Frontier orbitals rules

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

Thermal and photochemical electrocyclic reactions always take place with opposite stereochemistry because the symmetries of the frontier orbitals are always different. Table 30.1 gives some simple rules that make it possible to predict the stereochemistry of electrocyclic reactions. 

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

The last decade has witnessed an unprecedented strengthening of the bone between theory and experiment in organic chemistry. Much of this success may be credited to the development of widely applicable, unifying concepts, such as the symmetry rules of Woodward and Hoffmann, and the frontier orbital thee>ry of Eukui. Whereas the the ore tical emphasis had historically been on detailed structure and spectroscopy, the new methods are de signe d to solve pre)blems e>f special importance to organic chemists reactivity, stereochemistry, and mechanisms. 

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. 

Keywords Chemical orbital theory. Electron delocalization. Frontier orbital. Orbital amplitude, Orbital energy, Orbital interaction. Orbital mixing rule, Orbital phase, Orbital phase continuity, Orbital phase environment. Orbital synunetry, Reactivity, Selectivity... 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

The reaction first occurs between Cj and H with the largest amplitudes of the frontier orbitals, in agreement with the Markovnikov rule. 

According to the frontier orbital theory, a bond preferentially forms between the atoms with the largest frontier orbital amplitudes (Sect. 3.4 in the Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). This is applicable for the regioselectivities of Diels-Alder reactions [15]. The orbital mixing rules are shown here to be useful to understand and design the regioselectivities. 

It is thus evident that the reaction path is controlled by the frontier-orbital interaction. The position of reaction will be determined by the rule of maximum overlapping of frontier orbitals, that is, HO and LU MO s of the two reacting molecules. Sometimes SO takes the place of HO or LU in radicals or excited molecules. Hence, the general orientation principle would be as follows ... 

In a formal (E.A.N. rule) sense, the Os-Os bond order in each of the three clusters corresponds to 1, and yet it is clear that a variety of different Os- Os bond types exist since each of the different metal centers (A) — (D) will utilize a different basis set of hybrid (or frontier) orbitals. 

The frontier orbitals responses (or bare Fukui functions) f (r) and the Kohn-Sham Fukui functions (or screened Fukui functions)/, (r) are related by Dyson equations obtained by using the PRF and its inverse [32]. Indeed, by using Equation 24.57 and the chain rule for functional derivatives in Equation 24.36, one obtains... 

The above selection rules can also be derived from frontier orbital theory. 

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". 

Our next exan le, the TMM diradical, is a more challenging case because its frontier orbitals are exactly degenerate. The 7C-system of TMM is shown in Figure 6 four ic-electrons are distributed over four molecular ji-type orbitals. Due to the exact degeneracy between the two e orbitals at the Ds structure, Hund s rule predicts the ground state of the molecule to be a triplet 2 state (similar to the T-state in ethylene). This is confirmed by both the experimental and theoretical findings (38-43). 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offiilminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4-6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

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. 

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