Inverted Carbon Geometries: Challenges to Experiment and Theory

Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. J. Org. Chem. 2015, 80, 6520–6524
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Inverted carbon atoms, where the bonds from a single carbon atom are made to four other atoms which all on one side of a plane, remain a subject of fascination for organic chemists. We simply like to put carbon into unusual environments! Bremer, Fokin, and Schreiner have examined a selection of molecules possessing inverted carbon atoms and highlights some problems both with experiments and computations.¹

The prototype of the inverted carbon is propellane 1. The ­C_inv-C_inv bond distance is 1.594 Å as determined in a gas-phase electron diffraction experiment.² A selection of bond distance computed with various methods is shown in Figure 1. Note that CASPT2/6-31G(d), CCSD(t)/cc-pVTZ and MP2 does a very fine job in predicting the structure. However, a selection of DFT methods predict a distance that is too short, and these methods include functionals that include dispersion corrections or have been designed to account for medium-range electron correlation.

CASPT2/6-31G(d) CCSD(T)/cc-pVTZ MP2/cc-pVTZ MP2/cc-pVQZ B3LYP/6-311+G(d,p) B3LYP-D3BJ/6-311+G(d,p) M06-2x/6-311+G(d,p)	1.596 1.595 1.596 1.590 1.575 1.575 1.550

Figure 1. Optimized Structure of 1 at MP2/cc-pVTZ, along with C_inv-C_inv distances (Å) computed with different methods.

Propellanes without an inverted carbon, like 2, are properly described by these DFT methods; the C-C distance predicted by the DFT methods is close to that predicted by the post-HF methods.

The propellane 3 has been referred to many times for its seemingly very long C_inv-C_inv bond: an x-ray study from 1973 indicates it is 1.643 Å.³ However, this distance is computed at MP2/cc-pVTZ to be considerably shorter: 1.571 Å (Figure 2). Bremer, Fokin, and Schreiner resynthesized 3 and conducted a new x-ray study, and find that the C_inv-C_inv distance is 1.5838 Å, in reasonable agreement with the computation. This is yet another example of where computation has pointed towards experimental errors in chemical structure.

Figure 2. MP2/cc-pVTZ optimized structure of 3.

However, DFT methods fail to properly predict the C_inv-C_inv distance in 3. The functionals B3LYP, B3LYP-D3BJ and M06-2x (with the cc-pVTZ basis set) predict a distance of 1.560, 1.555, and 1.545 Å, respectively. Bremer, Folkin and Schreiner did not consider the ωB97X-D functional, so I optimized the structure of 3 at ωB97X-D/cc-pVTZ and the distance is 1.546 Å.

Inverted carbon atoms appear to be a significant challenge for DFT methods.

References

(1) Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. "Inverted Carbon Geometries: Challenges to Experiment and Theory," J. Org. Chem. 2015, 80, 6520–6524, DOI:10.1021/acs.joc.5b00845.

(2) Hedberg, L.; Hedberg, K. "The molecular structure of gaseous [1.1.1]propellane: an electron-diffraction investigation," J. Am. Chem. Soc. 1985, 107, 7257-7260, DOI: 10.1021/ja00311a004.

(3) Gibbons, C. S.; Trotter, J. "Crystal Structure of 1-Cyanotetracyclo[3.3.1.1^3,7.0^3,7]decane," Can. J. Chem.1973, 51, 87-91, DOI: 10.1139/v73-012.

InChIs

1: InChI=1S/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYSA-N

3: InChI=1S/C11H13N/c12-7-9-1-8-2-10(4-9)6-11(10,3-8)5-9/h8H,1-6H2
InChIKey=KTXBGPGYWQAZAS-UHFFFAOYSA-N

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Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?

McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. Angew. Chem. Int. Ed. 2014, 53, 7875-7878
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Trying to get carbon to bond in unnatural ways seems to be a passion for many organic chemists! Schleyer has been interested in unusual carbon structures for decades and he and Schaefer now report a molecule with a pentacoordinate carbon bound to five other carbon atoms. Their proposed target is pentamethylmethane cation C(CH₃)₅⁺ 1.¹ The optimized geometry of 1, which has C_3h symmetry, at MP2/cc-pVTZ is shown in Figure 1. The bonds from the central carbon to the equatorial carbon are a rather long 1.612 Å, but the bonds to the axial carbon are even longer, namely 1.736 Å. Bader analysis shows five bond critical points, each connecting the central carbon to one of the methyl carbons. Wiberg bond index and MO analysis suggests that the central carbon is tetravalent, with a 2-electron-3-center bond involving the central and axial carbons.

1
TS1	TS2

Figure 1. MP2/cc-pVTZ optimized geometries of 1 and dissociation transition states.

So while 1 is a local energy minimum, it sits in a very shallow well. One computed dissociation path, which passes through TS1 (Figure 1) on its way to 2-methyl-butyl cation and methane has a barrier of only 1.65 kcal mol^-1 (CCSD(T)/CBS + ZPE). A second dissociation pathway goes through TS2 to t-butyl cation and ethane with a barrier of only 1.34 kcal mol^-1. Worse still is that the free energy estimates suggest “spontaneous dissociation … through both pathways”.

Undoubtedly, this will not be the last word on trying to torture a poor carbon atom.

References

(1) McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. "Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?," Angew. Chem. Int. Ed. 2014, 53, 7875-7878, DOI: 10.1002/anie.201403314.

InChIs

1: InChI=1S/C6H15/c1-6(2,3,4)5/h1-5H3/q+1
InChIKey=GGCBGJZCTGZYFV-UHFFFAOYSA-N

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A two-coordinate boron cation featuring C–B+–C bonding

Shoji, Y.; Tanaka, N.; Mikami, K.; Uchiyama, M.; Fukushima, T.  Nat. Chem. 2014, 6, 498-503

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

This paper is a bit afield from the usual material I cover but this is an interesting reaction. Shoji and coworkers have prepared the two-coordinate boron species 1,¹ and confirmed its geometry by an x-ray crystal structure. What I find interesting is its reaction with CO₂, which gives 2 and organoboranes that are not identified, though presumably derived from 3.

M06-2x/6-311+G(d,p) computations support a hypothetical mechanism whereby first a complex between1 and CO₂ is formed (CP1), that is 4.4 kcal mol^-1 above isolated reactants. Then passing through TS1, which is 4.2 kcal mol^-1 above CP1, an intermediate is formed (INT), which is almost 6 kcal mol^-1 below starting materials. A second transition state is then traversed (about 1 kcal mol^-1 below starting materials), to form an exit complex between 2 and 3, which can then separate to the final products with an overall exothermicity of 10.6 kcal mol^-1. The structures of these critical points are shown in Figure 1.

1 (0.0)	CP1 (4.4)
TS1 (8.6)	INT (-5.7)
TS2 (-1.1)	CP2 (-9.0)

Figure 1. M06-2x/6-311+G(d,p) optimized structures. Relative energy in kcal mol^-1.

References

(1) Shoji, Y.; Tanaka, N.; Mikami, K.; Uchiyama, M.; Fukushima, T. "A two-coordinate boron cation featuring C–B⁺–C bonding," Nat. Chem. 2014, 6, 498-503, DOI: 10.1038/nchem.1948.

InChIs

1: InChI=1S/C18H22B/c1-11-7-13(3)17(14(4)8-11)19-18-15(5)9-12(2)10-16(18)6/h7-10H,1-6H3/q+1
InChIKey=WLUJABFTLHAEMI-UHFFFAOYSA-N

2: InChI=1S/C10H11O/c1-7-4-8(2)10(6-11)9(3)5-7/h4-5H,1-3H3/q+1
InChIKey=CUJVTHUIQVMVHD-UHFFFAOYSA-N

3: InChI=1S/C9H11BO/c1-6-4-7(2)9(10-11)8(3)5-6/h4-5H,1-3H3
InChIKey=ZJKBFARYTPYYGV-UHFFFAOYSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Gas-Phase Structure Determination of Dihydroxycarbene, One of the Smallest Stable Singlet Carbenes

Womack, C. C.; Crabtree, K. N.; McCaslin, L.; Martinez, O.; Field, R. W.; Stanton, J. F.; McCarthy, M. C.  Angew. Chem. Int. Ed. 2014, 53, 4089
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Dihdroxycarbene was the subject of a post a few years ago relating to how this carbene does not undergo tunneling,¹ while related hydroxycarbene do undergo a tunneling rearrangement.

