Pericyclic reactions description

Modern Valence-Bond Description of the Mechanisms of Six-Electron Pericyclic Reactions... 

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 wavefunction appropriate for the description of a six-electron pericyclic reaction can be written as... 

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 offulminic 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-Hoffmarm mles [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. 

The characteristic feature of all pericyclic reactions is the concertedness of all the bond making and bond breaking, and hence the absence of any intermediates. Naturally, organic chemists have worked hard, and devised many ingenious experiments, to prove that this is true, concentrating especially on the Diels-Alder reaction. The following is an oversimplified description of some of the most telling experiments. 

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 ... 

Please note—these orbitals are just p Ofbitals, and do not make up HOMOs or LUMOs or any particular molecular orbital. Do not attempt to mix frontier orbital and Wo dward--Hbffmann descriptions of pericyclic. reactions. 

To summarize this section, for the Diels-Alder reaction, HF and CASSCF vastly overestimate the reaction barrier. Dynamical correlation is essential for the description of the Diels-Alder transition state. MP2 underestimates the barrier. MP4 and Cl methods both provide very good results, but triples configurations must be included. The preferred method, when one combines both computational efficiency and accuracy, is clearly DFT. It is likely the strong performance of B3LYP with pericyclic reactions, typified by the Diels-Alder results described here, that propelled this method to be one of the most widely used among computational organic chemists. 

In the sense of lattice theory, pericyclic reactions with an even number of chemical centers will differ essentially from those with an odd number of centers. In the latter case we restrict ourselves to the description of monocyclic molecular systems. Whether we look at... 

The principle of valency conservation (X-model) -An algebraic approach to the description of pericyclic reactions (2,22,31)... 

The single-parameter X-model is now extended to a parametric description of complex reactions with an arbitrary number of reaction parameters. Let p( 3) be the number of reaction partn s (reactants, products or intermediates) the reaction lattice is then isomorphic to the lattice Pip + 1) 2 with a diagram of a higher dimensional cube (6.32). Accordin y, the dynamic sublattice is isomorphic to P(p) = 2 and thus contains at least one element of the non-roechanistic dimension A (see Ch. "Generalized reaction lattice"). Ck>nsequently, the choice of the reaction path is no longer unique - in contrast to the sin e-parameter X model for pericyclic reactions with a well defined reaction path (via an aromatic or antiaromatic transition state.). The formal algebraic description of... 

The description of pericyclic reactions by the dynamic graph D suggests connecting the graph D with the time development of the system during reaction. 

The Principle of Conservation of Orbital Symmetry for pericyclic reactions as enunciated by R. B. Woodward and R. Hoffmann comes closest to this description. 

Abstract A discussion on conservation of orbital symmetry and its application to select pericyclic reactions is presented. Initially, effort is made to explore the symmetry characteristics of the cr, cr, n and n molecular orbitals (MOs). This is followed by a description of the MOs and their symmetry characteristics for allyl cation, allyl radical, allyl anion, and 1,3-butadiene. This concept is applied to n2 + n2, n4 + it2 (Diels-Alder) and electrocyclic reactions. 

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