8/13/2019 Ball - Beyond the Bond (Nature 2011)

1/3

Not so long ago, the chemistry stu-dents standard text on the theory ofchemical bonding was Charles Coul-

sonsValence(1952). Absent from it was thistheoretical chemists real view on the sticksthat generations of students have drawn tolink atoms into molecules. A chemical bondis not a real thing: it does not exist: no one hasever seen it, no one ever can. It is a figment ofour own imagination, he later wrote1.

There is a good reason for postponing thisawkward truth. The bond is literally the gluethat makes the entire discipline cohere; toconsider it an objective reality is necessaryfor any kind of discourse on chemistry. Thediscipline is in fact riddled with such conven-ient (and contested) fictions, such as electro-negativity, oxidation state, tautomerismand acidity.

Disputes about the correct descriptionof bonding have ruffled chemists featherssince the concept of molecular structurefirst emerged in the mid-nineteenth century.Now they are proliferating, as new theoreti-

cal and experimental techniques present

fresh ways to probe and quantify chemi-cal bonds2. Traditional measures such ascrystallographic interatomic distances anddissociation energies have been supple-mented by spectroscopic techniques fordetermining vibrational frequencies, meth-ods such as nuclear magnetic resonance tomeasure shifts in the electronic environmentof atoms and their magnetic interactions,measurements of force constants (bond

stiffness) and a host of quantum-chemicaltools for calculating such aspects as electrondistributions or localization.

An indication of the shifting ground is therecent decision to redefine the nature of thehydrogen bond in the light of experimentalresults that alter the traditional electrostaticdescription.

The nature of the chemical bond is nowfurther complicated by the introduction of

the dynamical dimension. Molecules havetraditionally been regarded, if not as static,then as having clear architectural frame-works that are merely shaken and rotated bythermal motions. The bonds get stretchedand bent, but they still have an equilibriumlength and strength that seems to justifytheir being pictured as lines and stalks. Now,thanks to ultrafast spectroscopies, such time-average values may not always accurately

characterize either structure or reactivity.What is measured in a bond depends not juston how but on when it is measured.

Some chemists argue that as a result of this,the very existence (or not) of a bond dependson how the problem is probed. Others arecommitted to absolute criteria. This differ-ence of opinion goes to the heart of whatchemistry is about: can all be reduced toquantum physics, or are fuzzy rules of thumbessential? More pressingly, the issue of howbest to describe a chemical bonding patternhas tangible implications for a wide rangeof problems in chemistry, from molecules

in which atoms are coerced out of their

Beyond the bondMore 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.

20: YEAR OF CHEMISTRYCelebrating the central sciencenature.com/chemistry20

ILLUSTRATIONS

BY

ROZCHAST

2 6 | N A T U R E | V O L 4 6 9 | 6 J A N U A R Y 2 0 1 1

COMMENT

2011 Macmillan Publishers Limited. All rights reserved

8/13/2019 Ball - Beyond the Bond (Nature 2011)

2/3

usual bonding geometry to the symmetrichydrogen bond (in which a bound hydrogenatom is shared equally between two otheratoms), and new variations on old themessuch as aromaticity (special patterns of delo-calized bonds, like those in benzene)3.

Just about every area of chemistry har-bours its own bonding conundrums. Most

illustrate that we have a far from exhaustiveunderstanding of the ways in which quan-tum rules will permit atoms to unite andthat in consequence, the synthetic inventive-ness of chemists suffers from a limited viewof the possibilities.

CARVING UP ELECTRONS

We can all agree on one thing: chemicalbonding has something to do with elec-trons. Two atoms stick together becauseof the arrangement of electrons aroundtheir nuclei. In the nineteenth century, itwas commonly thought that this attraction

was electrostatic: that atoms in moleculesare positively or negatively ionized. Thatleft the puzzle of how identical atoms canform diatomic molecules such as H2and O2.American chemist G. N. Lewis proposed thatbonding can instead result from the sharingof electrons to create filled shells of eight,visualized as the corners of a cube.

In the 1920s and 1930s another Ameri-can chemist, Linus Pauling, showed howthis interaction could be formulated in thelanguage of quantum mechanics as the over-lap of electron orbitals (see Nature468,1036;2010). In essence, if two atomic orbitals eachcontaining a single electron can overlap, abond is formed. Pauling generalized earlierwork on the quantum description of hydro-gen to write an approximate equation forthe wavefunction created by orbital overlap.This became known as the valence-bond(VB) description.

But an approximation is all it is. Aroundthe same time, Robert Mulliken and Frie-drich Hund proposed another approximatewavefunction, which led to an alternative wayto formulate bonds: not as overlaps betweenspecific orbitals on separate atoms, but aselectron orbitals that extend over many atoms,called molecular orbitals (MOs). The relative

merits of the VB and MO descriptions weredebated furiously for several decades, withno love lost between the protagonists: Mul-likens much-repeated maxim, I believe thechemical bond is not so simple as some peopleseem to think, was possibly a jibe at Pauling.By the 1960s, for all Paulings salesmanship,MO theory was generally agreed to be moreconvenient for most purposes. But the debateis not over4, and Roald Hoffmann of CornellUniversity in Ithaca, New York, insists thatdiscarding any one of the two theories under-mines the intellectual heritage of chemistry.