Now we have a gas-phase microwave determination of the trans,cis isomer of dihydroxycarbene.² The computed CCSD(T)/cc-pCVQZ structure is shown in Figure 1. What is truly remarkable here is the amazing agreement between the experimental and computed structure – as seen in Table 1.The bond distance are in agreement within 0.001 Å and the bond angles agree within 0.3°! Just further evidence of the quality one can expect from high-level computations. And computing this structure was certainly far easier than the experiments!

Figure 1. CCSD(T)/cc-pCVQZ optimized geometry of dihydroxycarbene.

Table 1. Experimental and computed (CCSD(T)/cc-pCVQZ) geometric parameters of dihydroxycarbene.^a

	Expt.	Comp.
C-O	1.335	1.336
C-O	1.309	1.309
O-Htrans	0.961	0.960
O-Hcis	0.976	0.975
O-C-O	107.30	107.25
C-O-H­­trans	106.8	106.8
C-O-H­­cis	110.7	110.4
aDistances in Å and angles in deg.

References

(1) Schreiner, P. R.; Reisenauer, H. P. "Spectroscopic Identification of Dihydroxycarbene," Angew. Chem. Int. Ed. 2008, 47, 7071-7074, DOI: 10.1002/anie.200802105.

(2) Womack, C. C.; Crabtree, K. N.; McCaslin, L.; Martinez, O.; Field, R. W.; Stanton, J. F.; McCarthy, M. C. "Gas-Phase Structure Determination of Dihydroxycarbene, One of the Smallest Stable Singlet Carbenes,"Angew. Chem. Int. Ed. 2014, 53, 4089-4092, DOI: 10.1002/anie.201311082.

InChIs

Dihydroxycarbene: InChI=1S/CH2O2/c2-1-3/h2-3H
InChIKey=VZOMUUKAVRPMBY-UHFFFAOYSA-N

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Predicting Kinetically Unstable C-C Bonds from the Ground-State Properties of a Molecule

Markopoulos, G.; Grunenberg, J. Angew. Chem. Int. Ed. 2013, 52, 10648
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Can one identify a labile bond in a molecule without computing activation barriers? Markopoulos and Grunenberg suggest that examination of the bond length and its associated relaxed force constant might provide some guidance.¹

The relaxed force constant comes from identifying the force constant for some coordinate while allowing for other coordinates to relax. Badger’s rule relates the (normal) force constant to bond distance (k = a/(r_eq – d)³). For a series of 36 molecules, covering 71 C-C single bonds, Badger’s rule fits the data well, except for a set of molecules which undergo rapid Cope rearrangements (like bullvalene and semibullvalene). For these molecules, the relaxed force constants are much lower than Badger’s rule predicts, and indicates a weakened bond. This gives rise to their low activation barriers.

Another example is provided with the highly strained polycyclic hydrocarbon 1. This compound is predicted (B3LYP/6-31G(d)) to undergo a [1,2]-shift to give the carbene 2 (see Figure 1), and this is extremely exothermic: -105.7 kcal mol^-1, reflecting the enormous strain of 1. The barrier, through TS1 (Figure 1), is only 6.7 kcal mol^-1. This rearrangement was predicted by examining the relaxed force constants which identified a very weak bond, despite a short bond distance of 1.404 Å. It is unlikely that without this guidance, one would have predicted that this short bond is likely to rupture and produce this particular product.

1	2
TS1

Figure 1. B3LYP/6-31G(d) optimized structures of 1, 2, and TS1.

