Robert Mulliken was one of the few researchers who, like Pauling, knew both physics and chemistry. Mulliken, the son of an MIT chemist, roomed next to Slater while on a fellowship at Harvard and, also like Pauling, made a pilgrimage to Europe in the late 1920s to learn quantum mechanics.

At Göttingen, Mulliken had come under the influence of one of Born's assistants, Friedrich Hund, who was thinking through an approach to the chemical bond different from Pauling's. Hund was interested in molecular spectroscopy, the study of the characteristic light absorbed and emitted by molecules, and he found that viewed this way, molecules behaved in important ways like individual atoms. Hund and Mulliken came up with a concept of the chemical bond that seemed radically different from Pauling's. Instead of electrons concentrating between two nuclei to bind atoms together, Hund and Mulliken theorized that binding electrons were spread around the molecule's surface, forming what Mulliken would call molecular orbitals. They conceived of the hydrogen molecule, H₂, for instance, not as two hydrogen atoms approaching each other and forming a bond by pairing their electrons, as Heitler and London had proposed, but as a two-electron helium atom splitting into two nuclei with its surrounding electron cloud reshaping into a new molecular orbital.

"In general no attempt is made to treat the molecule as consisting of atoms or ions," Mulliken wrote in 1932. "Attempts to regard a molecule as consisting of specific atoms or ionic units held together by discrete numbers of bonding electrons or electron pairs are considered as more or less meaningless." This was radical thinking; the molecular-orbital concept seemed diametrically opposed to everything chemists had thought about the nature of the chemical bond for decades. It did, however, fit the spectroscopic data, and Mulliken stuck with his ideas after returning to the United States to teach at the University of Chicago.