Stable Alkanes Containing Very Long Carbon–Carbon Bonds

Fokin, A. A.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Dahl, J. E. P.; Carlson, R. M. K.; Schreiner, P. R. J. Am. Chem. Soc., 2012, 134, 13641 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Schreiner has expanded on his previous paper¹ regarding alkanes with very long C-C bonds, which I commented upon in this post. He and his colleagues report² now a series of additional diamond-like and adamantane-like sterically congested alkanes that are stable despite have C-C bonds that are longer that 1.7 Å (such as 1! In addition they examine the structures and rotational barriers using a variety of density functionals.

1

2

For 2, the experimental C-C distance is 1.647 Å. A variety of functionals all using the cc-pVDZ basis predict distances that are much too long: B3LYP, B96, B97D, and B3PW91. However, functionals that incorporate some dispersion, either through an explicit dispersion correction (Like B3LYP-D and B2PLYP-D) or with a functional that address mid-range or long range correlation (like M06-2x) or both (like ωB97X-D) all provide very good estimates of this distance.

On the other hand, prediction of the rotational barrier about the central C-C bond of 2 shows different functional performance. The experimental barrier, determined by ¹H and ¹³C NMR is 16.0 ± 1.3 kcal mol^-1. M06-2x, ωB97X-D and B3LYP-D, all of which predict the correct C-C distance, overestimate the barrier by 2.5 to 3.5 kcal mol^-1, outside of the error range. The functionals that do the best in getting the rotational barrier include B96, B97D and PBE1PBE and B3PW91. Experiments and computations of the rotational barriers of the other sterically congested alkanes reveals some interesting dynamics, particularly that partial rotations are possible by crossing lower barrier and interconverting some conformers, but full rotation requires passage over some very high barriers.

In the closing portion of the paper, they discuss the possibility of very long “bonds”. For example, imagine a large diamond-like fragment. Remove a hydrogen atom from an interior position, forming a radical. Bring two of these radicals together, and their computed attraction is 27 kcal mol^-1 despite a separation of the radical centers of more than 4 Å. Is this a “chemical bond”? What else might we want to call it?

A closely related chemical system was the subject of yet another paper³ by Schreiner (this time in collaboration with Grimme) on the hexaphenylethane problem. I missed this paper somehow near
the end of last year, but it is definitely worth taking a look at. (I should point out that this paper was already discussed in a post in the Computational Chemistry Highlights blog, a blog that acts as a journals overlay – and one I participate in as well.)

So, the problem that Grimme and Schreiner³ address is the following: hexaphenylethane 3 is not stable, and 4 is also not stable. The standard argument for their instabilities has been that they are simply too sterically congested about the central C-C bond. However, 5 is stable and its crystal structure has been reported. The central C-C bond length is long: 1.67 Å. But why should 5 exist? It appears to be evenmore crowded that either 3 or 4. TPSS/TZV(2d,2p) computations on these three compounds indicate that separation into the two radical fragments is very exoergonic. However, when the “D3” dispersion correction is included, 3 and 4 remain unstable relative to their diradical fragments, but 5 is stable by 13.7 kcal mol^-1. In fact, when the dispersion correction is left off of the t-butyl groups, 5 becomes unstable. This is a great example of a compound whose stability rests with dispersion attractions.

3: R₁ = R₂ = H
4: R₁ = tBu, R₂ = H
5: R₁ = H, R₂ = tBu

References

(1) Schreiner, P. R.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Schlecht, S.; Dahl, J. E. P.; Carlson, R. M. K.; Fokin, A. A. "Overcoming lability of extremely long alkane carbon-carbon bonds through dispersion forces," Nature 2011, 477, 308-311, DOI:10.1038/nature10367

(2) Fokin, A. A.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Dahl, J. E. P.; Carlson, R. M. K.; Schreiner, P. R. "Stable Alkanes Containing Very Long Carbon–Carbon Bonds," J. Am. Chem. Soc., 2012, 134, 13641-13650, DOI: 10.1021/ja302258q

(3) Grimme, S.; Schreiner, P. R. "Steric Crowding Can tabilize a Labile Molecule: Solving the Hexaphenylethane Riddle," Angew. Chem. Int. Ed., 2011, 50, 12639-12642, DOI:10.1002/anie.201103615

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A simple, exact DFT embedding scheme

Fredrick R. Manby, Martina Stella, Jason D. Goodpaster and Thomas F. Miller III

JCTC, 2012, 8, 2564-2568

 

Embedding methods have become a useful tool to perform molecular electronic structure calculations on large systems at relatively modest computational cost, and (hopefully) acceptable accuracy, compared to full blown calculations on the entire system. These methods rely on the short-range nature of chemical interactions between molecular fragments, which allows (most) systems to be subdivided. 

