Resonance Theory

Resonance Theory 

in chemistry, a conceptual extension of the classical theory of chemical structure. Resonance theory holds that if classical theory allows a given compound several structures that satisfy the requirements of valence, then the actual state of the molecules of this compound will correspond not to any single structure but rather to some combination, or hybrid, of structures.

Resonance theory is based on chemical concepts inferred from the results of experiments in which shortcomings of classical theory regarding structure and discrepancies between theoretical and experimental results became apparent. It is also based on one of the quantum mechanical methods used in molecular computations, the method of valence-bond structure. In the valence-bond method, a wave function constructed in a specified way from atomic orbitals is associated with each classical structure (valence-bond structure), and the wave function for the actual state is approximated by a linear combination of the wave functions. In resonance theory, these concepts are supplemented by criteria for selecting the most important structure from the alternative structures.

As an illustration, if a particular valence-bond diagram shows a line connecting widely separated atoms, this diagram will be less important than one in which the lines connect only adjacent atoms. For benzene, in addition to the two equivalent classical structures (Kekulé structures)

and

the following structures (Dewar structures) can be written:

Since in the Dewar structures one of the valence lines connects nonadjacent atoms, these structures will be less important than the Kekulé structures in describing the actual structure of the benzene molecule.

The role played by various structures is dictated by the qualitative effects of the variation principle from quantum mechanics. According to this principle, the most important ground-state structures are those possessing a minimum of energy. The higher the energy of a particular structure in relation to the lowest energy for all the structures, the less important is that structure to the general description of the molecule. According to the variation principle, the energy E calculated through an optimal linear combination of wave functions for structures i is less than the energy E_i of any individual structure. The minimum value of the difference E_i - E is called the resonance energy. As a rule, the larger the difference, the more the actual structure of the molecule will depart from the description given by classical theory, which uses only one structure. In practice, a different energy, termed the experimental resonance energy, is generally used; this energy is defined as the difference between the experimentally determined heat of formation of a compound and the energy corresponding to a particular classical structure, as calculated from tables of bond energies.

For many classes of compounds, for example, saturated hydrocarbons, molecules can be satisfactorily described on the basis of a single valence-bond structure. Other molecules, such as those with conjugated double and triple bonds, require the concept of superposition (resonance) of several valence-bond structures. In these cases, resonance theory incorporates the totality of alternative structures rather than selecting a single structure; in this respect it differs from other descriptive methods, where, for example, dotted lines represent valence lines and arrows indicate shifts in electron density. The alternative structures do not, however, represent actual existent states of a molecule. They merely serve as components of the resonance hybrid in much the same way as the separate elements in classical theory, for example, single and double bonds, contribute to the structure of the molecule as a whole.

Resonance theory makes possible a qualitative and, to a certain extent, quantitative (through calculations based on simplified versions of the valence-bond method) estimation of molecular symmetries, the equivalence of certain bonds and structural elements, and the stability and reactivity of molecules. In addition, resonance theory leads to an understanding and, to some extent, a prediction of experimental results. While these predictions are not precise, they at least do not involve the laborious quantum mechanical calculations that rigor would require. Resonance theory has led to the introduction of such widely used concepts as one-half and one-and-a-half bonds, hybrid orbitals, hyperconjugation, and the partially ionic character of covalent bonds between different types of atoms (resonance of covalent and ionic structures).

The theory of resonance was proposed by L. Pauling in the years 1928–31 and was developed in succeeding years by his followers. The term “resonance” was borrowed from W. Heisenberg, who traced the analogy between the quantum mechanical description of a system, for example, a system of coupled oscillators, and the system’s classical description, which took resonance into account.

REFERENCES

Pauling, L. Priroda khimicheskoi sviazi. Moscow-Leningrad, 1947. (Translated from English.)
Wheland, G. Teoriia rezonansa i ee primenenie ν organicheskoi khimii. Moscow, 1948. (Translated from English.)
Pauling, L. “Teoriia rezonansa ν khimii.” Zhurnal Vsesoiuznogo khimicheskogo obshchestva im. D. I. Mendeleeva, 1962, vol. 7, no. 4, p. 462.
Pauling, L. The Nature of the Chemical Bond, 3rd ed. Ithaca, N. Y., 1960.