But is it art? Representing structure in chemistry

National Forum, Summer 2001 by Berger, Daniel

An online companion to this column, which includes three-dimensional structures discussed below, may be found at http://cs.bluffton.edu/~berger/nf/.

Anyone who has paged through a book on chemistry has seen some representation of a chemical compound. The compound may be simple or complex, but the representation has to satisfy certain requirements: the trained eye must be able to discern both structure and function, yet the picture must be quickly reproducible by an artistic tyro. Chemistry is a profoundly visual discipline. To do chemistry on anything more than an elementary level, you have to deal with objects in three dimensions, usually via representations in two. Chemists often think in such representations, and creative chemists use them to build mental structures as elegant and rich as a Tolstoy novel.

Chemical representation is not abstract art; it is intended to represent something visual. It has as much kinship with the diagrams in your VCR manual as it does with a seventeenth century pastorale or the eleventh century Bayeaux "tapestry." But what is it that is represented? And how is it done?

What's more, Figure la assigns apparently equal importance to every atom; chemically we do not want that. Carbon-hydrogen units are chemically inert, and we want to call attention to the points at which chemistry is most likely to happen -- just as ancient Egyptian or medieval European artists made the most important people in a painting larger than surrounding objects -- without losing sight of the carbon and hydrogen scaffolding on which the molecule is built. And why write a symbol for every carbon and hydrogen atom?

What is normally done is to leave out carbon and hydrogen atoms entirely! Only the bonds between carbon atoms are shown; a carbon is assumed at each vertex. This shorthand takes advantage of the fact that, almost without exception, carbon forms four bonds: no more, no less. "Missing" bonds are assumed to be to hydrogen atoms; compare Figure 1c with Figure la. "Heteroatoms" -- atoms other than carbon and hydrogen -- are shown explicitly, as are the hydrogens attached to heteroatoms. This is appropriate; it is at or near heteroatoms and their attendant hydrogens that organic chemistry largely takes place. Such schematic drawings greatly simplify the task of chemists, who may have to draw complex structures at a moment's notice, in an informal discussion or during a formal talk.

But other structural features must be represented. All molecules with more than three atoms have the possibility of three dimensions: the geometry of carbon, with its four bonds, was proved to be tetrahedral more than a century ago. Organic molecules can be and often are represented by flat structures, but they exist in space. We could draw a fully proportional model, with highlights and shadows and the other appurtenances of artistic perspective, but that would make chemical structures inaccessible for any but trained artists. Instead, a simpler system is used. For each carbon atom, two bonds are treated as being in the "plane of the paper" while the other two are in front of and behind that plane; such bonds are represented by thickened and dashed lines respectively.

2-Methylcyclopentanol contains a ring of carbon atoms, and atoms bonded to the ring can be either above or below the plane of the ring. This means that the methyl and alcohol groups can be on the same face of the ring (cis) or on opposite faces (trans). The two arrangements are shown in a typical fashion in Figure 2; the spatially gifted reader will notice that there are two possible cis and two possible trans arrangements, all four of which give different structures. Such diagrams not only give a lot of structural information, but also are easy to draw, even for an artistic incompetent.

The anticancer compound taxol presents a more interesting case. Its three-dimensional structure is almost impossible to represent using just a single perspective view (Figure 3), even if we take the common route of showing only the framework of the molecule, with no explicit atoms at all. Instead, the schematic drawing of taxol (Figure 4a) is a cubist portrait, bringing hidden parts of the molecule to the fore and showing several points of view simultaneously. Each carbon atom's local geometry is drawn with little reference to the configurations of neighboring atoms. Less important substructures may even be represented by abbreviations, as in Figure 4b. The drawing of taxol allows the trained eye to instantly understand the three-dimensional environment of each atom in the molecule, while not obscuring any part of the structure by allowing it to hide behind another part. In this way all the important structural information is given at once, simply, in a way that allows easy construction of a more "correct" three-dimensional model while emphasizing the points at which chemistry is most likely to occur.

The essential feature of a chemical drawing is the ability to represent three-dimensional structure in a few seconds, without extensive artistic training. Most chemists think in these types of pictures -- and their thinking is constrained by them. But such constraints are no more onerous than the constraints imposed on the poet by language, on the painter by pigments and brushes, or on the sculptor by a piece of stone and a chisel. As long as we can think of things that do not exist -- or things that might exist someday -- we cannot say that we have reached the limits of representation.