References

(1) Markopoulos, G.; Grunenberg, J. "Predicting Kinetically Unstable C-C Bonds from the Ground-State Properties of a Molecule," Angew. Chem. Int. Ed. 2013, 52, 10648-10651, DOI: 10.1002/anie.20130382.

InChIs

1: InChI=1S/C14H12/c1-2-8-11-5-3-9-7(1)10(9)4-6-12(8,11)14(8,11)13(7,9)10/h1-6H2
InChIKey=LNBZAENQMFDBJW-UHFFFAOYSA-N

2: InChI=1S/C14H12/c1-3-11-12-4-2-9-7-8(1,9)10(9)5-6-13(11,12)14(10,11)12/h1-6H2
InChIKey=UKVODHRLGFPZPT-UHFFFAOYSA-N

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Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation

Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. Science 2013, 341, 62
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

A long sought-after data point critical to the non-classical cation story has finally been obtained. The elusive x-ray crystal structure of a norbornyl cation was finally solved.¹ The [C₇H₁₁]⁺[Al₂Br₇]^- salt was crystallized in CH₂Br₂ at low temperature (40 K). This low temperature was needed to prohibit rotation of the norbornyl cation within the crystal (the cation is near spherical and so subject to relatively easy rotation within the crystal matrix) and hydride scrambling among the three carbons (C₁, C₂, and C₆) involved in the non-classical cation structure.

The authors report a number of different structures, all very similar, depending on slight differences in the crystals used. However, the important features are consistent with all of the structures. The cation is definitely of the non-classical type (see Figure 1) with the basal C₁-C₂ bond length of 1.39 Å similar that in benzene and long non-classical C₁-C₆ and C₂-C₆ distances of 1.80 Å. These distances match very well with the MP2(FC)/def2-QZVPP optimized distances of 1.393 and 1.825 Å, respectively.

Figure 1. X-ray structure of norbornyl cation.

References

(1) Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation," Science 2013, 341, 62-64, DOI:10.1126/science.1238849.

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Three interesting recent Angew. Chem. papers

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

A note here on a few recent Angew. Chem. articles of interest to readers of this blog. The first is a comment by Frenking¹ concerning the “trilogue” by Shaik, Hoffmann and Rzepa² which discusses the nature of C₂, especially the notion that this molecules may possess a quadruple bond (see this post for a previous post on this article.) Frenking argues that the force constant associated with the C-C stretch in C₂ is smaller than that in acetylene, so how can one argue that there is some quadruple bond character in C₂? A reply from the original authors³ accompanies the comment by Frenking, and they respond by noting that the PES for bond stretching is unusually flat. I had the generally sense, though, that the authors of both articles were really talking past each other and that an opportunity for a more fruitful discussion has been missed.

The other article of note is an excellent review of de novo enzyme design as performed by the Baker and Houk labs.⁴ This review, authored by leaders of this effort, highlights their approach to this “holy grail” problem. The general notion is to use standard tools of computational chemistry to design a theozyme. Next, this theozyme is placed into known protein motifs with the attempt to have it fit without too much steric clash. The protein is then mutated one residue at a time to optimize the fit and binding of the theozyme to substrate. Lastly, the best targets are synthesized and tested. (The reader can see my post one of their projects: synthetic Diels-Alderase.)

References

(1) Frenking, G.; Hermann, M. "Critical Comments on “One Molecule, Two Atoms, Three
Views, Four Bonds?”," Angew. Chem. Int. Ed. 2013, 52, 5922-5925. DOI: 10.1002/anie.201301485.

(2) Shaik, S.; Rzepa, H. S.; Hoffmann, R. "One Molecule, Two Atoms, Three Views, Four
Bonds?," Angew. Chem. Int. Ed. 2013, 52, 3020-3033, DOI: 10.1002/anie.201208206.

(3) Danovich, D.; Shaik, S.; Rzepa, H. S.; Hoffmann, R. "A Response to the Critical Comments on “One Molecule, Two Atoms, Three Views, Four Bonds?”," Angew. Chem. Int. Ed. 2013, 52, 5926-5928, DOI:10.1002/anie.201302350.

