexane and a number of branched alkanes with a slew of functionals, covering the second through fifth rung of Perdew’s Jacob’s ladder. The paper has a whole lot of data – and the supporting
materials include Jmol-enhanced visualization of the structures! – but the bottom line is the following. The traditionally used functionals (B3LYP, PBE, etc) overestimate conformer energies while the MO6 family underestimates the interaction energies that occur in GG-type conformers. A dispersion correction tends to overcorrect and leads to wrong energy ordering of conformers. But the new double-hybrid functionals (B2GP-PLYP and B2K-PLYP) with the dispersion correction provide quite nice agreement with the CCSD(T) benchmarks.

Also worrisome is that all the functionals have issues in geometry prediction, particularly in the backbone dihedral angles. So, for example, B3LYP misses the τ₁ dihedral angle in the GG conformer by 5° and even MO6-2x misses the τ₂ angle in the TG conformer by 2.4&deg.

References

(1) Gruzman, D.; Karton, A.; Martin, J. M. L., "Performance of Ab Initio and Density Functional Methods for Conformational Equilibria of CnH2n+2 Alkane Isomers (n = 4-8),"
The Journal of Physical Chemistry A 2009, 113, 11974–11983 , DOI: http://dx.doi.org/10.1021/jp903640h

Jacobsen has been pioneering the use of small organic molecules as catalysts where the interaction between the substrate and catalyst is non-covalent. At the 2009 Welch Conference last week, he spoke about the use of amido-thiourea catalysts in the enantioselective Strecker reaction. This post discusses how computations were used to determine the mechanism and helps explain the enantioselectivity.

The thiourea 1 was found to be the best catalyst for the hydrocyanation of imines. An example of this catalysis is Reaction 1. The system is quite tolerant to changes of the group attached to the carbon of the imine: with R = t-butyl group, the yield is 99% with an enantiomeric excess of 93% and with a phenyl group, the yield is 98% with 98% ee.¹

In a follow-up article, Jacobsen employs a nice combination of experiments and DFT computations to shed light on the mechanism.² Kinetic studies established that the rate of the hydrocyanation is first order in HCN, imine and catalyst. This suggested two possible mechanisms, Scheme 1a (where protonation of the imine is followed by formation of the C-CN bond) and Scheme 1b (where cyanide adds first, followed by protonation).

Scheme 1.

A Hammett study of phenyl-substituted imines indicates a negative ρ value, indicative of positive charge build up on nitrogen, suggesting the mechanism shown in Scheme 1a. Now on the computations!

A model study was first performed at B3LYP/6-31G(d) for the reaction of HCN with imine 2a with the catalyst 3a. Three complexes involving the three species of nearly equivalent energy were found. The first mechanism examined is for direct addition of cyanide to imine with the catalyst activating the imine. This pathway was identified but it has a very high barrier (46 kcal mol^-1) and the rates of the urea and thiourea-catalyzed reactions are nearly identical, but the computations for this mechanism suggest that the thiourea-catalyzed reaction should be substantially faster. This mechanism can be discounted.

Next, they examined two related mechanism whereby either HCN or HNC complex to the catalysts and then transfer their proton to the imine. This is followed by cyanide attack on the protonated imine. The reaction involving HNC is slightly lower than that of HCN, and so this mechanism is pursued further with catalyst 3b, which more closely mimics the true catalyst, and imine 2b. The lowest energy pathway for the addition of HCN to 2b with catalyst 3b is schematically shown in Scheme 2. From A to E is transfer of the proton from HNC to the imine and rotation of the CN anion. The highest barrier is through TS F, which involves moving the imine over to the carbonyl group. The last step is the attack of the cyanide group. The structures of E through I are shown in Figure 1.

Scheme 2

E	F
G	H
I

Figure 1. B3LYP/6-31G(d) optimized geometries for steps along Scheme 2.

The step involving the transition state F is rate determining. They then computed the difference in the activation barrier through TS F for a variety of different imines using the R– and S-catalyst and compared that with the experimental enantioselectivity. These turn out to correlate extremely well, suggesting that in fact the enantioselectivity is discriminated through TS F! And the structural feature that best correlates with this enantioselectivty is the sum of the O^…H and N^…H distances in F for the R– and S-catalysts. So it is the ability to stabilize the iminium cation that is key.

