Orbitals frontier orbital symmetry

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

According to one classification (15,16), symmetrical dinuclear PMDs can be divided into two classes, A and B, with respect to the symmetry of the frontier molecular orbital (MO). Thus, the lowest unoccupied MO (LUMO) of class-A dyes is antisymmetrical and the highest occupied MO (HOMO) is symmetrical, and the TT-system contains an odd number of TT-electron pairs. On the other hand, the frontier MO symmetry of class-B dyes is the opposite, and the molecule has an even number of TT-electron pairs. 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

Orbital symmetry control of subsequent ring opening could account for isomerization at only one of the double bonds. Taking ij/ as the controlling frontier orbital, it can be seen that a concerted return to ip2 to rotation at only one terminus of the diene ... 

See, e.g. (a) Woodward, R. B. Hoffmann, R. The Conservation of Orbital Symmetry, Verlag Chemie 1970 (b) Flfm-ING, L. Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, London, 1977. 

In any given sigmatropic rearrangement, only one of the two pathways is allowed by the orbital-symmetry rules the other is forbidden. To analyze this situation we first use a modified frontier-orbital approach. We will imagine that in the transition state the migrating H atom breaks away from the rest of the system, which we may treat as if it were a free radical. 

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. 

Frontier orbital approaches are not yet implemented in EROS. Nor does EROS take account of the features of reactivity which are controlled by orbital symmetries. This will follow the current work on stereochemistry and conformation. 

Roald Hoffmann, a former coworker of R.B. Woodward and Nobel Prize as well for his contribution to the frontier orbital theory (the famous Woodward-Hoffmann rules concerning the conservation of molecular orbital symmetry), has also emphasised the artistic aspects of organic synthesis "The making of molecules puts chemistry very close to the arts. We create the objects that we or others then study or appreciate. That s exactly what writers, visual artists and composers do" [15a]. Nevertheless, Hoffmann also recognises the logic content of synthesis that "has inspired people to write computer programs to emulate the mind of a synthetic chemist, to suggest new syntheses". 

Again it has to be noted that the frontier orbitals participating in such a valence isomerization are delocalized over the whole molecule [22]. This has consequences for the orbital symmetry and, thereby, a prior analogy with comparable processes involving 6 t-electrons only is not given. However, compared with smaller Jt-systems the selection rules for orbital symmetry controlled processes in fullerenes seem to be less restrictive, since a large number of tt-orbitals with small energy separation are available. Calculations at the AM 1 and PM3 level show that the photocycKzation... 

These reactions are characterized by the phenomenon that the frontier orbitals of the reactants maintain a defined stereochemical orientation throughout the w hole reaction. Most noteworthy in this respect, is the principle of orbital symmetry conservation ( Woodward-Hoffmann rules la), but the phenomenon is much more general, as shown by the following examples of Self-Immolative Stereoconversion or Chirality Transfer . This term describes processes by which a stereocenter in the starting material is sacrificed to generate a stereocenter in the product in an unambiguous fashion. This is, of course, the case in classical SN2-displacements. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

Considering the proliferation of MO calculations in recent years, it is remarkable how few calculations have been reported for these heterocycles. Frontier orbitals of several betaines have been calculated using the Hiickel method and electroselectivity correctly predicted on the basis of the orbital symmetry.Similar results have been obtained for pyridinium-3-olates (427) using the Pariser- Parr Pople (PPP) method. The CNDO... 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

Our understanding of organic chemistry has improved dramatically over the past few decades with the development of molecular orbital theory. In particular, the contributions of Woodward and Hoffmann have emphasised the importance of orbital symmetry in dictating the course of organic reactions. More recently, the symmetry properties of the orbitals close to the potential energy surface, the so-called frontier orbitals, have been shown to be of paramount importance. The basics of frontier orbital theory are... 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

McWeeny has written a tribute to the valence-bond theory pioneers of 1927-1935.362 Shavitt has outlined the history and evolution of Gaussian basis sets as employed in ah initio molecular orbital calculations.363 Hargittai has interviewed Roald Hoffmann (b. 1937)364 of Cornell University and Kenichi Fukui (1918-1998)365 of Kyoto University, who were jointly awarded the Nobel Prize in Chemistry in 1981. Fukui developed the concept of frontier orbitals and recognized the importance of orbital symmetry in chemical reactions, but his work was highly mathematical and its importance was not appreciated until Robert Woodward (1917-1979) and Hoffmann produced their rules for the conservation of orbital symmetry from 1965 onwards.366... 

In the preceding explanation, we have ignored bonding factors. In the norbornanes (106), at least, frontier electron reactivity indices (Fukui and Fujimoto, 1965) actually appear to favor syn-exo elimination. Normally, syw-elimination is in violation of the orbital symmetry rule, and we are inclined to accept anti elimination as the standard. Even so, we believe that powerful steric factors may overcome apparently unfavorable bonding factors to produce novel 55, as in 92-95. 

In 1965, the American chemists R. B. Woodward and R. Hoffmann ( conservation of orbital symmetry or Woodward-Hoffmann rules) and Japanese chemist K. Fukui ( frontier orbital theory ) proposed theories to explain these results as well as those for other reactions. (Woodward won the Nobel Prize in Chemistry in 1965 for his synthetic work. In 1981, after the death of Woodward, Hoffmann and Fukui shared the same prize for the theories discussed here.)... 

Both combinations of alkyne n orbitals find filled dir orbital symmetry matches in these d4 complexes. Extended Huckel calculations on Mo(HC=CH)2(S2CNH2)2 indicate a large HOMO-LUMO gap of 1.62 eV. These octahedral complexes have proved to be quite robust and resist exchange and substitution reactions in accord with a substantial frontier orbital energy gap (153). 

Kenichi Fukui and Roald Hoffmann won the Nobel prize in 1981 (Woodward died in 1979 and so couldn t share this prize he had already won the Nobel prize in 1965 for his work on synthesis) for the application of orbital symmetry to pericyclic reactions. Theirs is an alternative description to the frontier orbital method we have used and you need to know a little about it. They considered a more fundamental correlation between the symmetry of all the orbitals in the starting materials and all the orbitals in the products. This is rather too complex for our consideration here, and we shall concentrate only on a summary of the conclusions—the Woodward-Hoffmann rules. The most important of these states ... 

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