orbitals to make three equivalent orbitals (called sp hybrid orbitals), with the remaining 2p orbital unhybridized, which would be the appropriate orbitals to describe certain unsaturated carbon compounds such as ethylene. Other hybridization schemes are also found in other types of molecules. Another area which he explored was the relationship between ionic bonding, where electrons are transferred between atoms, and covalent bonding, where electrons are shared between atoms on an equal basis. Pauling showed that these were merely extremes, and that for most actual cases of bonding, the quantum-mechanical wave function for a polar molecule AB is a combination of wave functions for covalent and ionic molecules. Here Pauling's electronegativity concept is particularly useful; the electronegativity difference between a pair of atoms will be the surest predictor of the degree of ionicity of the bond. The third of the topics that Pauling attacked under the overall heading of "the nature of the chemical bond" was the accounting of the structure of aromatic hydrocarbons, particularly the prototype, benzene. The best description of benzene had been made by the German chemist Friedrich Kekulé. He had treated it as a rapid interconversion between two structures, each with alternating single and double bonds, but with the double bonds of one structure in the locations where the single bonds were in the other. Pauling showed that a proper description based on quantum mechanics was an intermediate structure which was a blend of each. The structure was a superposition of structures rather than a rapid interconversion between them. The name "resonance" was later applied to this phenomenon. In a sense, this phenomenon resembles those of hybridization and also polar bonding, both described above, because all three phenomena involve combining more than one electronic structure to achieve an intermediate result. Ionic crystal structures In 1929, Pauling published five rules which help to predict and explain crystal structures of ionic compounds. These rules concern (1) the ratio of cation radius to anion radius, (2) the electrostatic bond strength, (3) the sharing of polyhedron corners, edges and faces, (4) crystals containing different cations, and (5) the rule of parsimony. Biological molecules In the mid-1930s, Pauling, strongly influenced by the biologically oriented funding priorities of the Rockefeller Foundation's Warren Weaver, decided to strike out into new areas of interest. Although Pauling's early interest had focused almost exclusively on inorganic molecular structures, he had occasionally thought about molecules of biological importance,