Ethylene reaction with butadiene, theory

Advances in computational chemistry allow for the determination of stationary points by various approximations to the Schrodinger equation [4,35 43], Complete discussions and excellent reviews of the different methods can be found in the literature [6,33,44,45]. Over the years, the Diels-Alder reaction between 1,3-butadiene and ethylene has become a prototype reaction to evaluate the accuracy of many different levels of theory. A level of theory involves the specific combination of a computational method and basis set. For example, the RHF/3-21G level of theory involves the restricted Flartree-Fock method with the 3-21G basis set. Ken Flouk and his research group have pioneered many ideas concerning the fundamental ideas of pericyclic reactions by combining theory and experiment [3,4,37,38,46 48], For the Diels-Alder... 

Application of CM theory to explain pericyclic reactions was first attempted by Epiotis and coworkers (Epiotis, 1972, 1973, 1974 Epiotis and Shaik, 1978b Epiotis et al 1980). The following analysis is a much-simplified treatment of that approach. Let us compare, therefore, the CM analysis for the [4 + 2] allowed cycloaddition of ethylene to butadiene to give cyclohexene with the [2 + 2] forbidden dimerization of two ethylenes to give cyclobutane. For simplicity only the suprafacial-suprafacial approach is considered, although this simplification in no way weakens the argument. 

Figure 15-19 shows that the HOMO of butadiene has the correct symmetry to overlap in phase with the LUMO of ethylene. Having the correct symmetry means the orbitals that form the new bonds can overlap constructively plus with plus and minus with minus. These bonding interactions stabilize the transition state and promote the concerted reaction. This favorable result predicts that the reaction is symmetry-allowed. The Diels-Alder reaction is common, and this theory correctly predicts a favorable transition state. 

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene . With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

According to the frontier orbital theory, the orbitals that control these reactions are the aforementioned HOMO of one reactant and the LUMO (lowest unoccupied molecular orbital) of the other reactant. So, for this reaction, we have two possible scenarios interaction between HOMO ij/2 of butadiene and LUMO (p of ethylene or that between HOMO ti of ethylene and LUMO of butadiene. As the following illustration indicates, both possibilities lead to bonding overlap between the interacting orbitals of the reactants so the reaction is allowed, as we aU know. In addition, as fotmd by theory, between these two possible scenarios, we favor the interaction between the HOMO of the electron-rich reactant (butadiene in this case) with the LUMO of the electron-poor reactant (ethylene). 

The three- and four-layered schemes will be examined for two Diels-Alder reactions. The addition of acrolein to 2-t-butyl-1,3-butadiene will be examined with the threelayered ONIOM approach where the model will be taken as ethylene + butadiene, the intermediate model as acrolein 4-isoprene, and the real system as acrolein-f 2-l-butyl-1,3-butadiene. The three ab initio levels of theory will be G2MS CCSD(T)/6-31 G(d) -f MP2/6-311+G(2df,2p) -MP2/6-31G(d), MP4(SDQ), and MP2. This three-layered approach will be extended to a four-layered method by replacing the nine r-butyl hydrogens with methyl groups. This becomes the real system, acrolein -f 2-(trimethyl)-r-butyl-1,3-butadiene, with acrolein-f 2- -butyl-1,3-butadiene as the intermediate large model (int.L.model), acrolein -f isoprene as the intermediate small model (int.S.model), and ethylene-f butadiene as the small model (S.model). The four levels of theory are G2MS, MP4(SDQ), MP2, and HF. The geometry of the transition state and reactants have been optimized... 

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