What is your favorite deep, elegant or beautiful explanation (in chemistry)?

Over at Edge, they have a survey asking leading scientists, thinkers and writers about what they think is their favorite "elegant, deep or beautiful explanation". This is meant to be a very general question, not even limited to science and includes responses from people as diverse as the economist Richard Thaler, complexity theorist Stuart Kauffman and Stewart Brand (founder of the Whole Earth Catalog). The answers include ideas, explanations, experiments and entities as general and diverse as the scientific method, genes, Pascal's wager, bounded rationality, relativity and the limits of intuition.

The explanations run across the gamut of the sciences and the humanities including physics, biology, economics, neuroscience, politics and business. But conspicuously absent is chemistry, except for a few peripheral references like Charles Simonyi's listing of Besicovitch's theory of atomic forces. And this is in spite of our friend Derek Lowe of "In the Pipeline" being included in this august list. I was gratified to see a chemist being asked for his opinion, and was somewhat disappointed that Derek's favorite explanation was not chemical (his favorite is the rather deceptively simple notion of "freefall"). I of course don't blame Derek for his choice since there is no law dictating that a chemist's favorite explanation should be from chemistry just because he or she is a chemist. My own favorite beautiful explanation is probably Cantor's notion of multiple infinities.

But I did regret the striking omission of chemistry from the list. Sometime back I had a whole post on elegance in chemistry. And I certainly don't want people to think that deep and elegant explanations are limited to physics and biology, because they are not. Chemistry may not boast of profound philosophical explanatory frameworks like the Big Bang or evolution by natural selection. But it makes up for this fact by creating paradigms that directly touch the lives of millions of human beings in ways much more palpable than the Big Bang and evolution. So I thought I would add my own modest thoughts on my favorite deep idea in chemistry.

There's actually a few things at the top of my list; you certainly don't have to think hard to come up with several foundational chemical ideas. But if you really asked for my absolute favorite deep and elegant explanation, it is the shared-electron chemical bond. That's it. Right there is the simple concept that is at the heart of the material world, a concept that if you think about it has had a staggering impact on our quality of life, our relationships with other nations, our notion of prosperity itself. Chemical bonds as manifested in the foundations of modern civilization have certainly contributed as much to life, liberty and the pursuit of happiness as any scientific idea.

The idea itself as formulated by the great Gilbert Newton Lewis and comprehensible to any high-school student is simplicity incarnated; atoms combine into molecules and form a bond when electrons are shared. Everything that comes after the stating of this fact, important as it is, is details. All the quantum chemical wizardry, the thinking-in-orbitals, the great Gaussian simplification, it's after this basic groundwork has been laid. Heitler and London, Pauling, Slater, Mulliken, Pople, all of them made critical contributions to chemical bonding, but they all stood on Lewis's shoulders and built up from his landscape of the shared electron chemical bond.

Given the absolutely foundational role that the chemical bond plays in the thinking of chemists, it may be both ironic and a tad disturbing that chemists still cannot completely agree on the precise definition of every molecular bond out there. But that's not because the basic framework underlying bonding is uncertain. Part of the reason is simply because there is no such thing as "the" chemical bond. The bonding zoo sports a bewildering variety of animals, from the upstanding "normal" chemical bonds in, say the hydrogen or methane molecules, to the (literally) ready-to-snap pressure cooker entities in strained organic compounds, from the wily, shape-shifting bonds between metals and organic compounds to the ephemeral but biologically vital hydrogen bonds. Although the basic theory of the chemical bond is securely in place, it's going to take some time to craft a net wide and yet rigorous enough to snare the unruly and colorful creatures dotting the chemical landscape.

Now physicists may try to appropriate the chemical bond as their own, but they are out of luck. No explanation based purely on physics can truly impart a feel for the sheer diversity of bonds quoted above and their context-specific personalities. Just one bond serves to create a nightmare for purely reductionist approaches to defining chemical bonding- the hydrogen bond. Last year chemists convened at a meeting with the express purpose of tweaking their description of this all-important biological mediator, the glue that holds life together. Several questions were bandied about, but none more important than the very definition of a hydrogen bond. The problem was simple; hydrogen bonds can be weak or strong, sometimes so weak as to strain the definition of a bond, sometimes strong enough to suspiciously qualify as a covalent bond. How much of hydrogen bonding is electrostatic and how much is covalent? Is "bond" even the right term, or would "bridge" be more accurate? How do you define hydrogen bonds to metals? A consensus was finally reached on a new definition, but not even Linus Pauling could say that the definition would hold for all of eternity. Defining a hydrogen bond would give every physicist out there a run for his money. I find the concept of the chemical bond so enticing and elegant partly because even a single kind of bond like the hydrogen bond can hide a richly textured world of possibilities lurking behind its surface.