Manby and co-workers have developed embedding schemes that enforce Pauli exclusion by a projection technique to ensure orthogonality of the orbitals of the interacting subsystems. The authors use the fact that Kohn-Sham density functional theory (KS-DFT) provides a framework to perform exact calculations on a subsystem embedded in its full QM environment. This is achieved by partitioning the total density into subsystem densities. If the subsystem densities are constructed with non orthogonal orbitals, a non-additive term arises in the kinetic energy.  However, if the orbitals are orthogonal, this term vanishes. Methods to enforce orthogonality have been employed previously. Manby et al exploit one of these methods to formulate a formally exact DFT embedding scheme. To this end they employ a level shifting operator to keep the orbitals of  a subsystem orthogonal to those of other subsystems. They show that increasing the value of the level shifting parameter reduces the error in energy up to a point (numerical instabilities arise at very large values). The  interesting innovation comes in the use of perturbation theory to eliminate the dependence on the level shifting parameter.

The authors present applications with different embedding schemes combining DFT and wave-function methods. The first example consists of embedding the hydroxyl moiety of ethanol in the environment of the ethyl backbone. DFT-in-DFT embedding calculations at the PBE/6-31G* level with the level-shift and perturbation correction agree with the full DFT calculation to 7 pEH. The second example consists of the deprotonation reaction of ethanol in gas-phase. The PBE result on the full system is 10 mEH lower than the CCSD(T) reference. This can be compared with CCSD(T)-in-PBE embedding results which are as close as 1.5 mEH. Similar trends are observed for the activation barrier for the SN2 reaction of chloride with propyl chloride and water trimer.

As the authors note, this method is "limited to applications for which the electronic structure can be reasonably described using KS theory". However, it provides a simple and straightforward method to perform embedding calculations and can be easily implemented in most electronic structure programs.

Dynamics, transition states, and timing of bond formation in Diels–Alder reactions

Black, K.; Liu, P.; Xu, L.; Doubleday, C.; Houk, K. N. Proc. Nat. Acad. Sci. USA, 2012, 109, 12860 (Paywall)

Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Has there been an organic reaction more examined by computational methods than the Diels-Alder reaction? You’d think we would have covered all aspects of this reaction by now, but no, it appears that this reaction remains fertile hunting grounds.

Doubleday and Houk have examined the Diels-Alder reaction with an eye towards its synchronicity,¹ an area that Houk has delved into throughout his career. While most experiments show significant stereoselectivity, a few examples display a small amount of stereo loss. Computed transition states tend to have forming C-C bond distances that are similar, though with proper asymmetric substitution, the asymmetry of the TS can be substantial. In this paper,¹ they utilize reaction dynamics specifically to assess the time differential between the formation of the two new C-C single bonds. They examined the eight reactions shown below. The first six (R1-R6) have symmetric transition states, though with the random sampling about the TS for the initial condition of the trajectories, a majority of asymmetric starting conditions are used. The last two (R7 and R8) reactions have asymmetric TSs and the random sampling amplifies this asymmetry.

Nonetheless, the results of the dynamics are striking. The time gap, the average time between the formations of the first and second new C-C bond, for R1-R6 is less than 5 fs, much shorter than a C-C vibration. These reactions must be considered as concerted and synchronous. Even the last two reactions (R7 and R8), which are inherently more asymmetric, still have very short time gaps of 15 and 56 fs, respectively. One might therefore reasonably conclude that they too are concerted and synchronous.

There are some exceptions – a few trajectories in the last two reactions involve a long-lived (~1000 fs) diradical intermediate. At very high temperature, about 2% of the trajectories invoke a diradical intermediate. But the overall message is clear: the Diels-Alder reaction is inherently concerted and synchronous.

