Beyond the Bond

COMMENT

Beyond the bond More than ever before, new techniques show the bond to be a convenient fiction, albeit one that holds the field of chemistry together, finds Philip Ball.

ot so long ago, the chemistry stu fresh ways to probe and quantify chemi the dynamical dimension. Molecules have dent’s standard text on the theory of cal bonds2. Traditional measures such as traditionally been regarded, if not as static, oz Chast Chast oz

chemical bonding was Charles Coul crystallographic interatomic distances and then as having clear architectural frame r Nson’s Valence (1952). Absent from it was this dissociation energies have been supple works that are merely shaken and rotated by ons by by ons theoretical chemist’s real view on the sticks mented by spectroscopic techniques for thermal motions. The bonds get stretched I that generations of students have drawn to determining vibrational frequencies, meth and bent, but they still have an equilibrium link atoms into molecules. “A chemical bond ods such as nuclear magnetic resonance to length and strength that seems to justify is not a real thing: it does not exist: no one has measure shifts in the electronic environment their being pictured as lines and stalks. Now, Illustrat ever seen it, no one ever can. It is a figment of of atoms and their magnetic interactions, thanks to ultrafast spectroscopies, such time our own imagination,” he later wrote1. measurements of force constants (bond average values may not always accurately There is a good reason for postponing this stiffness) and a host of quantumchemical characterize either structure or reactivity. awkward truth. The bond is literally the glue tools for calculating such aspects as electron What is measured in a bond depends not just that makes the entire discipline cohere; to distributions or localization. on how but on when it is measured. consider it an objective reality is necessary An indication of the shifting ground is the Some chemists argue that as a result of this, for any kind of discourse on chemistry. The recent decision to redefine the nature of the the very existence (or not) of a bond depends discipline is in fact riddled with such conven hydrogen bond in the light of experimental on how the problem is probed. Others are ient (and contested) fictions, such as electro results that alter the traditional electrostatic committed to absolute criteria. This differ negativity, oxidation state, tautomerism description. ence of opinion goes to the heart of what and acidity. The nature of the chemical bond is now chemistry is about: can all be reduced to Disputes about the correct description further complicated by the introduction of quantum physics, or are fuzzy rules of thumb of bonding have ruffled chemists’ feathers essential? More pressingly, the issue of how since the concept of molecular structure 20��: YEAR OF CHEMISTRY best to describe a chemical bonding pattern first emerged in the midnineteenth century. Celebrating the central science has tangible implications for a wide range Now they are proliferating, as new theoreti nature.com/chemistry20�� of problems in chemistry, from molecules cal and experimental techniques present in which atoms are coerced out of their