So there it is, why the concept of the chemical bond is my favorite idea, certainly in chemistry. It is deep because it underlies the making of the material universe, explaining the stuff that everything from crab shells to the Crab Nebula is made of. It is elegant because of the virtually unlimited amount of explanatory power that it hides in a simple statement of definition. And it is beautiful because of the sheer diversity of materials and structures that are created from a simple law of attraction. A lot of the thinkers in the Edge survey quoted evolution as their favorite deep idea. It certainly is beautiful. But Darwin could well have slightly paraphrased his words to apply to Lewis's shared-electron chemical bond:

"There is grandeur in this view of the material world, with its several powers, having been originally breathed into a single bond; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a bond endless forms most beautiful and most wonderful have been, and are being, evolved."

What is 'elegance' in chemistry?

Physicists and mathematicians have their own notions of 'elegance'. These notions are often tied to mathematical beauty. Paul Dirac was famous for insisting that equations be beautiful. His own Dirac equation is a singular example of beauty; it can literally be written in half a line and yet completely explains the behavior of the electron, taking special relativity into account and predicting antimatter.

Chemistry is much more of an experimental science than physics, so does that mean that notions of elegance would be meaningless in chemistry? Not so at all, although chemists need their own definitions.

Organic synthesis, which is as close to architecture that a science can get, has defined elegance for a long time. Organic chemists will tell you that a complex synthesis is elegant when it can be accomplished in only a few steps, with maximum purity, yield and stereoselectivity, using the most benign reagents under the mildest of conditions. The Nobel laureate John Cornforth said it well: he defined the perfect synthesis as one which could be done by a one-armed operator by pouring down a mixture of chemicals down a drain and collecting the product in one hundred percent yield and stereoselectivity at the other end. Biomimetic reactions particularly lend themselves to definitions of elegance. In such reactions you can usually get a truly elegant cascade of bond formation and breaking that installs several stereochemical centers in one or a few steps. Robert Robinson's synthesis of atropine is a classic example. So is William Johnson's synthesis of progesterone through a stunning biomimetic cascade. I remember both these examples leaving me cold as an undergraduate.

Other kinds of chemists dealing with synthesis would have similar definitions of elegance. But in the age of supramolecular chemistry, elegance is being defined another way, through self-assembly. Traditional organic synthesis deals with the stepwise construction of complex molecules. In much of solid-state and structural chemistry though, simple building blocks self-assemble into some of the most complex chemical architectures and nanomaterials merely by mixing reagents together. A great example concerns the beautiful structures resulting from simply mixing sodium oxalate and calcium chloride under hydrothermal conditions. Solid-state and supramolecular chemists are harkening back to the old days of chemistry, when you got interesting results just by combining simple chemicals together in different proportions.

Whereas an organic chemist would define elegance in the context of yield, stereoselectivity and mild conditions, that definition would not be of much use to a biochemist studying enzymes, since it's child's play for virtually all enzymes to accomplish this goal every single moment of their existence. Carbonic anhydrase, nitrogenase and peroxidase are only three examples of enzymes that nonchalantly go about their business at room temperature with a devastating efficiency that would put an organic chemist to shame. For biochemists, this kind of elegance is passé. Or it's an everyday miracle, depending on how you look at it. For biochemists, signal transduction cascades in which the binding of a single molecule causes a shower of precise protein-binding events involving dozens of biomolecules that usually culminates in genetic expression must seem like a true miracle. The binding of adrenaline to the beta-adrenergic receptor and the ensuing perfectly choreographed symphony of biomolecular music must surely seem elegant.

In other areas of chemistry elegance may be trickier to define. In theoretical chemistry you can use quantum mechanics to describe a chemical system. Given a relatively simple system, it's possible to describe it extremely accurately using high-level basis sets and theory. You can get answers accurate to a dozen decimal places using such techniques. Indeed, in principle, quantum mechanics can describe all of chemistry.

Is it elegant? A first thought may be that it is, since you are using the most fundamental theory available in nature for achieving an unprecedented degree of accuracy. But consider that you can usually get the same result accurate to a lesser number of decimal places (but still quite accurately) using a judiciously parametrized force field. A force field is simply a set of terms describing bond stretching, bending, torsional angles and Van der Waals and electrostatic forces, thrown in with a set of parameters drawn usually from experiment. Given a choice between reams of complex math and days of computer time, and minutes of computer time and a bleedingly simple molecular mechanics equation that you can write on the back of a cocktail napkin (try this out on a girl or boy the next time you are at a party; they will be very impressed), which one would you say is more elegant? Granted, the latter is parametrized with experimental measurements and is not as accurate as the former, but it's still good enough. More importantly, if simplicity is one of the important hallmarks of elegance, then the latter approach is surely more elegant, isn't it?

Ultimately, what matters so much is not elegance but the ability to discover new things. The one thing that sets chemistry apart is its ability to make new stuff that did not exist before. If chemists can find techniques that accomplish this goal more efficiently, they can be forgiven for not thinking too much about elegance.

After all, it was a famous physicist himself who once said, "Matters of elegance should be left to the cobbler and tailor...".