A couple of caveats: first, the potential energy surface of this reaction is quite complex – Jacobsen suggests a pathway with 9 critical points. One might imagine that there could be other pathways and other important critical points, and fully characterizing this surface would be an enormous task! The nice agreement between the computations and the available experiments do give the computed pathway some credence. Second, the reactions are run in solution, and solvent has been neglected in these computations. Given that charge-separated species are being formed, solvent could be a factor. Nonetheless, this remains an interesting set of papers as it shows how computations are now a standard tool even amongst synthetic chemists!

References

(1) Zuend, S. J.; Coughlin, M. P.; Lalonde, M. P.; Jacobsen, E. N., "Scaleable catalytic asymmetric Strecker syntheses of unnatural α-amino acids," Nature, 2009, 461, 968-970, DOI: 10.1038/nature08484.

(2) Zuend, S. J.; Jacobsen, E. N., "Mechanism of Amido-Thiourea Catalyzed Enantioselective Imine Hydrocyanation: Transition State Stabilization via Multiple Non-Covalent Interactions," J. Am. Chem. Soc. 2009, 131, 15358-15374, DOI: 10.1021/ja9058958.

Here’s another extensive benchmarking study – this time on the use of TD-DFT to predict excitation energies.¹ This study looks at the performance of 28 different functionals, and compares the TD-DFT excitation energies against a data set of (a) computed vertical energies and (b) experimental energies. The performance is generally about the same for both data sets, with many functionals (especially the hybrid functionals) giving errors of about 0.3 eV. Performance can be a bit better when examining subclasses of compounds. For example, PBE0 and mPW1PW91 have a mean unsigned error of only 0.14 eV for a set of organic dyes.

References

(1) Jacquemin, D.; Wathelet, V.; Perpete, E. A.; Adamo, C., "Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules," J. Chem. Theory Comput., 2009, 5, 2420-2435, DOI: 10.1021/ct900298e

An emerging theme in this blog is Möbius systems, ones that can be aromatic or antiaromatic. Rzepa has led the way here, especially in examining annulenes with a twisted structure. Along with Schleyer and Schaefer, they have now explored a series of Möbius annulenes.¹ The particularly novel aspect of this new work is the examination of higher-order Möbius systems. In the commonly held notion of the Möbius strip, the strip contains a single half twist. Rzepa points out that the notion of twist must be considered as two parts, a part due to torsions and a part due to writhe.² We can think of the Möbius strip as formed by a ladder where the ends are connect such that the left bottom post connects with the top right post and the bottom right post connects with the top left post. Let’s now consider the circle created by joining the midpoints of each rug of the ladder. If this circle lies in a plane, then the torsion is π/N where N is the number of rungs in the ladder. But, the collection of midpoints does not have to lie in a plane, and if these points distort out of plane, that’s writhe and allows for less torsion in the strip.The sum of these two parts is called L_k and it will be an integral multiple of π. So the common Möbius strip has L_k = 1.

An example of a molecular analogue of the common Möbius strip is the annulene C₉H₉⁺ (1) – see figure 1. But Möbius strips can have more than one twist. Rzepa, Schleyer, and Schaefer have found examples with L_k = 2, 3, or 4. Examples are C₁₄H₁₄ (2) with one full twist (L_k = 2, two half twists), C₁₆H₁₆^2- (3) with three half twists, and C₂₀H₂₀²⁺ (4) with four half twists.

1	2
3	4

Figure 1. Structures of annulenes 1-4.

These annulenes with higher-order twisting, namely 2-4, are aromatic, as determined by a variety of measures. For example, all express negative NICS values, all have positive diagmagnetic exaltations, and all express positive isomerization stabilization energies (which are a measure of aromatic stabilization energy).

References

(1) Wannere, C. S.; Rzepa, H. S.; Rinderspacher, B. C.; Paul, A.; Allan, C. S. M.; Schaefer Iii, H. F.; Schleyer, P. v. R., "The Geometry and Electronic Topology of Higher-Order Charged M&oml;bius Annulenes" J. Phys. Chem. A 2009, ASAP, DOI: 10.1021/jp902176a

(2) Fowler, P. W.; Rzepa, H. S., "Aromaticity rules for cycles with arbitrary numbers of half-twists," Phys. Chem. Chem. Phys. 2006, 8, 1775-1777, DOI: 10.1039/b601655c.