How short can a C-C single bond get? The bonding in a set of molecules that are related structurally to previously synthesized or theoretically examined systems with short C-C bonds is investigated. According to calculations, a single C-C bond could be compressed to 1.313 A! To the best of our knowledge, this is the shortest single C-C bond reported to date. This shortening is a consequence of a change in the C-C-C bond angle, θ, to minimize strain in the cages and an effort to offset the tension in the surrounding bridges

Donald, Kelling J.

Martinez-Guajardo, Gerarso

Merino, Gabriel

Vazquez, Miguel Angel

Wittmaack, Bernard K.

English

University of Richmond

University of RichmondUR Scholarship RepositoryChemistry Faculty Publications Chemistry2010Shorter Still: Compressing C-C Single BondsGerarso Martinez-GuajardoKelling J. DonaldUniversity of Richmond, kdonald@richmond.eduBernard K. WittmaackMiguel Angel VazquezGabriel MerinoFollow this and additional works at: http://scholarship.richmond.edu/chemistry-faculty-publicationsPart of the Other Chemistry CommonsThis Article is brought to you for free and open access by the Chemistry at UR Scholarship Repository. It has been accepted for inclusion in ChemistryFaculty Publications by an authorized administrator of UR Scholarship Repository. For more information, please contactscholarshiprepository@richmond.edu.Recommended CitationMartinez-Guajardo, Gerardo, Kelling J. Donald, Bernard K. Wittmaack, Miguel Angel Vazquez, and Gabriel Merino. "Shorter Still:Compressing C-C Single Bonds." Organic Letters 12, no. 18 (2010): 4058-4061. doi:10.1021/ol101671m.Shorter Still: Compressing C-C SingleBondsGerardo Martı´nez-Guajardo,† Kelling J. Donald,*,‡ Bernard K. Wittmaack,‡Miguel Angel Vazquez,† and Gabriel Merino*,†Departamento de Quı´mica, DiVisio´n de Ciencias Naturales y Exactas, UniVersidad deGuanajuato, Col. Noria Alta s/n C.P. 36050, Guanajuato, Gto., Me´xico, andDepartment of Chemistry, Gottwald Center for the Sciences, UniVersity of Richmond,Richmond, Virginia 23173gmerino@quijote.ugto.mx; kdonald@richmond.eduReceived July 20, 2010ABSTRACTHow short can a C-C single bond get? The bonding in a set of molecules that are related structurally to previously synthesized or theoreticallyexamined systems with short C-C bonds is investigated. According to calculations, a single C-C bond could be compressed to 1.313 Å! Tothe best of our knowledge, this is the shortest single C-C bond reported to date. This shortening is a consequence of a change in theC-C-C bond angle, θ, to minimize strain in the cages and an effort to offset the tension in the surrounding bridges.How short can a C-C single bond get?1 Several properties ofmolecular fragments such as polarizabilities, interatomic separa-tions, and force constants remain very roughly constant frommolecule to molecule. In chemistry, understanding such trans-ferable properties and the limits of their transferability isimportant.Significant chemical insight is bound up, for example, inthe knowledge that a typical C-C single bond is ∼1.54 Å,a C-C double bond is ∼1.34 Å, and a C-C triple bond, at∼1.23 Å, is shorter still. But there are significant exceptions,and we should explore, understand, and exploit them. AsHoffmann and Ho¨pf pointed out, “the making of moleculesthat are untypical or abnormal tests our understanding of thatfundamental yet fuzzy entity, the chemical bond”.2 Unusualcharacteristics in bonding, such as interatomic separationsthat are way shorter (or longer) than expected, are interestingpartly because they suggest new possibilities for structuralchemistry. So, the exploration of the edge of bondingpossibilities strengthens our intuition and appreciation ofwhat is possible in structural chemistry.A wide collection of compounds with short single bondsbetween saturated C atoms have been synthesized. A remarkableexample is the hexakis(trimethylsilyl)tetrahedryltetrahedranereported by Tanaka and Sekiguchi: X-ray crystallographicanalysis revealed that the linking C-C single bond is 1.436Å.3 This is the shortest known noncyclic C-C single bond ina saturated hydrocarbon system. Using the block-localized wavefunction (BLW) method, Mo4 demonstrated that both hybrid-† Universidad de Guanajuato.‡ University of Richmond.(1) Hopf, H. Chem. Unserer Zeit 1976, 10, 114.(2) Hoffmann, R.; Hopf, H. Angew. Chem., Int. Ed. 2008, 47, 4474.