Now, two researchers at Cornell University have made important theoretical discoveries that, similarly, have long eluded chemists: They have established the principles of crystal bonding of a group of thousands of compounds. But history repeats itself in that, thus far, nearly all of these unusual compounds have no industrial uses, although many have interesting electronic and magnetic properties.

"This is an important step in understanding the bonding in alloys and intermetallic compounds," says Roald Hoffmann, Cornell's Nobel laureate chemist who also serves as the Frank H.T. Rhodes Professor in Humane Letters.

Hoffmann, despite his seniority, was led in this pioneering work by his graduate student, Garegin Papoian, who came from Armenia to study under the Cornell scientist and now is a postdoctoral researcher at the University of Pennsylvania. The two chemists have laid out a theory that extends the understanding of bonding in an important class of alloys.

Hoffmann's and Papoian's "novel bonding scheme" was described in more than 40 pages in the July 17 issue of the authoritative journal of chemistry Angewandte Chemie, published by the German Chemical Society.

The two researchers began by looking at the bonding of compounds of antimony, tellurium, tin and selenium, all called "main group elements," below carbon, nitrogen and oxygen in the periodic table.

The compounds have names like europium and lithium antimonide and neodymiun distannide, and although they have been known for many decades, "experimentalists have said nothing about what holds these compounds together," says Hoffmann.

It was known that these compounds have in them curious structural motifs, quite uncommon in organic or other inorganic molecules. The compounds, in fact, blur the line between the different types of bonds that hold atoms together in a molecule or a crystal. In this case, the bonds are a melange of metallic bonds, covalent bonds -- created by the sharing of electrons -- and ionic bonds -- formed by the transfer of electrons.

These "isolated puzzles" are now explained by the two researchers in a formula that is based on "magic numbers." In physics and chemistry, magic numbers designate the sum of electrons in a molecule that leads to special stability.

In the Papoian-Hoffmann bonding formula, magic numbers refer to the electron counts that indicate whether a stable compound is linear or square: seven electrons per atom for a linear chain; six electrons per atom for a two-dimensional square lattice; and five electrons per atom for a simple cube lattice.

The crystal structures themselves can be seen in a series of computer-generated drawings -- not based on theory but on direct experimental work -- that have an interlocking, architectural perfection.

The molecular structures, ranging from simple geometries to complex lattices, reveal their bonding networks in a series of multidimensional building blocks.

"Some look terribly complicated," says Hoffmann, "but take them apart and you can see square lattices with atoms above and below, and squares forming octahedrons -- fantastic structures with a certain 'Star Wars' quality."

But how can such structures reveal themselves sometimes as compounds of antimony and other times as tellurium or tin? "Because it's the number of electrons that determines the chemistry, less so the identity of the nucleus underneath," Hoffmann explains.

"What we have here is theory at its best -- qualitative theory, building connections between different parts of the chemical universe, even though to outsiders these units appear not to be close to each other," Hoffmann comments.

"I pride myself on seeing connections, which is what I also try to build between science and humanities. Anything I can do to connect diverse things feels worth doing."

Papoian's and Hoffmann's paper in Angewandte Chemie is titled "Hypervalent Bonding in One, Two and Three Dimensions: Extending the Zintl-Klemm Concept to Nonclassical Electron-Rich Networks."

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Huntsville - June 1, 2000
Research contributing to better materials on Earth and seeking resources in space to fuel future exploration will be featured at NASA's Microgravity Materials Science Conference in the North Hall of the Von Braun Center in Huntsville, Ala., June 6-8.

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