In 1931 American chemist and biochemist Linus Pauling at Caltech presented six rules for the shared electron bond:
"The first three, restatements of Lewis's, Heitler's, and London's, and his own earlier work, noted that the electron-pair bond was formed through the interaction of an unpaired electron on each of two atoms; that the spins of the electrons had to be opposed; and that once paired, the two electrons could not take part in additional bonds. His last three rules were new. One stated that the electron-exchange terms for the bond involved only one wave function from each atom; another, that available electrons in the lowest energy levels would form the strongest bonds. Pauling's final rule asserted that of two orbitals in an atom, the one that could overlap the most with an orbital from another atom would form the strongest bond and that the bond would tend to lie in the direction of that concentrated orbital. This allowed the prediction and calculation of bond angles and molecular structures.
"Appropriately for his audience of mathematics-shy chemists, Pauling did not present lengthy mathematical proofs of his rules, for, as he wrote in the paper, "even the formal justification of the electron-pair bond in the simplest cases. . . requires a formidable array of symbols and equations." But he outlined the way others could work through the proofs and presented a number of examples of his reasoning at work.
"From the principles of quantum mechanics he was now able to derive everything from the strengths and arrangements of bonds to a complete theory of magnetism in molecules and complex ions. Even better, using his new system Pauling was also able to predict new electronic structures and properties for atoms. Quantum mechanics, in other words, did not just confirm what was already known; it pointed the way to new insights" (http://scarc.library.oregonstate.edu/coll/pauling/bond/narrative/page24.html, accessed 01-16-2014).
Pauling, “The Nature of the Chemical Bond. Application of Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules,” Journal of the American Chemical Society 53 (1931) 1367-1400. In January 2014 images of Pauling's original manuscript for this paper could be downloaded from Oregon State University's Pauling website at this link.
Goertzel & Goertzel, Linus Pauling, 70-77.