Both options are imperfect, because they

insist on writing the electronic wavefunction

as some combination of the wavefunctionsof individual electrons. Thats also the basisof the HartreeFock method for calculatingthe wavefunction and energy of the lowest-energy state (ground state) of a molecularsystem a method that became practicalin the 1950s, when computers made it pos-sible to solve the equations numerically.

But separating the wavefunction into one-electron components is a fiction, as theyall influence one another: the behaviour ofone electron depends on what all the oth-ers are doing. The difference between trueground-state energy and that calculatedusing the HartreeFock approach is calledthe correlation energy. More recent com-putational methods can capture most ofthe correlation energy, but none can givean exact solution. As a result, describingthe quantum chemical bond remains a mat-ter of taste: all descriptions are, in effect,approximate ways of carving up the electron

distribution.If that were the limit of the bondsambiguity, there would be little to argueabout. It is not. There is, for example, thematter of when to regard two atoms as beingbonded at all. Paulings somewhat tautologi-cal definition rather gave the game away: agroup of atoms is to be considered bondedwhen it is convenient for the chemist toconsider it as an independent molecular spe-cies. Pauling admitted some of the conse-quent ambiguities: for example, although his

definition in general excludes the weak vander Waals attraction that occurs between allatoms, occasionally as in the associationof two oxygen molecules into the O4cluster even this force can be strong enough to beregarded as a chemical bond.

Its no use, either, to suggest (as Coulsondid) that a bond exists whenever the com-bined energy of the atoms is lower than thatwhen they are separated by an infinite dis-tance. For this is essentially always the case ,at least for electrically neutral atoms. Even

two helium atoms experience mutual van

der Waals attraction, which is why heliumis a liquid at very low temperatures; but theyare not generally thought to be chemicallybonded as a result.

Besides, the bonded or not questionbecomes context-dependent once atomsare embedded in a molecule, where theymay be forced close together merely by

the atoms around them, and where thereis inevitably some arbitrariness in decid-ing which electronsbelong to whichatoms. The result-ing ambiguities wereillustrated recentlywhen three expertsfailed to agree aboutwhether two sulphuratoms in an organo-

metallic compound are linked by a bond5.The argument involved different interpre-tations of quantum-chemistry calculations,

tussles over the best criteria for identifyinga bond, and evidence of precedent fromcomparable compounds.

All this is merely a reminder that amol-ecule is ultimately a set of nuclei embeddedin a continuous electron cloud that stabilizesa particular configuration, which balls andsticks can sometimes idealize and some-times not. But disputes about the nature ofthe chemical bond are not simply semantic.It matters, for example, whether we regarda very strong multiple bond as quintuple orsextuple, even if this is a categorization thatonly textbooks, and not nature, recognize not least, because textbook concepts arewhat provide a discipline with intellectualcoherence and consistency.

Besides, how we talk about bonds candetermine our ability to rationalize realchemical behaviour. For example, the differ-ent descriptions of the bonds in what are nowcalled non-classical ions of hydrocarbons whose relative merits were furiously debatedin the 1950s and 1960s have direct implica-tions for the way these species are predictedto react. Whether to consider the bondingnon-classical, involving electrons spread overmore than two atomic nuclei, or tautomeric,involving rapid fluctuations between con-

ventional two-atom bonds, had immediateconsequences for organic chemistry.

Perhaps one might seek a distinctionbetween bonded and not-bonded in terms ofhow the force between two atoms varies withtheir separation? Yes, there is an exponentialfall-off for a covalent bond such as that inH2, and a power-law decay for van der Waalsattraction. But the lack of any clear distinc-tion between these two extremes has beenemphasized in the past two decades by thephenomenon of aurophilicity6, in which goldatoms that have only a few chemical groupsattached to them in organometallic com-

pounds tend to aggregate, forming dimers

Chemistsinventivenesssuffers froma limitedview of thepossibilities.

6 J A N U A R Y 2 0 1 1 | V O L 4 6 9 | N A T U R E | 2 7

COMMENT

2011 Macmillan Publishers Limited. All rights reserved

8/13/2019 Ball - Beyond the Bond (Nature 2011)

3/3

and linear chains. The basic interaction inthese aurophilic bonds between gold has thesame origin as the van der Waals force: theelectron clouds feel each others movements,so that random fluctuations of one inducemirror-image fluctuations of the other. Butthat interaction is modified here by relativisticeffects: changes in electron energies resultingfrom their high speeds around golds highlycharged, massive nuclei6,7. Aurophilic bondshave therefore been described as a super vander Waals interaction. Does that make themtrue bonds? Its chemically meaningful to treatthem that way (theyll even serve for cement-ing new designer molecular crystals8), butperhaps at the cost of relinquishing anotherpotential criterion for real bonds.

MOVING TARGET

Perhaps the biggest challenge to thesimple notion of a chemical bond is dynam-ics. Atomic motions make even a simplemolecule complex; any movement of onenucleus demands that the entire electroncloud adjusts. A jiggle of one group of nucleican make it easier to cleave off another.

