NATURE CHEMISTRY | VOL 1 | APRIL 2009 | www.nature.com/naturechemistry 17

thesis

Teetering towards chaos and complexityThe closest that most chemists get to the concepts of nonlinearity and emergent properties is a passing acquaintance with a well-known oscillating reaction. Bruce C. Gibb suggests that looking a little deeper into chaos and complexity could help us to answer some very important questions.

Lets start with a short quiz. Defi ne the following terms: (a) Phase diagram. (b) Phase space. (c) Bifurcated hydrogen bond. (d) Pitchfork bifurcation. (e) Moderator. (f) Brusselator. Even without looking at the answers (see end), I expect that those to (a), (c) and (e) tripped off the tongue. But how did you do in the others? If you managed to rattle off these answers as well, then the chances are that youre a physical chemist. Furthermore, youre quite likely to be one of those relatively rare breeds of chemist who dabbles in chaos and complexity1,2. So what have chaos and complexity to do with mainstream chemistry? And if you didnt do so well in the quiz, should you be concerned? Th e answers to these questions are, respectively, relatively little and probably yes the latter because, like it or not, the relatively small role that chaos and complexity have played in chemistry is likely to grow.

Chaos theory has been popularized by the notion that a butterfl y in geographical location X [add your favourite idyllic locale] can, by fl apping its wings, trigger a catastrophic weather event in geographical location Y [pick somewhere far from X that routinely gets in the news for such events]. Th e term itself is a bit of a misnomer. It is not the study of true chaos, but the study of the area between order and disorder

where unanticipated patterns, oscillations, self-similarities and long-range correlations are observed; there is underlying order in the apparently random system. Chaotic systems are dynamic, far from equilibrium, deterministic, yet hard to predict. Th ey are inherently nonlinear. Complexity subsumes chaos; as one of its alternative names high-dimensional chaos suggests. It is a synergistic sum of countless chaotic and non-chaotic systems perplexingly intertwined. Th e end result? Emergence;

properties and phenomena that only arise through synergism. In short, life.

Now we all know a good deal about life, but as chemists weve been a bit neglectful of chaos, complexity and emergence. Most of us have either ignored it or been happy with a viewpoint analogous to Associate Justice of the US Supreme Court Potter Stewarts view of hard-core pornography: defi ning it is diffi cult, but we know it when we see it. Speaking of seeing it, the most famous example of chaos in chemistry is the beautiful BelousovZhabotinsky (BZ) reaction3,4. When conducted in solution, this chemical clock displays rhythmic oscillations between two diff erent colours, whereas in two dimensions a thin fi lm of reagent leads to chemical turbulence and wave propagation (pictured). Photographs do not do this reaction justice, but internet sites such as YouTube do provide some spectacular examples (for example, see http://tinyurl.com/dj3cpc). Buttressed by the BZ and other reactions3, the notion of chaos and complexity in chemistry has taken a fi rm hold in physical chemistry5, but several factors have slowed its progress through the rest of the fi eld. One factor is where chaos and complexity came from.

Th e birth of chaos theory is generally attributed to meteorologist Edward Lorenz and his experiments involving an in silico Earth and its rudimentary weather system.6 He would set his global weather running by inputting parameters into a series of equations and watch it unfold. One day, however, he decided to repeat a run and started at the halfway point of the previous simulation. He diligently took the printout from the midpoint, re-entered the numbers and began the simulation again. Quickly, however, the weather began to diverge from the fi rst run, and before long his replay of weather was not a replay; it was completely

diff erent. Th e cause? Th e printout from the midpoint had been to three decimal points, but his equations describing his world worked to six decimal points. Th ose minute changes, that butterfl y fl apping its wings, had changed everything.

I digress. Th e point is that Lorenz was a meteorologist formally trained as a mathematician, and it was at the

boundary between physics and mathematics that the fi eld

grew. Subsequently, it quickly moved into the

biological realm when it was realized that the mathematics of chaos theory could be used to explain population changes. All this was occurring some way from mainstream

chemistry, a fact that has undoubtedly held

back our embracing of chaos. Another possible

factor, one a bit closer to home, is the fact that were well

chemists. Lets face it, we tend to be a bit reductionist in outlook. We want to be able to predict and control. How many of us have gone into the lab and pointed out to a researcher that we cannot conclude what is behind the change he or she observed between two experiments because two variables were changed? Two! Our training, then, is perhaps not ideally suited to embracing chaos and complexity.

