Theory of Resonance and its Application

Wheland GW (1953) The theory of resonance and its application to organic chemistry, Wiley, New York... 

G. W. Wheland, The Theory of Resonance and its Application to Organic Chemistry, Wiley, New York, Chapman and Hall, London, 1944. 

Chemical Bond (1939), were often misunderstood by traditional organic chemists who frequently confused this entirely theoretical construct with the physical process of tautomerism. [8] This misapprehension probably increased its popularity rather than the opposite, and the application of resonance to organic chemistry was given a further boost by the publication in 1944 of Theory of Resonance and its Application to Organic Chemistry by George W. Wheland (1907-1972). [9]... 

G. W. Wheland, Theory of Resonance and Its Application to Organic Chemistry (New York J. Wiley and Sons London Chapman and Hall, 1944). The Pauling-Wheland controversy on the ontological status of resonance is described in the contribution of K. Gavroglu and A. Simoes in this volume. 

Wheland s The Theory of Resonance and its Application to Organic Chemistry first appeared in 1944, and it attempted to make as complete a presentation of resonance theory as was then possible. It was a partisan textbook. At a time when there was, really, no outstanding experimental reasons to choose between resonance theory and molecular orbital theory, Wheland s first lines in his preface left no doubts about the "correct" approach "the theory of resonance is the most important addition to chemical structural theory that has been made since the concept of the shared-electron bond was introduced by G. N. Lewis" (Wheland 1944, iii). 

Wheland, G. W. 1944. The theory of resonance and its applications to organic molecules. New York John WUey Sons. 

Henry, C. H. (1986). Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiars, J. Lightwave Technol. LT-4, 288-297. 

The classic HLSP-PP-VB (Heitler-London-Slater-Pauling perfect-pairing valence-bond) formalism and its chemical applications are described by L. Pauling, The Nature of the Chemical Bond. 3rd edn. (Ithaca, NY, Cornell University Press, 1960 G. W. Wheland, The Theory of Resonance (New York, John Wiley, 1944) and H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (New York, John Wiley, 1944). 

It is true that the idea of resonance energy was then provided by quantum mechanics. . . but the theory of resonance in chemistry has gone far beyond the region of application in which any precise quantum mechanical calculations have been made, and its great extension has been almost entirely empirical.. . . The theory of resonance in chemistry is an essentially qualitative theory, which, like the classical structure theory, depends for its successful application largely upon a chemical feeling that is developed through practice. 46... 

All of these early studies, however, contained, in addition to suggestions that have since been incorporated into the present theory, many others that have been discarded. The refinement of the electronic theory of valence into its present form has been due almost entirely to the development of the theory of quantum mechanics, which has not only provided a method for the calculation of the properties of simple molecules, leading to the complete elucidation of the phenomena involved in the formation of a covalent bond between two atoms and dispersing the veil of mystery that had shrouded the bond during the decades since its existence was first assumed, but has also introduced into chemical theory a new concept, that of resonance, which, if not entirely unanticipated in its applications to chemistry, nevertheless had not before been clearly recognized and understood. 

I feel that the greatest advantage of the theory of resonance, as compared with other ways (such as the molecular-orbital method) of discussing the structure of molecules for which a single valence-bond structure is not enough, is that it makes use of structural elements with which the chemist is familiar. The theory should not be assessed as inadequate because of its occasional unskillful application. 11 becomes more and more powerful, just as does classical structure theory, as the chemist develops a better and better chemical intuition about it. 

The method of averaging for all valence-bond structures, asTdescribed above for diborane, is extremely laborious for any except very simple molecules. A statistical theory of resonating valence bonds that can be easily applied to complex as well as simple molecules has been developed.87 It can be illustrated by application to B6H9. Let us begin by assigning the probability 1 to the nonbridging B—II bonds and to the other bonds in the molecule ... 

One of the lasting practical results of treating metals in this model has been the tabulation of atomic radii and interatomic distances in metals [39-42]. Another interesting application of the unsynchronized-resonating-covalent-bond-theory of metal is its use in the elucidation of the to the structure and properties of elemental boron and the boranes [43]. 

L. Pauling and Z. S. Herman, Recent advances in the unsynchronized-resonating-covalent-bond theory of metals, alloys, and intermetallic compounds and its application to the investigation of the structure of such systems, in Modelling of Structure and Properties of Molecules, Z. B. Maksic, ed., Ellis Horwood, Chichester, England, 1987, pp. 5-37. 

As already pointed out, this description of the Raman effect is based on the polarizability theory (Placzek, 1934) which is valid in a good approximation if the exciting frequency is much higher than the frequency of the vibrational transition // , but lower than the frequency of the transition to the electronic excited state If, on the other hand, is approaching then resonances occur which considerably enhance the intensities of the Raman lines, i.e., the resonance Raman effect. This effect and its applications are described in Sec. 6.1 and also in Secs. 4.2 and 4.8. 

In the recent past, analytical research in Celestial Mechanics has centred on KAM theory and its applications to the dynamics of low dimensional Hamiltonian systems. Results were used to interpret observed solutions to three body problems. Order was expected and chaos or disorder the exception. Researchers turned to the curious exception, designing analytical models to study the chaotic behaviour at resonances and the effects of resonant overlaps. Numerical simulations were completed with ever longer integration times, in attempts to explore the manifestations of chaos. These methods improved our understanding but left much unexplained phenomena. 

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