This complication never used to mattermuch in chemistry, because the movementswere too rapid to be observable, much less

exploitable. Ultrashort pulsed lasers movedthe goal posts. For example, energy can bepumped into a vibrational mode to weakena specific bond, enabling selective molecularsurgery9. Chemists can ask about the chemi-cal behaviour of a molecule at a particularmoment in its dynamical evolution. Even astrong bond is weakened when a vibrationstretches it beyond its average, equilibriumlength, so in ultrafast chemistry it may nolonger be meaningful to characterize bondssimply as strong or weak. As Fleming Crimof the University of WisconsinMadisonputs it: A bond is an entity described by

quantum mechanics but not a fixed entity

in that it will behave differently dependingon how we perturb and interrogate it. Thetrajectory of a chemical reaction must thenbe considered not as a making and breakingof bonds but as an evolution of atoms on apotential-energy surface. This was alwaysimplicit in classical drawings of transitionstates as molecular groupings containingdashed lines, a kind of almost bond in theprocess of breaking or forming. Now that pic-ture is explicitly revealed as a mere caricatureof a complicated dynamical process in spaceand time.

Underlying most of these discussions is anunspoken assumption that it is meaningfulto speak, if not of a bond as an unchangingentity, then at least of an instantaneous bound

state for a particularconfiguration of nuclei.This assumes that theelectrons can adjustmore or less instantlyto any change in thenuclear positions: theBornOppenheimer

approximation. Because electrons are somuch lighter than nucleons, this assumptionis usually justified. But some clear break-downs of the approximation are now well

documented10. They are best known in solid-state systems, and in fact superconductivityis one of the consequences, resulting froma coupling of electron and nuclear motions.Such things may also happen in molecules,particularly in the photochemistry of poly-atomic molecules, which have a large numberof electronic states close in energy11; they havealso been observed for simple diatomic mole-cules in strong electric fields12. As a result, themolecular degrees of freedom may becomeinterdependent in strange ways: rotation ofthe molecule, for example, can excite vibra-tion. In such situations, the very notion of an

electronic state begins to crumble10.

These advances in dynamical control ofquantum states amount to nothing less thana new vision of chemistry. The static pictureof molecules with specific shapes and bondstrengths is replaced by one of a bag of atomsin motion, which can be moulded and coaxedinto behaviours quite different from those ofthe equilibrium species. Such a vision does

not demand that we abandon old ideas aboutchemical bonds, nor does it truly challenge theability of quantum theory to describe atomsand their unions. It recommends that we viewthese bonds as degrees of attraction that waxand wane or as cartoon representations ofa molecules perpetual tour of its free-energylandscape.

At a meeting in 1970, Coulson assertedthat the simple notion of a chemical bondhad 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

upon us.Yet we neednt fret that the rules of bondingare up for grabs quite the reverse. Althoughthere may be some parts of science fortunateenough to be exhaustively explained by a sin-gle, comprehensive theory, this isnt likely tobe a general attribute. We are typically facedwith several theories, some overlapping, someconflicting, some just different expressionsof the same thing. Our choice of theoreticalframework might be determined less by thetraditional criterion of consistency with exper-iment than by subjective reasons. Accordingto Hoffmann, these preferences often have anaesthetic component, depending on factorssuch as simplicity, utility for telling a storyabout chemical behaviour, the social needsof the community and whether a descriptionis productive.

As Hoffmann says: Any rigorous defi-nition of a chemical bond is bound to beimpoverishing. His advice to have fun withthe fuzzy richness of the idea is well worthheeding.

Philip Ballis a writer based in London.

1. Coulson, C. A. The Spirit of Applied Mathematics2021 (Clarendon Press, 1953).

2. J. Comput. Chem.special issue 28,1466

(2007).3. Corts-Guzmn, F. & Bader, R. F. W. Coord. Chem.Rev.249,633 (2005).

4. Hoffmann, R., Shaik, S. & Hiberty, P. C.Acc. Chem.Res.36,750756 (2003).

5. Alvarez, S., Hoffmann, R. & Mealli, C.Chem. Eur. J.15,83588373 (2009).

6. Pyykk, P. Chem. Soc. Rev.37,19671997(2008).

7. Schmidbaur, H., Cronje, S., Djordjevic, B. &Schuster, O. Chem. Phys.311,151161 (2005).

8. Katz, M. J., Sakai, K. & Leznoff, D. B.Chem. Soc.Rev.37,18841895 (2008).

9. Crim, F. F.Science249,1387 (1990).10. Sukumar, N. Found. Chem.11,720 (2009).11. Worth, G. A. & Cederbaum, L. S.Ann. Rev. Phys.

Chem.55, 127158 (2004).12. Sindelka, M., Moiseyev, N. & Cederbaum, L.

S. preprint at www.arxiv.org/abs/1008.0741

(2010).

The biggestchallengeto the simplenotion ofa bond isdynamics.

2 8 | N A T U R E | V O L 4 6 9 | 6 J A N U A R Y 2 0 1 1

COMMENT

2011 Macmillan Publishers Limited. All rights reserved