Pauling-Wheland Resonance Theory

Klein DJ, Seitz WA (1988) Pauling-Wheland resonance theory of benzenoid hydrocarbons. J Mol Stmct (Theochem) 169 167-181... 

The matrix elements of the Pauling-Wheland resonance theory between Kekule structures K and K are given as °... 

Pauling s resonance theory raised questions as to the ontological status of theoretical entities very similar to the problematique associated with discussions about scientific realism. Differences in the assessment of the methodological and ontological status of resonance were the object of a dispute between Pauling and Wheland, who worked towards the extension of resonance theory to organic... 

The top panel in the accompanying figure depicts valence bond structures for the two major resonance contributors of benzene. Contrary to earlier notions of two rapidly fluctuating structures, Pauling s resonance theory, developed with his student George W. Wheland (1907-74), viewed benzene as represented by two idealized but fictional resonance... 

As suggested by the original resonance theory of Pauling and Wheland,51 such delocalization effects appear to represent some type of average of multiple resonance structures. A general goal of resonance theory is to represent each property (P)true of the true delocalized system in resonance-averaged form... 

The NRT resonance weights, bond orders, and valencies are generally comparable to those of the older Pauling-Wheland theory (particularly for species of low ionicity) and can be used to rationalize chemical phenomena in a similar fashion. Pauling s classic, The Nature of the Chemical Bond, brilliantly illustrates such reasoning. 

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). 

The resonance theory of Pauling and Wheland is brought into readier contact with classical ideas with the introduction of the resonance-theoretic wavefunction Ansatz appropriate for alternant systems. This is simply an equal-weighted sum over Kekule structures... 

Pauling, Wheland 1930 Resonance, valence bond theory... 

B. S. Park, Chemical translators Pauling, Wheland and their strategies for teaching the theory of resonance , Brit. J. Hist. Sci., 1999, 32, 21 —4(5. 

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. 

Nevertheless, acknowledging or denying the existence of differences between resonance theory and classical structural theory was dependent on their different assessments of the role of alternative methods to study molecular structure. Wheland equated resonance theory to the valence bond method and viewed them as alternatives to the molecular orbital method. Pauling conceded that the valence bond method could be compared with the molecular orbital method, but not with... 

With the advent of the computer era, it is now possible to reexamine and rethink the resonance theory at the ab initio level. For example, throughout Pauling and Wheland s books, benzene is supposed to be a hybrid of two Kekule structures, by noting that Dewar and other ionic structures make little contribution to the resonance in benzene. However, classical ab initio VB calculations with all possible 175 resonance structures by Norbeck et al. [51] and Tantardini et al. [3], where strictly atomic orbitals are used to construct VB functions, manifested that the five covalent Kekule and Dewar structures make even less contribution to the ground state of benzene than the other 170 ionic structures. This prompts us to reconsider the mathematical formulations for resonance structures [52]. 

The VB theory described molecular structure by a set of resonating structures. This did not mean that each structure in such a set would be considered as present individually, but that the sum of these would correspond to the set. The resonance theory provided merely a model, an approach, rather than a unique reflection of reality. There were proponents and opponents of the theory as is the case with most theories. George Wheland (Fig. 1.8a) published a book in 1944 about the theory of resonance [36]. Linus Pauling (Fig. 1.8b) also contributed to the theory especially... 

Pauling could not disagree more. For him, the double bond in ethylene was as "man-made" as resonance in benzene. Pauling summarized their divergent viewpoints by saying that for Wheland, there was a "quantitative difference" in the man-made character of resonance theory compared with ordinary structure theory—a difference he could not find anywhere. He further asserted that his former student made a disservice to resonance theory by overemphasizing its "man-made character." Wheland conceded that resonance theory and classical structural theory were qualitatively alike, but he still defended, contrary to Pauling, that there was a "quantitative difference" between the two. 

Stork [1963] completely rejects the Russian accusation that resonance theory as developed by Pauling, Wheland, and Ingold fails both empirically and philosophically. However, it should be noted that these criticisms (in the GDR) of the events in Moscow appeared well after the hype was over in the USSR. Furthermore, as Brush [1999, 268] correctly remarks For chemists in the West, the apparent absurdity of the Marxist ideological critique obscured a significant difference between VB and MO. According to Brush the molecular orbital theory permits a more realistic interpretation than the valence bond (or resonance) theory. However that may be, reflection on resonance hybrids, tautomerism, the riddle of benzene, and such like is still a relatively neglected theme in the philosophy of chemistry. 

Note that a comprehensive mesomeric theory of aromatic structure and reactivity was developed by Robinson, Ingold, and others in the years preceding the quantal resonance formulation of Pauling and Wheland. 

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