So as chemists we arguably fi nd ourselves behind the curve relative to other scientists: the mathematicians, the physicists, the biologists and the biochemists, the anthropologists and the economists (to name just a few). Which is a shame, because it almost seems to be [WARNING: strange phrase for essay in chemistry] our destiny. When Friedrich Whler demonstrated that reaction between the inanimate (inorganic) materials silver isocyanate and ammonium chloride gave the animate (organic) urea, he not only hammered the fi rst nail in the coffi n of vitalism, he also set us on the path to

We all know a good deal about life, but as chemists weve been a bit neglectful of chaos, complexity and emergence.

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18 NATURE CHEMISTRY | VOL 1 | APRIL 2009 | www.nature.com/naturechemistry

thesis

being able to understand the tangibles of life, build wholly artifi cial ones, and ultimately merge the two together. For nearly 200 years now weve slowly narrowed the gap between the animate and inanimate.

By craft and imagination, synthetic chemists have synthesized increasingly complicated molecules and materials, both natural and non-natural, while analytical and physical chemists have built increasingly sophisticated instrumentation and used increasingly powerful computers to study these substances, their properties, and the complex world around us. Th is is a very reasonable foundation for embracing complexity, but how do we go about doing this? How do we take chemistry to the next level? Th ese are diffi cult questions.

Th e good news is that although were not whole-heartedly embracing the complexity being waved in front of our eyes by the nonlinear chemical dynamicists, as the

central science, chemistry is perfectly positioned for rapid infusion. Th is is of course happening, most recently via the biochemical realm under the banner chemical biology. At the same time, systems chemistry, the study of chemical networks, is becoming more prominent (although it is worth adding that a system need not be complex and demonstrate emergence, it can just be complicated). Th at said, there is still much to do.

Although we can synthesize molecules that with a bit of imagination resemble everyday objects, such as the molecular [add favourite macroscale object here], this is quite diff erent from building a molecular action.7 So, you can build a pair of molecular tennis rackets and a molecular tennis ball but can you use them to build a molecular tennis rally? Switching to a top-down perspective, do we understand the chemistry of the human brain? Have we translated the Gaia hypothesis the view that the Earth is a single organism into

chemistry? To all these questions we are forced to stare at our feet and respond, No. But by embracing chaos and complexity, chemists should be able to move towards these goals. Aft er all, who is better placed to explain lifes tangibles from the bottom up?

Bruce C. Gibb is in the Department of Chemistry at the University of New Orleans, New Orleans, Louisiana 70148, USA.e-mail: bgibb@uno.edu

References1. Bar-Yam, Y. Dynamics of Complex Systems (Westview, 1997).2. Gleik, J. Chaos: Making a New Science (Penguin, 2008).3. Epstein, I. R. & Showalter, K. J. Phys. Chem. 100,

1313213147 (1996).4. Zaikin, A. N. & Zhabotinsky, A. M. Nature 225, 535537 (1970).5. Nicolis, G. & Prigogine, I. Exploring Complexity (Freeman, 1989).6. Lorenz, E. J. Atmos. Sci. 20, 130141 (1963).7. Kay, E. R., Leigh, D. A. & Zerbetto, F. Angew. Chem. Int. Ed.

46, 72191 (2007).8. Scott, S. K. Oscillations, Waves, and Chaos in Chemical Kinetics 44

(Oxford Univ. Press, 1994).

(a) Most commonly, a pressuretemperature plot revealing under what conditions a substance exists in its solid, liquid or vapour phase. (b) A means to visualize the evolution of a

system in which each point plotted in space corresponds to a unique state of the system. (c) A three-centred hydrogen bond in which two hydrogen bond donors (or acceptors) form

attractive non-covalent interactions with a hydrogen bond acceptor (or donor). (d) A phenomenon associated with a system whereby variation of a control parameter switches the

system from a singular, stable, state (or thermodynamic branch) to a regime in which two stable states exist. (e) A material that slows down a process, for example, neutrons as they

pass between fuel rods. (f) A kinetic model for a chemical system involving two coupled intermediates and one autocatalytic step (A B; B + C D + E; 2B + D 3B; B F).

Answers to the quiz

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