RESONANCE, THEORY OF

in chemistry, theory by which the actual normal state of a molecule is represented not by a single valence-bond structure but by a combination of several alternative distinct structures. The molecule is then said to resonate among the several valence-bond structures or to have a structure that is a resonance hybrid of these structures. The energy calculated for a resonance hybrid is lower than the energies of any of the alternative structures; the molecule is then said to be stabilized by resonance. The difference between the energies of any one of the alternative structures and the energy of the resonance hybrid is designated resonance energy. The classic example of the application of the theory of resonance is the formulation of the structure of benzene. The structure of benzene as a six-membered ring of carbon atoms was introduced by the German chemist F.A. Kekule in 1865. To make the structure compatible with the quadrivalence of carbon, he introduced alternating single and double bonds in the ring, and in 1872, in order to account for the fact that no isomers of benzene (no isomeric orthosubstituted benzenes differing in having single or double bonds between the substituted carbon atoms) had been observed, he introduced the idea of an oscillation between structures of the form: In the years following 1920, several scientists proposed the idea that the true state of the molecule may be intermediate between those represented by several different valence-bond structures. Further clarification of the structure of benzene was provided by a U.S. chemist, Linus Pauling, in 1931 with the proposal that the normal state of the molecule can be represented as a hybrid of the two Kekule structures and the three structures of the form: The actual configuration of the molecule is a suitable average of the configurations corresponding to the individual structures. Because of resonance the six carboncarbon bonds are equivalent, in agreement with conclusions derived from experimental measurements. Furthermore, the energy of the resonance structure, calculated from quantum-mechanical considerations, is successfully predicted to be less than the energy of any one of the alternative structures. The concept of resonance has similarly been used to formulate structures for polynuclear aromatic hydrocarbons, molecules containing conjugated systems of double bonds (e.g., biphenyl, butadiene), free radicals, and other molecules to which no satisfactory single structure in terms of single bonds, double bonds, and triple bonds can be assigned (e.g., carbon monoxide, oxygen). Some general rules are used in the selection of suitable resonance structures for a molecule. These rules are: the structures must have energies of similar magnitudes; the arrangement of the atoms must be approximately the same in all the structures; and the structures must have the same numbers of unpaired electrons. The theory of resonance is based on the fundamental principle of quantum mechanics, which states that the wave function representing a stationary state of a system can be expressed as a weighted sum of the wave functions that correspond to several hypothetical structures for the system and that the proper combination is that sum which leads to a minimum calculated energy for the system.