Molecular orbitals product rule

What do molecular orbitals and their nodes have to do with pericyclic reactions The answer is, everything. According to a series of rules formulated in the mid-1960s by JR. B. Woodward and Roald Hoffmann, a pericyclic reaction can take place only if the symmetries of the reactant MOs are the same as the symmetries of the product MOs. In other words, the lobes of reactant MOs must be of the correct algebraic sign for bonding to occur in the transition state leading to product. 

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. 

There have been attempts to apply formal methods to the representation of organic compounds [1],[2], some attempts to apply artificial intelligence to organic synthesis [3],[4], and numerous attempts to apply the use of molecular orbital calculations to the verification of the validity of compounds in the synthesis route. This effort was a moderate attempt to examine the representation issues involved in writing production rules for Diels-Alder disconnections. 

Individual molecular orbitals, which in symmetric systems may be expressed as symmetry-adapted combinations of atomic orbital basis functions, may be assigned to individual irreps. The many-electron wave function is an antisymmetrized product of these orbitals, and thus the assignment of the wave function to an irrep requires us to have defined mathematics for taking the product between two irreps, e.g., a 0 a" in the Q point group. These product relationships may be determined from so-called character tables found in standard textbooks on group theory. Tables B.l through B.5 list the product rules for the simple point groups G, C, C2, C2/, and C2 , respectively. 

The ring opening of cyclopropyl cations (pp. 345, 1076) is an electrocyclic reaction and is governed by the orbital symmetry rules.389 For this case we invoke the rule that the o bond opens in such a way that the resulting/ orbitals have the symmetry of the highest occupied orbital of the product, in this case, an allylic cation. We may recall that an allylic system has three molecular orbitals (p. 32). For the cation, with only two electrons, the highest occupied orbital is the one of the lowest energy (A). Thus, the cyclopropyl cation must... 

Direct product rule for assigning molecular symmetry from orbital symmetry... 

A preliminary analysis of the absorption spectrum was given in Example 5.4-1 as an illustration of the application of the direct product (DP) rule for evaluating matrix elements, but the analysis was incomplete because at that stage we were not in a position to deduce the symmetry of the electronic states from electron configurations, so these were merely stated. A more complete analysis may now be given. The molecular orbitals (MOs)... 

The alkene metathesis reaction was unprecedented - such a non-catalysed concerted four-centred process is forbidden by the Woodward-Hoffmann rules - so new mechanisms were needed to account for the products. Experiments by Pettit showed that free cyclobutane itself was not involved it was not converted to ethylene (<3%) under the reaction condition where ethylene underwent degenerate metathesis (>35%, indicated by experiments involving Di-ethylene) [10]. Consequently, direct interconversion of the alkenes, via an intermediate complex (termed a quasi-cyclobutane , pseudo-cyclobutane or adsorbed cyclobutane ) generated from a bis-alkene complex was proposed, and a detailed molecular orbital description was presented to show how the orbital symmetry issue could be avoided, Scheme 12.14 (upper pathway) [10]. 

In addition, Diels-Alder adducts are formed through two types of approaches that lead to endo or exo isomers. The endo isomer is usually favored over the exo isomer, although the exo isomer is generally the thermodynamically preferred product. This is known as the Alder, or endo, rule and can be attributed to the additional stability gained by secondary molecular orbital overlap during the cycloaddition.22 26 27 Again, the use of a Lewis acid catalyst can alter the endo/exo ratio and has even been shown to give the thermodynamic exo adduct as the major product.28... 

Although IMDA reactions are entropically less disfavored than the intermolecular versions, they are nonetheless not as simple as might at first appear. The well-known Alder endo rule and its frontier molecular orbital theoretical interpretation involving secondary orbital interactions, together with steric considerations, serve to explain the kinetic preference for the endo-product and the thermodynamic preference for the < o-product in IMDAs. For the IMDA reaction, an additional parameter, the effect of the tether that connects the diene to the dienophile to control the conformation available to a transition state has to be considered. 

Although the state correlation diagram is physically more meaningful than the orbital correlation diagram, usually the latter is used because of its simplicity. This is similar to the kind of approximation made when the electronic wave function is replaced by the products of one-electron wave functions in MO theory. The physical basis for the rule that only orbitals of the same symmetry can correlate is that only in this case can constructive overlap occur. This again has its analogy in the construction of molecular orbitals. The physical basis for the noncrossing rule is electron repulsion. It is important that this applies to orbitals—or states—of the same symmetry only. Orbitals of different symmetry cannot interact anyway, so their correlation lines are allowed to cross. 

Acetic acid treatment of the transition metal Ge(IV) hydride salt Kb/5-C5H5Mn(CO)2GeH3] yields a red product, b/5-C5H5Mn (CO)2]2Ge, which contains a linear Mn-Ge-Mn system in which the germanium atom occupies a special position with equal Ge-Mn distances of 2.204 A. Solution infrared spectra show four v(CO) stretching absorptions instead of the two expected from the cen-trosymmetric structure in the solid state, implying free rotation about the Ge-Mn bonds. Simple application of the rare-gas rule would favor a double-bonded formulation containing Ge(IV), but a molecular-orbital... 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Pukui... 

Cycloadditions are controlled by orbital symmetry (Woodward-Hoffman rules) and can take place only if the symmetry of all reactant molecular orbitals is the same as the symmetry of the product molecular orbitals. Thus, an analysis of all reactant and product orbitals is required. A useful simplification is to consider only the frontier molecular orbitals. These orbitals are the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). The orbital symmetry must be such that bonding overlap of the terminal lobes can occur with suprafacial geometry that is, both new bonds are formed using the same face of the diene. 

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