References

(1) Black, K.; Liu, P.; Xu, L.; Doubleday, C.; Houk, K. N. "Dynamics, transition states, and timing of bond formation in Diels–Alder reactions," Proc. Nat. Acad. Sci. USA, 2012, 109, 12860-12865, DOI:10.1073/pnas.1209316109

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The Last Globally Stable Extended Alkane

Lüttschwager, N. O. B.; Wassermann, T. N.; Mata, R. A.; Suhm, M. A. Angew. Chem. Int. Ed. 2012, ASAP

Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

The role of dispersion in understanding organic chemistry, both structure and reactivity, is truly coming into prominence (see for example this blog post for a compound whose stability is the result of dispersion). This has been driven in part by new computational techniques to properly account for dispersion. An interesting recent example is the structure of long chain alkanes, with a question posed and answered by Mata and Suhm:¹ What is the largest alkane whose most stable conformation is the extended chain?

The question is attacked by computation and experiment. The computational methodology involves corrections to the local MP2-F12 energy involving the separation of orbital pairs that are treated with a coupled clusters method. The straight chain (having only anti arrangements about the C-C bonds) and the hairpin conformer (having three gauche arrangements) were completely optimized. The C₁₇H₃₆hairpin isomer is shown in Figure 1. For chains with 16 or fewer carbons, the all-anti straight chain is lower in energy, but for chains with 17 or more carbon atoms, the hairpin is lower in energy. Gas-phase low temperature IR and Raman spectra suggest that dominance of the hairpin occurs when the chain has 18 carbons, though careful analysis suggests that this is likely an upper bound. At least tentatively the answer to the question is that heptadecane is likely the longest alkane with a straight chain, but further lower temperature experiments are needed to see if the C16 chain might fold as well.

Figure 1. Optimized geometry of the hairpin conformation of heptadecane.

(I thank Dr. Peter Schreiner for bringing this paper to my attention.)

References

(1) Lüttschwager, N. O. B.; Wassermann, T. N.; Mata, R. A.; Suhm, M. A. "The Last Globally Stable Extended Alkane," Angew. Chem. Int. Ed. 2012, ASAP, DOI: 10.1002/anie.201202894.

InChIs

Heptadecane: InChI=1S/C17H36/c1-3-5-7-9-11-13-15-17-16-14-12-10-8-6-4-2/h3-17H2,1-2H3
InChIKey=NDJKXXJCMXVBJW-UHFFFAOYSA-N

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Dispersion corrections and bio-molecular structure and reactivity

Richard Lonsdale, Jeremy N. Harvey, and Adrian J. Mulholland "Effects of Dispersion in Density Functional Based QM/ MM Calculations on Cytochrome P450 Catalysed Reactions"Journal of Chemical Theory and Computation 2012, ASAP (Paywall)

Takeshi Nagata, Dmitri G. Fedorov, Hui Li, and Kazuo Kitaura "Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method" Journal of Chemical Physics 2012, 136, 204112 (Paywall)

The DFT dispersion correction developed by Grimme and co-workers was recently highlighted in Computation Chemistry Highlights. Recently two papers have appeared that quantify the importance of the dispersion correction on modeling bio-molecular structure and reactivity.

Cytochrome P450 barrier heights in better agreement with experiment using B3LYP-D2 and -D3

Lonsdale et al. used QM/MM to compute barrier heights for oxidation reactions, catalyzed by P450$_{cam}$, with an without dispersion corrections in the QM region.  Invariably the dispersion correction lowered the barrier significantly (usually by ca 5 kcal/mol), yielding results that were in better agreement with experimental values.  The effect of the dispersion correction on the transition state geometries was less pronounces though not negligible, with bond lengths changing by as much as 0.2 Å.

It is worth noting that the QM region contains a conjugated porphyrin ring and that three of the four substrates considered in the study contain one or more double bonds.  Thus, the QM region contains very polarizable functional groups and, since the magnitude of dispersion interactions increases with the polarizability of the groups involved, it is possible that the effect of dispersion on barrier heights for other enzymes will be less than observed here.  It will be interesting to find out.

MP2 quality Trp-cage structure using RHF-D

Nagata et al. have implemented analytical MP2/PCM gradients for the fragment molecular orbital method and used it to geometry optimize the small protein Trp-cage at the MP2/6-31(+)G(d) level of theory [the (+) indicates diffuse functions on carboxylate groups].  The resulting structure compared well with the experimental NMR structures, with a backbone RMSD of only 0.426 Å. This is a significant improvement in agreement compared to the corresponding RHF/PCM optimized structure (RMSD 1.107 Å) and demonstrates the importance dispersion in bio-molecular structure.  Interestingly, the corresponding RHF-D structure compared equally well to experiment (0.414 Å) and was virtually identical to the MP2 structure (RMSD 0.068 Å).

Disclaimer: I was involved in the implementation of the FMO RHF/PCM interface.

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