26 | NATURE | VOL 469 | 6 JANUARy 2011 © 2011 Macmillan Publishers Limited. All rights reserved COMMENT usual bonding geometry to the symmetric as some combination of the wavefunctions der Waals attraction, which is why helium hydrogen bond (in which a bound hydrogen of individual electrons. That’s also the basis is a liquid at very low temperatures; but they atom is shared equally between two other of the Hartree–Fock method for calculating are not generally thought to be chemically atoms), and new variations on old themes the wavefunction and energy of the lowest bonded as a result. such as aromaticity (special patterns of ‘delo energy state (ground state) of a molecular Besides, the ‘bonded or not’ question calized’ bonds, like those in benzene)3. system — a method that became practical becomes contextdependent once atoms Just about every area of chemistry har in the 1950s, when computers made it pos are embedded in a molecule, where they bours its own bonding conundrums. Most sible to solve the equations numerically. may be forced close together merely by illustrate that we have a far from exhaustive But separating the wavefunction into one the atoms around them, and where there understanding of the ways in which quan electron components is a fiction, as they is inevitably some arbitrariness in decid tum rules will permit atoms to unite — and all influence one another: the behaviour of ing which electrons that in consequence, the synthetic inventive one electron depends on what all the oth “Chemists’ ‘belong’ to which ness of chemists suffers from a limited view ers are doing. The difference between true inventiveness atoms. The result of the possibilities. groundstate energy and that calculated ing ambiguities were using the Hartree–Fock approach is called suffers from illustrated recently Carving up eleCtrons the correlation energy. More recent com a limited when three experts We can all agree on one thing: chemical putational methods can capture most of view of the failed to agree about bonding has something to do with elec the correlation energy, but none can give possibilities.” whether two sulphur trons. Two atoms stick together because an exact solution. As a result, describing atoms in an organo of the arrangement of electrons around the quantum chemical bond remains a mat metallic compound are linked by a bond5. their nuclei. In the nineteenth century, it ter of taste: all descriptions are, in effect, The argument involved different interpre was commonly thought that this attraction approximate ways of carving up the electron tations of quantumchemistry calculations, was electrostatic: that atoms in molecules distribution. tussles over the best criteria for identifying are positively or negatively ionized. That If that were the limit of the bond’s a bond, and evidence of precedent from left the puzzle of how identical atoms can ambiguity, there would be little to argue comparable compounds. form diatomic molecules such as H2 and O2. about. It is not. There is, for example, the All this is merely a reminder that a mol American chemist G. N. Lewis proposed that matter of when to regard two atoms as being ecule is ultimately a set of nuclei embedded bonding can instead result from the sharing bonded at all. Pauling’s somewhat tautologi in a continuous electron cloud that stabilizes of electrons to create filled shells of eight, cal definition rather gave the game away: a a particular configuration, which balls and visualized as the corners of a cube. group of atoms is to be considered bonded sticks can sometimes idealize and some In the 1920s and 1930s another Ameri when it is “convenient for the chemist to times not. But disputes about the nature of can chemist, Linus Pauling, showed how consider it as an independent molecular spe the chemical bond are not simply semantic. this interaction could be formulated in the cies”. Pauling admitted some of the conse It matters, for example, whether we regard language of quantum mechanics as the over quent ambiguities: for example, although his a very strong multiple bond as quintuple or lap of electron orbitals (see Nature 468, 1036; sextuple, even if this is a categorization that 2010). In essence, if two atomic orbitals each only textbooks, and not nature, recognize containing a single electron can overlap, a — not least, because textbook concepts are bond is formed. Pauling generalized earlier what provide a discipline with intellectual work on the quantum description of hydro coherence and consistency. gen to write an approximate equation for Besides, how we talk about bonds can the wavefunction created by orbital overlap. determine our ability to rationalize real This became known as the valencebond chemical behaviour. For example, the differ (VB) description. ent descriptions of the bonds in what are now But an approximation is all it is. Around called nonclassical ions of hydrocarbons — the same time, Robert Mulliken and Frie whose relative merits were furiously debated drich Hund proposed another approximate in the 1950s and 1960s — have direct implica wavefunction, which led to an alternative way tions for the way these species are predicted to formulate bonds: not as overlaps between to react. Whether to consider the bonding specific orbitals on separate atoms, but as nonclassical, involving electrons spread over electron orbitals that extend over many atoms, more than two atomic nuclei, or tautomeric, called molecular orbitals (MOs). The relative involving rapid fluctuations between con merits of the VB and MO descriptions were ventional twoatom bonds, had immediate debated furiously for several decades, with consequences for organic chemistry. no love lost between the protagonists: Mul definition in general excludes the weak van Perhaps one might seek a distinction liken’s muchrepeated maxim, “I believe the der Waals attraction that occurs between all between bonded and notbonded in terms of chemical bond is not so simple as some people atoms, occasionally — as in the association how the force between two atoms varies with seem to think”, was possibly a jibe at Pauling. of two oxygen molecules into the O4 cluster their separation? Yes, there is an exponential By the 1960s, for all Pauling’s salesmanship, — even this force can be strong enough to be falloff for a covalent bond such as that in MO theory was generally agreed to be more regarded as a chemical bond. H2, and a powerlaw decay for van der Waals convenient for most purposes. But the debate It’s no use, either, to suggest (as Coulson attraction. But the lack of any clear distinc is not over4, and Roald Hoffmann of Cornell did) that a bond exists whenever the com tion between these two extremes has been University in Ithaca, New York, insists that bined energy of the atoms is lower than that emphasized in the past two decades by the “discarding any one of the two theories under when they are separated by an infinite dis phenomenon of aurophilicity6, in which gold mines the intellectual heritage of chemistry”. tance. For this is essentially always the case, atoms that have only a few chemical groups Both options are imperfect, because they at least for electrically neutral atoms. Even attached to them in organometallic com insist on writing the electronic wavefunction two helium atoms experience mutual van pounds tend to aggregate, forming dimers

