the structures of only 4,000 are known (in 2005) and we cannot predict structures for the others, because we do not sufficiently understand the nature of the chemical bond. This study was not successful, in part because the calculation time required for intermetallic compounds was out of reach in the 1960s, but intermediate goals involving boron bonding were achieved, sufficient to be awarded a Nobel Prize. The three-center two-electron bond is illustrated in diborane (diagrams at right). In an ordinary covalent bond a pair of electrons bonds two atoms together, one at either end of the bond, the diboare B-H bonds for example at the left and right in the illustrations. In three-center two-electron bond a pair of electrons bonds three atoms (a boron atom at either end and a hydrogen atom in the middle), the diborane B-H-B bonds for example at the top and bottom of the illustrations. Lipscomb's group did not propose or discover the three-center two-electron bond, nor did they develop formulas that give the proposed mechanism. In 1943, Longuet-Higgins, while still an undergraduate at Oxford, was the first to explain the structure and bonding of the boron hydrides. The paper reporting the work, written with his tutor R. P. Bell, also reviews the history of the subject beginning with the work of Dilthey. Shortly after, in 1947 and 1948, experimental spectroscopic work was performed by Price that confirmed Longuet-Higgins' structure for diborane. The structure was re-confirmed by electron diffraction measurement in 1951 by K. Hedberg and V. Schomaker, with the confirmation of the structure shown in the schemes on this page. Lipscomb and his graduate students further determined the molecular structure of boranes (compounds of boron and hydrogen) using X-ray crystallography in the 1950s and developed theories to explain their bonds. Later he applied the same methods to related problems, including the structure of carboranes (compounds of carbon, boron, and hydrogen). Longuet-Higgins and Roberts discussed the electronic structure of an icosahedron of boron atoms and of the borides MB6. The mechanism of the three-center two-electron bond was also discussed in a later paper by Longuet-Higgins, and an essentially equivalent mechanism was proposed by Eberhardt, Crawford, and Lipscomb. Lipscomb's group also achieved an understanding of it through electron orbital calculations using formulas by Edmiston and Ruedenberg and by Boys. The Eberhardt, Crawford, and Lipscomb paper discussed above also devised the "styx number" method to catalog certain kinds