Valence bond structure systems

Benzene has already been mentioned as a prime example of the inadequacy of a connection table description, as it cannot adequately be represented by a single valence bond structure. Consequently, whenever some property of an arbitrary molecule is accessed which is influenced by conjugation, the other possible resonance structures have to be at least generated and weighted. Attempts have already been made to derive adequate representations of r-electron systems [84, 85]. 

It is often asked whether or not the constituent structures of a resonating system, such as the Kekul4 structures for the benzene molecule, are to be considered as having reality. There is one sense in which this question may be answered in the affirmative but the answer is definitely negative if the usual chemical significance is attributed to the structures. A substance showing resonance between two or more valence-bond structures does not contain molecules with the configurations and properties usually associated with these structures. The constituent structures of the resonance hybrid do not have reality in this sense. 

Thieno[3,4-d]thiepin (58) superficially resembles the benzothiepins although X-ray structure analysis reveals that the thiepin ring is in fact planar (69JA3995). The bond length for the central C—C bond (1.46 A) is also consistent with the valence bond structure (59a). The stability of this system has been attributed disparately to contributions from the oppositely charged separated resonance structures (59a and 59b) (70JA1453,73JA2860). 

Neither of the above species is a ground-state quintet (four unpaired electrons). The pairing indicated by the valence bond structures shown above apparently occurs, leaving the unpaired electrons localized in a orbitals that are approximately orthogonal to the n system. The very small zero-field splitting is perhaps a measure of the validity of the o—7r separation which constitutes the basic assumption of 7r-electron theory. 

Why is the excited state of a conjugated system of double bonds stabilized more, relative to the ground state, than for a nonconjugated system Resonance theory provides an explanation (see Section 6-5). Of the several conventional valence-bond structures that can be written for 1,3-butadiene, four of which are shown here, 2a-2d, only structure 2a has a low enough energy to be dominant for the ground state of 1,3-butadiene ... 

It is perhaps valuable to compare electronic excitation with one-electron redox processes. For example, an n- -n excitation is equivalent to oxidizing the n-orbital and reducing the Tt-system. The predominant valence bond structure of the... 

Valence bond and molecular orbital approaches to descriptions of one-electron bonds and Pauling three-electron bonds are reviewed, and attention is given to the incorporation of Pauling three-electron bonds into the valence bond structures for molecular systems that involve four-electron three-centre, five-electron three-centre and six-electron four-centre bonding units. Many of these valence bond structures are examples of increased-valence structures. Examples are provided for a few of the large number of phenomena that involve these types of bonds and valence bond structures. 

The mathematical chemist will recognize a as one of the Kekule valence-bond structures of the hydrocarbon, while is the corres nd-ing molecular graph Model is called an inner dual or dualist [2], is a caterpillar tree [3], and is called a Clar graph [4]. The latter two models are apparently quite different from the original skeleton, however, as it will turn out later, the topological properties of this benzenoid system are best modeled by either d or e-... 

It is usually found that where there is a large difference between the calculated and the observed values of heats of formation, the calculated value of - J Hf is less than the observed that is, the actual molecule is more stable than the hypothetical molecule consisting of normal bonds. This difference has been ascribed to stabilization by resonance between a variety of valence bond structures, and is sometimes known as the observed or empirical resonance energs The concept of resonance is derived from a procedure used for obtaining approximate solutions of the wave equation. Its use is therefore a matter of convenience rather than theoretical necessity. Moreover it is often applied to systems of such complexity that no question of even an approximate solution of the wave equation arises in these cases its status is therefore that of an empirically used concept similar to the earlier notion of mesomerism . 

The structures of a number of compounds that contain a conjugated jt-system can be written as the combination of a number of contributory valence bond structures. Thus benzene can be written as a combination of the two valence bond structures 1.48 and 1.49. These contributory but non-isolable structures are known as resonance structures. The delocalization of the jt-electrons, arising from the combination of these valence bond structures, leads to enhanced stability. 

In cis azobenzene, steric factors prevent the molecule being flat owing to the interference of the two hydrogen atoms in the ortho position, and the C—N—N system (the C being in a benzene ring) is not linear, with the result that a valence bond structure of the type VIII cannot contribute to the molecular resonance. The CN bond distance is found to be 1 46 A as in the single bond and the molecule is represented correctly by the formula IX. 

To place the mfp approach in a broader context, we now extend Eq. 1 to deal more explicitly with the ultimate formation of equilibrated product P [83]. In the case of weak D/A coupling, where a diabatic basis comprised of charge-localized valence-bond structures may be employed to represent the relevant states of the reacting system, the first-passage process can be viewed as the conversion of the activated reactants to the resonant state of activated products (El) subsequently e1 may recross to R (i.e., pass back through the hypersurface in configuration space defining the transition state) or proceed irreversibly to P ... 

A further factor that has a marked influence upon the arene oxide-oxepin distribution is the effect of substituents. With the numbering system shown below, arene oxides, monosubstituted arene 1,2-, or 3,4-, and 1,2 disubstituted 1,2-oxides prefer their oxepin forms whereas arene 2,3-oxides prefer their oxide tautomers. These observations concur with MINDO/3 calculations and may be rationalized in terms of the maximum number of low-energy valence-bond structures for tt-electron-donating or withdrawing substituents (Figure 1). 

Returning, then, to the expansion of Equation (2), we note that the terms represent different valence bond structures. Why should they all have the same amplitude and phase This situation is very similar to the problem of determining the "resonance energy" of ben-zenoid molecules (25,26,27). In that case, of all the possible valence bond structures which might contribute, only the Kekule structures are used. For large benzenoid systems this is only a small fraction of the total number of structures. Furthermore, it is assumed that they all enter with equal expansion coefficients (i.e., equal amplitude and phase). In addition, the matrix elements which convert one structure into another are set equal to a common value, determined empirically. Thus, the energy lowering associated with "resonance" in benzenoid molecules has a mathematical structure which maps onto the discussion in the Introduction. However, there are some important differences. 

The Cashion-Herschbach treatment of H3 can be extended to more complicated systems. This has been done recently by Blais and Truhlar213 for the F + H2 system. All the valence electrons were explicitly considered (i.e. 2p5 on F and Is on each of the hydrogen atoms). There are four covalent valence-bond structures of the correct symmetry to contribute to the lowest... 

El-Basil S, Randic M (1992) Equivalence of Mathematical Objects of Interest in Chemistry and Physics. Adv Quant Chem 24 239-290 Graovac A, Gutman I, Randic M, Trinajstic N (1973) Kekule Index for Valence Bond Structures of Conjugated Polycyclic System. J Am Chem Soc 95 6267-6273... 

The perturbational MO method of Longuet-Higgins (11) and Dewar (12), which was thoroughly reviewed by Dewar and Dougherty (6), has been the pencil-and-paper method of choice in numerous applications. More recently, a modified free-electron (MFE) MO approach (13-15) and a valence-bond structure-resonance theory (VBSRT) (7, 16, 17) have been applied to several PAH structure and reactivity problems. A new perturbational variant of the free-electron MO method (PMO F) has also been derived and reported (8, 18). Both PMO F and VBSRT qualify as simple pencil-and-paper procedures. When applied to a compilation of electrophilic substitution parameters (ct+) (19-23), the correlation coefficients of calculated reactivity indexes with cr+ for alternant hydrocarbons are 0.973 and 0.959, respectively (8). In this case, the performance of the PMO F method rivals that of the best available SCF calculations for systems of this size, and that of VBSRT is sufficient for most purposes. 

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