(3) Tanaka, M.; Sekiguchi, A. Angew. Chem., Int. Ed. 2005, 44, 5821.ORGANICLETTERS2010Vol. 12, No. 184058-406110.1021/ol101671m  2010 American Chemical SocietyPublished on Web 08/18/2010ization and hyperconjugation contribute to the shortening of thecentral C-C bond in tetrahedryltetrahedrane.More recently, Huntley et al. investigated several structuralstrategies for squeezing C-C single bondssusing cages,intramolecular repulsion, or strain, rather than electroniceffects.5 A tour through several structures uncovered a C-Csingle bond of 1.32 Å, for 1.6As Huntley et al. showed, it is expensive to compressmolecules. Squeezing ethane to reduce the C-C bond by0.15 Å costs about 37.7 kJ·mol-1.5 For several molecules inwhich exceptionally short C-C or other bonds have beenobserved, the cost for the bond contraction is paid for by adestabilization and elongation of some of the other bonds inthe structure. In endohedral systems, for example, bonds inthe cages elongate, while bonds in the molecule within thecage are compressed.5,7 Thus, the (theoretical and experi-mental) quest to understand the tolerance of C-C singlebonds for structural compression is a real challenge inmolecular design. The viable candidate structures must havefragments that absorb (by stretching) the cost to shorten one ortwo bonds. If the system is to be a minimum on the potentialenergy surface, however, it is important to maximize the strainat the target C-C bonds while preserving some flexibility inother parts of the structure.In this contribution, we investigate the bonding in a set ofmolecules that are related structurally to previously synthesizedor theoretically examined systems with a short C-C bond(group A in the Supporting Information, SI). We focus onunexplored cases in which the primary motivation for the C-Cbond contraction is structural strain, rather than electroniceffects. For comparison, we include some familiar molecules,such as 1,3-butadiyne, with a range of C-C bond lengths forwhich electronic effects are more important (group B).All our geometry optimizations have been carried out withthe Gaussian 03 suite of programs8 using the B3LYP9functional in conjunction with the 6-311G(d,p) basis sets.The nature of each stationary point has been determined bycalculating and diagonalizing the Hessian matrix. To analyzethe bonding mechanisms, a natural bond orbital analysis(NBO)10 was carried out.Tetrahedryltetrahedrane 2 and cubylcubane 311 were chosenas our basic building blocks. The central C-C bond lengths inthese systems are 1.426 and 1.475 Å, respectively. The systemswe examine differ primarily in the nature of the bridgesconnecting the two vertex-bonded polyhedra.Let us consider the tetrahedryltetrahedrane derivatives.According to our calculations, the central C-C bond iscompressed from 1.426 Å in 2 to 1.313 Å in 7! The C-Cbond contraction that is accomplished in 7 outstrips, to thebest of our knowledge, all the previously published recordsfor the single C-C bond.A reoptimization of structures 1 and 7 at the B3LYP andMP2(full) levels for several basis sets (see SI) confirms thatthe bond in 7 is significantly shorter.(4) Mo, Y. Org. Lett. 2006, 8, 535.(5) Huntley, D. R.; Markopoulos, G.; Donovan, P. M.; Scott, L. T.;Hoffmann, R. Angew. Chem., Int. Ed. 2005, 44, 7549.(6) Our results show that the central C-C bond length in 1 is 1.350 Å,which is slighly larger than that reported by Huntley et al. at the samelevel (1.32 Å).(7) Cerpa, E.; Krapp, A.; Flores-Moreno, R.; Donald, K. J.; Merino, G.Chem.sEur. J. 2009, 15, 1985.(8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,revision C.02; Gaussian, Inc.: Wallingford CT, 2004.Org. Lett., Vol. 12, No. 18, 2010 4059How to explain this squeezing? A number of systems withshort bonds have been identified in the past few years, buta model of C-C bond contraction that allows us to predictthat a given bonding environment will stabilize short bondsis still illusive.As a step toward such an understanding, we investigatedthe relationship between bond distance and the chargedistribution in the short C-C bonds formed by the C atomsat highly strained vertices (Figure 1).Interestingly, the WBIs in the highly strained group Asystems decrease slightly as the bond gets shorter in Figure1. Does this suggest that in the backstrapped vertex bondedpolyhedra the short C-C bonds are stabilized by movingcharge density out of the internuclear region into the rest ofthe molecule? The situation is not clear. Going from 4 to 7,for example, the index changes by only a tiny ∆WBI ) -0.07(Table S.1, SI). As one