(4) Kiss, G.; Çelebi-Ölçüm, N.; Moretti, R.; Baker, D.; Houk, K. N. "Computational Enzyme Design," Angew. Chem. Int. Ed. 2013, 52, 5700-5725, DOI: 10.1002/anie.201204077.

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Musings about C2

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

A short note here mainly to call to the reader’s attention a fascinating “trialogue” on the C₂ molecule.¹Shaik, Danovich, Wu, Su, Rzepa, and Hiberty² recently presented a full CI study of C₂ and concluded that the molecule contains a quadruple bond (see my previous post on this paper). This work was inspired in part by a blog post by Henry Rzepa.

The trialogue¹ is a conversation between Sason Shaik, Henry Rzepa and Roald Hoffmann about the nature of C₂, its 4^th bond, its diradical character, and some historical detours to see how some of our theoretical chemistry ancestors came close to proposing a quadruple bond. The discussion weaves together simple MO pictures, simple VB models, and the need for much more sophisticated analysis to ultimately approach the truth. Very much worth pointing out is the careful analysis of trying to tease out bond dissociation energies, especially analyzing the assumptions made here – including the possibility of errors in the experiments and not just errors in the computations! This is a very enjoyable read, following these three theoreticians as they traipse about the complex C₂ landscape!

References

(1) Shaik, S.; Rzepa, H. S.; Hoffmann, R. "One Molecule, Two Atoms, Three Views, Four Bonds?," Angew. Chem. Int. Ed. 2013, 52, 3020-3033, DOI: 10.1002/anie.201208206.

(2) Shaik, S.; Danovich, D.; Wu, W.; Su, P.; Rzepa, H. S.; Hiberty, P. C. "Quadruple bonding in C2 and analogous eight-valence electron species," Nat. Chem. 2012, 4, 195-200, DOI: 10.1038/nchem.1263.

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Extreme oxatriquinanes and a record C–O bond length

Gunbas, G.; Hafezi, N.; Sheppard, W. L.; Olmstead, M. M.; Stoyanova, I. V.; Tham, F. S.; Meyer, M. P.; Mascal, M. Nat. Chem. 2012, 4, 1018
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

I have written a number of posts discussing long C-C bonds (here and here). What about very long bonds between carbon and a heteroatom? Well, Mascal and co-workers¹ have computed the structures of some oxonium cations that express some very long C-O bonds. The champion, computed at MP2/6-31+G**, is the oxatriquinane 1, whose C-O bond is predicted to be 1.602 Å! (It is rather disappointing that the optimized structures are not included in the supporting materials!) The long bond is attributed not to dispersion forces, as in the very long C-C bonds (see the other posts), but rather to σ(C-H) or σ(C-C) donation into the σ*(C-O) orbital.

1

Inspired by these computations, they went ahead and synthesized 1 and some related species. They were able to get crystals of 1 as a (CHB₁₁Cl₁₁)^- salt. The experimental C-O bond lengths for the x-ray crystal study are 1.591, 1.593, and 1.622 Å, confirming the computational prediction of long C-O bonds.

As an aside, they also noted many examples of very long C-O distances within the Cambridge
Structural database that are erroneous – a cautionary note to anyone making use of this database to identify unusual structures.

References

(1) Gunbas, G.; Hafezi, N.; Sheppard, W. L.; Olmstead, M. M.; Stoyanova, I. V.; Tham, F. S.; Meyer, M. P.; Mascal, M. "Extreme oxatriquinanes and a record C–O bond length," Nat. Chem. 2012, 4, 1018-1023, DOI: 10.1038/nchem.1502

InChIs

1: InChI=1S/C21H39O/c1-16(2,3)19-10-12-20(17(4,5)6)14-15-21(13-11-19,22(19)20)18(7,8)9/h10-15H2,1-9H3/q+1/t19-,20+,21-
InChIKey=VTBHIDVLNISMTR-WKCHPHFGSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.