Orbiting resonance theory

The electronic theory of organic chemistry, and other developments such as resonance theory, and parallel developments in molecular orbital theory relating to aromatic reactivity have been described frequently. A general discussion here would be superfluous at the appropriate point a brief summary of the ideas used in this book will be given ( 7- )-... 

It appears now that, whatever its usefulness, the resonance theory is somewhat inadequate in explaining and predicting either chemical or physical characteristics of dyes compared to more or less sophisticated molecular orbital calculations. 

The radical is much more stable if both stmctures exist. Quantum mechanical theory implies that the radical exists in both states separated by a small potential. Moreover, both molecular orbital theory and resonance theory show that the allyl carbocation is relatively stable. 

Simple resonance theory predicts that pentalene (48), azulene (49), and heptalene (50) should be aromatic, although no nonionic canonical form can have a double bond at the ring junction. Molecular orbital calculations show that azulene should be stable but not the other two, and this is borne out by experiment. Heptalene has been prepared but reacts readily with oxygen, acids, and bromine, is easily hydrogenated, and polymerizes on standing. Analysis of its NMR spectrum shows that it is... 

Interactions of vicinal bonds have been extensively studied and are well known as hyperconjugation, resonance, and others [89-91], The a bonds vicinal to a reacting 71 bond have been proposed to participate in organic reactions and to control the selectivity [92, 93], Recently, we noticed the importance of the participation of the a bonds geminal to a reacting % bond (Scheme 35) [94] and have made extensive applications [95-102], Here, we present an orbital phase theory for the geminal bond participation and make a brief review. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

The next-nearest-neighbor-orbital resonance integrals, /JI3, also remain unaffected by the pure twisting motion. We conclude that a pure twisting motion can therefore represent at best only a relatively small perturbation of the electronic structure of the polysilane chain, suitable for treatment by first-order perturbation theory. The perturbation is represented by changes in the resonance integrals between more distant hybrid orbitals, among which / 14 clearly is the most important. 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

Natural resonance theory (NRT) allows these conflicting pictures of the oxyan-ion electron distributions to be tested quantitatively.149 Table 3.36 compares the geometries, NRT bond orders, atomic charges, and d-orbital occupancies for a representative variety of first- and second-row XOm"+ species,... 

Resonance such as (5.28a)-(5.28c) is inherently a quantal phenomenon, with no classical counterpart. In NBO language, each of the resonance interactions (5.28a)-(5.28c) corresponds to a donor-acceptor interaction between a nominally filled (donor Lewis-type) and unfilled (acceptor non-Lewis-type) orbital, the orbital counterpart of G. N. Lewis s general acid-base concept. As mentioned above, Lewis and Werner (among others) had well recognized the presence of such valence-like forces in the dative or coordinative binding of free molecular species. Thus, the advent of quantum mechanics and Pauling s resonance theory served to secure and justify chemical concepts that had previously been established on the basis of compelling chemical evidence. 

Because we are both computational chemistry researchers, we have naturally directed the book also to specialists in this field, particularly those wishing to incorporate natural bond orbital (NBO) and natural resonance theory (NRT) analysis into their methodological and conceptual toolbox. Researchers will find here a... 

One of the most used approaches for predicting homoaromaticity has been the perturbational molecular orbital (PMO) theory of Dewar (1969) as developed by Haddon (1975). This method is based on perturbations in the Hiickel MO theory based on reducing the resonance integral (/3) of one bond. This bond represents the homoaromatic linkage. The main advantage of this method is its simplicity. PMO theory predicted many potential homoaromatic species and gave rise to several experimental investigations. 

It is into the LUMO, the energetically most accessible unfilled molecular orbital, that any further electrons will go. Hence, it may be thought of as demarking the location of positive charge in a molecule. The LUMO in planar benzyl cation is delocalized away from the formal cation center and onto the ortho and para ring carbons, in accord with classical resonance structures. On the other hand, the LUMO in perpendicular benzyl cation remains primarily localized on the benzy lie carbon. Resonance theory suggests that delocalization of the positive charge leads to stabilization. Thus, planar benzyl cation is more stable than perpendicular benzyl cation. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

The simple resonance theory fails to explain the singular lack of effectiveness of delocalization in cyclobutadiene and cyclooctatetraene, but we may turn to molecular orbitals for the solution. 

Modem descriptions of the benzene structure combine resonance theory with molecular orbital theory. 

The influence of fluorine substituents on the stability of alkyl radicals derives from the same complex interplay of inductive and resonance effects that affects their structure. Simple orbital interaction theory predicts that substituents of the -X type (that is, electronegative substituents bearing lone pairs) should destabilize inductively by virtue of their group electronegativities, and stabilize by resonance to the extent of their ability to delocalize the odd electron. 

Most organic chemists are familiar with two very different and conflicting descriptions of the 7r-electron system in benzene molecular orbital (MO) theory with delocalized orthogonal orbitals and valence bond (VB) theory with resonance between various canonical structures. An attitude fostered by many text books, especially at the undergraduate level, is that the VB description is much easier to understand and simpler to use, but that MO theory is in some sense more fundamental . 

A brief account of the earlier history of the molecular orbital theory and the resonance theory of chemical bonding is given 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... 

Although the theory behind BLW is more general, a typical application of the method is the energy calculation of a specific resonance structure in the context of resonance theory. As a resonance structure is, by definition, composed of local bonds plus core and lone pairs, a bond between atoms A and B will be represented as a bonding MO strictly localized on the A and B centers, a lone pair will be an AO localized on a single center, and so on. With these restrictions on orbital extension, the SCF solution can be... 

In the case of a scattering resonance, bound-free correlation is modified by a transient bound state of fV+1 electrons. In a finite matrix representation, the projected (fV+l)-electron Hamiltonian H has positive energy eigenvalues, which define possible scattering resonances if they interact sufficiently weakly with the scattering continuum. In resonance theory [270], this transient discrete state is multiplied by an energy-dependent coefficient whose magnitude is determined by that of the channel orbital in the resonant channel. Thus the normalization of the channel orbital establishes the absolute amplitude of the transient discrete state, and arbitrary normalization of the channel orbital cannot lead to an inconsistency. 

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