Classical chemical structural theory provided a number of examples of molecules which could not be represented by a single structure, as in the leading case of benzene, for which August Kekulé (1829-1896) had proposed in 1872 an 'oscillation' between the two alternative 'Kekulé structures', each with three single and three double carbon-carbon bonds forming a hexagon. This oscillation was required to account for the absence of two isomers of a given 1,2-disubstituted derivative. For Pauling the two Kekulé structures were classical analogues of quantum-mechanical 'valence structures'. The actual benzene molecule cannot be regarded as 'intermediate' between the hypothetical Kekulé structures. The molecule is more stable than either of these structures by a resonance energy of some 36 kcal mol^-1 (1 cal = 4.184 J). The carbon-carbon bond lengths of benzene are shorter than the mean of standard carbon-carbon single double bond lengths.

The resonance energy of benzene, on division by Planck's constant, gives a resonance frequency on the order of 10¹⁵ Hz, comparable to that derived similarly from the bond energies of simple molecules. Such a frequency refers to electronic motions, being a thousand times greater than that of the nuclear motions implied by Kekulé's proposal of 1872; the nuclear motions involved in tautomerism are slower still¹² Pauling's disciple, George Wheland, remarked that the benzene molecule is analogous to the real animal, the rhinoceros, described by a medieval traveller as a cross between two mythical beasts, the dragon and the unicorn.¹³

In 1935 Pauling judged the Heitler-London theory of bonding in the hydrogen molecule as 'the greatest single contribution to the clarification of the chemist's conception of valence since G. N. Lewis's suggestion in 1916 that the chemical bond between two atoms consists of a pair of electrons held jointly by the two atoms'.¹⁴ Fritz London was appalled by the compliment, and was irritated by 'this Pauling', who had not only taken over and vulgarised the VB theory but had also associated the theory with the physically absurd notions of G. N. Lewis, who postulated a static cubical array of electrons around the atomic nucleus. In 1929 London began a book on Quantum Mechanics and Chemistry, but soon abandoned the project. By 1930 he had moved on to investigate the non-polar intermolecular forces, the 'London dispersion forces', and by 1935 worked out the 'London equations' governing superconductivity, with his brother Heinz.¹⁵ Heitler moved on to radiation theory, also satisfied, as were Schröedinger and Dirac, that quantum mechanics had now, in principle, solved all problems in chemistry.

The first of Pauling's seven papers on the nature of the chemical bond¹⁶ was especially important in reconciling 'spectroscopic orbitals' with 'chemical orbitals'. Quantum mechanics developed symbiotically with atomic and diatomic spectroscopy during the interwar period.¹⁷ The atomic orbitals took their designations s-, p-, d- . . . from the sharp, principal, diffuse ... series of lines observed in atomic spectra. The angular forms of these atomic orbitals, based on the spherical harmonic functions, bore no direct and systematic relation to the stereochemical forms of polyatomic molecules, and the character of the 'chemical orbitals' governing the angles between bonds in polyatomic systems had become problematic by 1930. On a spectroscopic basis, the four valency electrons of the carbon atom formed the atomic ground state with two electrons spin-paired in the spherically symmetric 2s orbital and the remaining two with parallel spin occupying two of the mutually orthogonal 2p_x, 2p_y, and 2p_z orbitals. In 1931, Pauling and the MIT physicist John Slater showed, independently, that the angular functions of the 2s and the three 2p orbitals of the carbon atom, taken with equal weight and mutually exclusive phase relationships give rise to four equivalent hybrid (sp³) atomic orbitals, directed tetrahedrally. Each of these four hybrid chemical orbitals has an equal binding propensity, which is twice that of the 2s-orbital alone, as measured by the fractional overlap with, say, a 1 s-orbital of a hydrogen atom at a bonding position. Pauling extended his scheme to trigonal and digonal hybrids for molecules containing the carbon-carbon double and triple-bond and to octahedral and square-planar hybrids from the 4s-, 4p-, and 3d-orbitals of the transition metals in the first long period for the bonding established in coordination compounds.

A major element of Pauling's comprehensive ordering of inorganic bonding lay in this derivation of a quantitative scale of the electronegativities of the chemical elements through the resonance theory. Chemists during the eighteenth century had endeavoured to order the known variety of chemical combinations by drawing up hierarchical 'Tables of Chemical Affinities', based on such observations as the displacement of one acid from its salts by another acid with a greater 'affinity' for the base of the salt.¹⁸ After the chemical revolution at the end of the century, attention turned to the avidity with which oxygen combined with other elements, resulting in the 'Scale of Oxygenicity' or of universal acidity, evolved from 1809 by Amedeo Avogadro (1776-1856). Jöns Jacob Berzelius (1779-1848), one of the pioneers of electrochemistry, reformulated and extended Avogadro's concept into a 'universal scale of electronegativity' of the elements in 1818, based on the observations that oxygen, acids, and oxidised substances accumulated around the positive pole of an electrolytic cell, while metals, bases, and combustible substances passed to the negative pole.