reviewer suggested, the reduction inthe WBIs in group A may be explained by changes in theextent of the C(s-p) - C(s-p) valence hybrid orbital overlapcoupled with the repulsion of the core (s) shells causing anet reduction in the electron density in the bonding region.How does the nature of the C-C σ bond change in thesecompressed systems? How “single” are these extremely shortbonds? In structures 4-7 and in the short bonds in group Ain general, the overlap between the s-p hybridized orbitalsalong the bond axis is the primary bonding interaction. Aqualitative molecular orbital (MO) analysis confirms this net(s-p) σ-character of the C-C bonds; Figure S.2a in the SIillustrates, e.g., a σ-type C-C orbital interaction in 4. SeveralC-C (px-px and py-py) π-like interactions (Figure S.2b, SI)are observed as well among the MOs in structures 4-7, butthese interactions are counterbalanced by C-C π-antibondingMOs such as that shown in Figure S.2c (SI).To understand the squeezing of the C-C bond in 4-7, weassessed the overlap populations (see Table S.4, SI). An orbitalby orbital break down of the overlap population has beendifficult to achieve using the ab initio computational softwareavailable to us. An analysis at the extended Hu¨ckel (EH) MOlevel12 suggests, however, extremely weak net (px-px and py-py) πinfluences on the short C-C bonds in 4-7 (compared, forexample, to ethane) in addition to the dominant (s-p) σcharacter of the bond. Moreover, we find that the total (bondor reduced) overlap population (ROP) for the short C-Cbond increases, but only slightly (∆ROP ) +0.16 e), as thebond contracts going from 4 to 7 (Table S.3, SI). This EHresult runs contrary to the WBI data (∆WBI ) -0.07)mentioned previously. However, a basic (qualitative) consensusbetween the two results is that the charge density in the bondingregion of the C-C bond changes rather insignificantly going from1.421 Å in 4 to 1.313 Å in 7.In moderately strained systems or those controlled byelectronic effects such as 1,3-butadiyne (blue in Figure 1), theopposite and more common relationship between bond orderand bond length is observed where the bond order increasesas the bond distance decreases. The difference in the behaviorof the molecules in groups A and B is obvious, for example,from a comparison of 7 and 1,3-butadiyne. 7 has one of thelowest bond orders (0.95) and the shortest bond (1.313 Å). 1,3-Butadiyne on the other hand has the shortest bond in group B(1.366 Å) while boasting the highest bond order.Given this dramatic disparity in the bond order vs the bondlengths in groups A and B (Figure 1), the reactivity andspectroscopic properties of the short C-C single bonds inthe two groups will likely be quite different, even if the bondlengths are identical (cf. structure 12 in Table S.1, and 1,3-butadiyne).An increase in the s orbital composition is typicallyassociated with a shortening of C-X bonds. This has beenexplained in terms of the increase in orbital electronegativitiesas the ns composition increases.The results in Figure 2 are instructive. Here we find, as well,a systematic difference in the behavior of the group A and Bmolecules. For the group B systems, bond contraction isaccompanied by an increase in the % s compositions at the Catoms in the C-C bond (following the trend line in Figure 2).Put another way, the electronically stabilized short C-C bondsrelax and elongate as the C sites involved in the bond aresaturated (i.e., rehybridized, going progressively from sp to sp3).For the group A systems, this correlation breaks downdramatically in the high-strain regime. The group A systemsthat are not backstrapped, such as 2, 3, 10, and 13 (see the SI),and those with long loose bridges such as 4 follow the samebehavior described by the best fit line for group B. As the bridgebecomes shorter and stiffer, however (going from 4 to 7 above,(9) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C. T.;Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785.(10) (a) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys.1985, 83, 735. (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV.1988, 88, 899.(11) Gilardi, R.; Maggini, M.; Eaton, P. E. J. Am. Chem. Soc. 1988,110, 7232.