These advances in dynamical control of quantum states amount to nothing less than a new vision of chemistry. The static picture of molecules with specific shapes and bond strengths is replaced by one of a bag of atoms in motion, which can be moulded and coaxed into behaviours quite different from those of the equilibrium species. Such a vision does not demand that we abandon old ideas about chemical bonds, nor does it truly challenge the ability of quantum theory to describe atoms and their unions. It recommends that we view these bonds as degrees of attraction that wax and wane — or as cartoon representations of a molecule’s perpetual tour of its freeenergy landscape. At a meeting in 1970, Coulson asserted that the simple notion of a chemical bond had already become lost, and that “some thing bigger” was needed to replace it — a subject, he suggested, for another meet ing 50 years hence. That moment is almost and linear chains. The basic interaction in in that it will behave differently depending upon us. these aurophilic bonds between gold has the on how we perturb and interrogate it.” The Yet we needn’t fret that the ‘rules’ of bonding same origin as the van der Waals force: the trajectory of a chemical reaction must then are up for grabs — quite the reverse. Although electron clouds ‘feel’ each other’s movements, be considered not as a making and breaking there may be some parts of science fortunate so that random fluctuations of one induce of bonds but as an evolution of atoms on a enough to be exhaustively explained by a sin mirrorimage fluctuations of the other. But potentialenergy surface. This was always gle, comprehensive theory, this isn’t likely to that interaction is modified here by relativistic implicit in classical drawings of transition be a general attribute. We are typically faced effects: changes in electron energies resulting states as molecular groupings containing with several theories, some overlapping, some from their high speeds around gold’s highly dashed lines, a kind of ‘almost bond’ in the conflicting, some just different expressions charged, massive nuclei6,7. Aurophilic bonds process of breaking or forming. Now that pic of the same thing. Our choice of theoretical have therefore been described as a ‘super van ture is explicitly revealed as a mere caricature framework might be determined less by the der Waals’ interaction. Does that make them of a complicated dynamical process in space traditional criterion of consistency with exper true bonds? It’s chemically meaningful to treat and time. iment than by subjective reasons. According them that way (they’ll even serve for cement Underlying most of these discussions is an to Hoffmann, these preferences often have an ing new ‘designer’ molecular crystals8), but unspoken assumption that it is meaningful aesthetic component, depending on factors perhaps at the cost of relinquishing another to speak, if not of a ‘bond’ as an unchanging such as simplicity, utility for telling a story potential criterion for ‘real’ bonds. entity, then at least of an instantaneous bound about chemical behaviour, the social needs state for a particular of the community and whether a description Moving target “The biggest configuration of nuclei. is productive. Perhaps the biggest challenge to the challenge This assumes that the As Hoffmann says: “Any rigorous defi simple notion of a chemical bond is dynam to the simple electrons can adjust nition of a chemical bond is bound to be ics. Atomic motions make even a ‘simple’ notion of more or less instantly impoverishing.” His advice to “have fun with molecule complex; any movement of one a bond is to any change in the the fuzzy richness of the idea” is well worth nucleus demands that the entire electron dynamics.” nuclear positions: the heeding. ■ cloud adjusts. A jiggle of one group of nuclei Born–Oppenheimer can make it easier to cleave off another. approximation. Because electrons are so Philip Ball is a writer based in London. This complication never used to matter much lighter than nucleons, this assumption 1. Coulson, C. a. The Spirit of Applied Mathematics much in chemistry, because the movements is usually justified. But some clear break 20–21 (Clarendon Press, 1953). were too rapid to be observable, much less downs of the approximation are now well 2. J. Comput. Chem. special issue 28, 1–466 10 (2007). exploitable. Ultrashort pulsed lasers moved documented . They are best known in solid 3. Cortés-Guzmán, F. & bader, r. F. W. Coord. Chem. the goal posts. For example, energy can be state systems, and in fact superconductivity Rev. 249, 633 (2005). pumped into a vibrational mode to weaken is one of the consequences, resulting from 4. hoffmann, r., shaik, s. & hiberty, P. C. Acc. Chem. Res. 36, 750–756 (2003). a specific bond, enabling selective molecular a coupling of electron and nuclear motions. 5. alvarez, s., hoffmann, r. & Mealli, C. Chem. Eur. J. 9 surgery . Chemists can ask about the chemi Such things may also happen in molecules, 15, 8358–8373 (2009). cal behaviour of a molecule at a particular particularly in the photochemistry of poly 6. Pyykkö, P. Chem. Soc. Rev. 37, 1967–1997 moment in its dynamical evolution. Even a atomic molecules, which have a large number (2008). 11 7. schmidbaur, h., Cronje, s., Djordjevic, b. & strong bond is weakened when a vibration of electronic states close in energy ; they have schuster, o. Chem. Phys. 311, 151–161 (2005). stretches it beyond its average, equilibrium also been observed for simple diatomic mole 8. Katz, M. J., sakai, K. & leznoff, D. b. Chem. Soc. 12 Rev. 37, 1884–1895 (2008). length, so in ultrafast chemistry it may no cules in strong electric fields . As a result, the 9. Crim, F. F. Science 249, 1387 (1990). longer be meaningful to characterize bonds molecular degrees of freedom may become 10. sukumar, n. Found. Chem. 11, 7–20 (2009). simply as strong or weak. As Fleming Crim interdependent in strange ways: rotation of 11. Worth, G. a. & Cederbaum, l. s. Ann. Rev. Phys. Chem. 55, 127–158 (2004). of the University of Wisconsin–Madison the molecule, for example, can excite vibra 12. sindelka, M., Moiseyev, n. & Cederbaum, l. puts it: “A bond is an entity described by tion. In such situations, the very notion of an s. preprint at www.arxiv.org/abs/1008.0741 quantum mechanics but not a fixed ‘entity’ electronic state begins to crumble10. (2010).