Berzelius linked the electronegativity scale to his dualistic electropolar theory of chemical combination, based on the two fluid theory of electricity. Each atom, Berzelius proposed, carried unequal amounts of the positive and the negative electrical fluid, and the ratio of the amounts registered the electronegativity of the element. Oxygen, the most electronegative element then known, carried the largest excess of negative fluid, and potassium at the other end of the scale carried the largest excess of positive fluid. Chemical combination entailed the partial neutralisation of the two electrical fluids, and their union resulted in the liberation of the caloric fluid (heat). The compound formed retained smaller amounts of the two electrical fluids, and so acids, with an excess of negative fluid, combined with bases, carrying an excess of positive fluid, to form salts. The dualistic theory of chemical combination lost ground during the 1840s, primarily because it was unproductive in the new field of organic chemistry. But the concept of electronegativity and chemical affinity lived on, assuming thermochemical forms with the rise of physical chemistry at the end of the nineteenth century.¹⁹

The qualitative electronegativity scale of Berzelius, based largely on his chemical experience and intuition, correlates element by element with the quantitative scale of atomic electronegativities which Pauling derived, from 1932. The electric dipole moment of heteronuclear molecules A-B indicated to Pauling that the bonding involved resonance between covalent and ionic valence structures, the fractional contribution of the ionic structure being gauged by the value of the dipole moment. The bond energy of the heteronuclear molecule A-B turned out to be larger than the arithmetic or geometric mean of the bond energies of the corresponding homonuclear molecules A-A and B-B by an increment Δ, which represented the additional stabilisation arising from the resonance between the covalent and ionic valence structures. The bond energy increment Δ (A-B) could be related to the difference between the traditional, but ill-defined, property of the two individual elementary atoms, their electronegativities. The direct relation between Δ (A-B) and the square of the electronegativity difference [(x_A-x_B)²] enabled Pauling to evaluate the differences quantitatively, and to draw up a comprehensive table of the atomic electronegativities, ranging from 0.7 for caesium to 4.0 for fluorine. The table of electronegativities gave expectations for the energy and the electric dipole moment of any new type of bond: e.g. 50% ionic character for a difference of 1.7 between the electronegativities of the two atoms. What an atomic electronegativity really respresented was not transparent. Pauling regarded electronegativity as a measure of the affinity of a bonded atom for electrons.

The resonance theory was extended to conjugated organic molecules in 1933, appearing in the last three of Pauling's seven papers on the nature of the chemical bond. Thereafter the theory of resonance in organic chemistry was developed mainly by his coworker, George Wheland at Caltech and then at the University of Chicago, who published two books on the subject (1944 and 1955). The application of resonance theory to conjugated organic molecules highlighted the wide latitude in the choice of hypothetical 'valence structures' contributing to the ground state of a given molecule. Pauling's approximation of the VB method gave benzene a theoretical resonance energy of 0.9 J for the two Kekulé structures alone, but of 1.1 J with the inclusion of the three Dewar structures, each with an elongated transannular bond between opposite positions. The empirical 'exchange integral' J, calibrated from thermochemical data, had a value dependent on the range of resonating structures considered. Pauling formulated rules limiting the choice of 'valence structures' to a 'canonical set', but the choice remained wide for polycyclic aromatic hydrocarbons. The stage at which to truncate the series of possible 'valence structures', judged by chemical intuition, was popularly termed the 'Pauling point' by students of chemistry in the 1940s.

A molecular orbital theory of conjugated organic molecules with much less latitude had been proposed in 1931 by Erich Hückel (1896-1980), a physicist at Stuttgart, who had been a coworker with Debye at Zürich, deriving the Debye-Hückel theory of strong electrolytes in 1923. Hückel divided the electrons of a conjugated molecule such as benzene into two distinct sets, later termed the σ and the π electrons. The molecular plane is defined by the framework of carbon-carbon σ-bonds, formed from sp² orbitals, while the π-electrons move over the framework in MOs nodal in the plane. Hückel showed that cyclic polyenes with [4n +2] π-electrons, where n is an integer, had a substantial additional stabilisation from the π-electron delocalisation, but not those with [4n] π-electrons.

Pauling pointed out that two Kekulé-like valence structures could be written for cyclobutadiene and for cyclooctatetraene, which belong to the [4n] series, and resonance between the two structures is expected to stabilise these molecules by a resonance energy comparable to that of benzene in the [4n+2] series. Richard Willstätter (1872-1942) at Munich had synthesised cyclooctatetraene in 1905 and in 1911. He found the substance to be olefinic in its properties, with none of the aromaticity predicted from a theory of partial valencies linking conjugated carbon-carbon double bonds, proposed in 1899 by his colleague Friedrich Thiele (1865-1918). Following the same prediction made by Pauling in 1935, groups of organic chemists from 1939 to 1943 at several American universities, Minnesota, Princeton, Northwestern and Purdue, attempted to synthesise cyclooctatetraene, but without success, on the supposition that Willstätter had inadvertently prepared the isomer styrene.

Willstätter, by now a refugee in Switzerland from the third Reich, heard of these efforts and commented in his autobiography that the American chemists appeared to be 'untroubled' by his reports of the reduction of his cyclooctatetraene to cyclooctane and its oxidation to suberic acid. Willstätter's synthesis of cyclooctatetraene was finally reproduced in 1947, after an Anglo-American scientific commission in 1945 discovered kilogram quantities of cyclooctatetraene in the IG Farbenindustrie laboratories at Ludwigshafen, prepared by Walter Reppe (1892-1969) by polymerising acetylene over a nickel(II) cyanide catalyst.²⁰ Cyclooctatetraene was shown by electron diffraction (1948) to have a tub-shaped structure: the dianion with 10 π-electrons, following the Hückel rule for aromaticity, was later found to be planar.

By the late 1930s Pauling's interest had shifted to structural problems in biological chemistry, and he made relatively few positive contributions to the new problems of chemical bonding in mainstream chemistry during the postwar period. His book The Nature of the Chemical Bond remained conceptually unchanged between the first two editions (1939, 1940) and the third (1960). The new and intellectually inspiring book of the 1940s became a classical inorganic text of the 1960s.