(12) (a) Mealli, C.; Proserpio, D. M. J. Chem. Educ. 1990, 67, 399. (b)Mealli, C.; Ienco, A.; Proserpio, D. M. Book of Abstracts of the XXXIIIICCC; ICCC: Florence, Italy, 1998; p 510.Figure 1. Wiberg Bond indices (WBI) for the short C-C bonds inthe groups A (red) and B (blue) systems. In group A, ° denotes asimple vertex bonded bipolyhedra like 2 and 3. The others arebackstrapped (for details, see Figure S.1 and Table S.1 in the SI).4060 Org. Lett., Vol. 12, No. 18, 2010for example), the aspiration toward the behavior representedby the best fit line is rapidly quenched. Indeed, the oppositebehavior is observed; the bond contraction is accompanied byslight decreases in the s orbital composition (see group A inFigure 2). Interestingly, Figure 2 accomplishes an even finerpartition of the group A systems. The group A systems arecleanly divided into (i) nonbridged systems, which generallybehave like group B systems, (ii) systems based on 2, withhigher % s contributions, and (iii) open and closed systemsbased on 3 with lower % s compositions (cf. Figure S.1 andTable S.1 in SI).Why do the backstrapped group A systems deviate from thelines in Figures 1 and 2? Evidently, the molecules compensatefor the strain of the bridge in two ways: by a contraction in thecentral C-C bond and simultaneously by a decrease in theC-C-C bond angle (see Figure 3). As Figure 3 confirms, thisdecrease in the bond angle is partnered by a decrease in the %s contribution of the hybrid orbital involved in the bonding.Remarkably, the linear relationshipbetween orbital composition and bond angle for group Asystems shown in Figure 3 extends down to as far as 79.4°in an adamantane-like C11H12 structure. The latter structure(11) is the only one we consider in group A in which thetwo C atoms are in different bonding environments.To be sure, simple empirical relationships have previouslybeen identified linking the bond angles between differentsubstituents in carbon compounds. We can mention animportant analysis by Root et al.,13 for example. Here, weshow that a simple direct correlation between orbitalcomposition and bond angle is obtained even for highlystrained systems that show exceptional behavior in otherregards as in Figures 1 and 2.Given the convincing correlation between orbital composi-tion and bond angle in Figure 3, it is apparent that for anybipolyhedryl structuresbridged or notswe can predict theorbital composition from θ. It is clear from Figures 2 and 3,however, that there is no universal relationship betweenorbital composition or θ and bond length. The bond lengthdepends on the exact structure of the molecule and not justthe orbital composition or bond angle at the C-C bond. Thisis obvious, for instance, from the clear separation in Figures2 and 3 between the bitetrahedryl series and the bicubylseries.In assessing the evidence outline above, we are quiteconvinced that the best chance at C-C bonds in hydrocar-bons as short as 1.31 Å, or even shorter still, is to be foundin systems where the C-C bond is formed by vertex bondedbipolyhedryls that are strongly strapped together by shortbridges. However, these bridges must be short enough tostrain the polyhedryls but long enough so that the cages donot disassemble to give, for example, propellane-like struc-tures. Ultimately, the shortest bonds we finds7, 8, and 9sareconsequences of a change in θ to minimize strain in the cagesand an effort to offset the tension in the surrounding bridges.Acknowledgment. This work was supported in Guana-juato by Conacyt (Grant 57892) and in Richmond by theResearch Corporation (Award No. 7742) and the ThomasF. and Kate Miller Jeffress Memorial Trust (Award J-903).G.M.G. thanks DAIP for PhD fellowship. B.K.W. is gratefulto the University of Richmond for the award of an Arts andSciences research fellowship.Note Added after ASAP Publication. The formula afterFigure 3 contained an error in the version published ASAPAugust 18, 2010; the correct version reposted August 24,2010.Supporting Information Available: Optimized geom-etries of the systems studied, representative molecular orbitalsand additional MO, and EH data. This material is availablefree of charge via the Internet at http://pubs.acs.org.OL101671M(13) Root, D. A.; Landis, C. R.; Cleveland, T. J. Am. Chem. Soc. 1993,115, 4201.Figure 2. C % s orbital composition vs the C-C bond length forsymmetric systems in groups A and B.Figure 3. Orbital composition as function of bond angle for themolecules in group A.% s composition ) 0.35 × bond angle/° - 8.58Org. Lett., Vol. 12, No. 18, 2010 4061

Shorter Still: Compressing C-C Single Bonds

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Shorter Still: Compressing C-C Single Bonds

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