Diels-Alder reactions basis sets

The two transition states in Figs 8.5 and 8.6 correspond in principle to a metal-catalyzed carho-Diels-Alder reaction under normal electron-demand reaction conditions and a hetero-Diels-Alder reaction with inverse electron-demand of an en-one with an alkene. The calculations by Houk et al. [6] indicated that with the basis set used there were no significant difference in the reaction course. 

Yamamoto et al. have developed a catalytic enantioselective carbo-Diels-Alder reaction of acetylenic aldehydes 7 with dienes catalyzed by chiral boron complexes (Fig. 8.10) [23]. This carbo-Diels-Alder reaction proceeds with up to 95% ee and high yield of 8 using the BLA catalyst. The reaction was also investigated from a theoretical point of view using ab-initio calculations at a RHF/6-31G basis set. 

This theory proves to be remarkably useful in rationalizing the whole set of general rules and mechanistic aspects described in the previous section as characteristic features of the Diels-Alder reaction. The application of perturbation molecular orbital theory as an approximate quantum mechanical method forms the theoretical basis of Fukui s FMO theory. Perturbation theory predicts a net stabilization for the intermolecular interaction between a diene and a dienophile as a consequence of the interaction of an occupied molecular orbital of one reaction partner with an unoccupied molecular orbital of the other reaction partner. 

Our results for the TS geometries for both reactions, obtained at the CASSCF(6,6)/4-31G level in the case of the Diels-Alder reaction [11] and at the CASSCF(6,6)/6-31G level in the case ofthe 1,3-dipolar cycloaddition [12], are in close agreement with the previous work of Houk and coworkers [28,29] and of McDouall et al. [30], respectively. All of our subsequent CASSCF and SC calculations were performed using the same basis sets as for the TS optimizations. 

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... 

Basis set orbitals for reactants (left) and product (right) in Diels-Alder reaction. 

This report stimulated considerable discussion among theoretical chemists. Borden and co-workers reported results of ab initio calculations indicating that the Diels-Alder reaction is, in fact, a synchronous reaction. These authors indicated, however, that this result was obtained "only when a flexible basis set is used and when electron correlation is properly treated." Otherwise, a nonsynchronous process was observed. Bemardi and coworkers also reported ab initio evidence for a S5mchronous Diels-Alder reaction. Houk and co-workers reported experimental evidence that the Diels-Alder reaction is concerted and is most likely synchronous as well. These authors also pointed out that different computational methods have built-in biases toward different transition structures. This controversy reminds us that, as noted before, computational methods should be considered as useful tools that are developed from particular conceptual models and not as windows into reality. ... 

Because of the relatively large number of atoms involved, only a few ab initio studies have been performed and only on the simplest Diels-Alder reaction, the addition of ethylene to 1,3-butadiene. The first ab initio studies were those of Burke et al. and of Townshend et a/. Burke et al. have carried out extensive calculations on the concerted approach of this reaction at the SCF level with an STO-3G basis set and have also recalculated several points on the hypersurface using a medium-size basis set (7s/3p). Townshend et al. have studied not only the concerted but also the two-step approach using an SCF treatment with limited Cl at the STO-3G level and have recalculated the energy pathways with an extended 4-3IG basis. However, even though these studies already involved a very signiflcant computational effort, they were performed without complete optimization and characterization of the critical points. 

Stanton and Merz examined more complex organic and organometallic reactions. Of particular interest is their work on the Diels-Alder reaction, the [1,5] sigmatropic shift of 1,3-pentadiene, and the reaction of ZnOH and CO2 to produce Zn + and HCOf. These studies used the gradient-corrected Becke exchange and Perdew correlation functionals. All calculations employed double- plus polarization level basis sets. 

The Diels-Alder reactions of 2,5-bis(trimethylsilyl)thiophene 1-oxide with dienophiles such as maleic anhydride and 1,4-benzoquinone are exclusively endo orientated and syn directed with respect to the S-O bond (Scheme 23) [36]. This stereochemistry is in good agreement with the results obtained from RHF and MP2 MO calculations using the 6-31G( ) basis set [37]. 

In the discussion of reaction paths of concerted reactions, it is helpful to classify transition states according to their aromatic properties. As an example, consider the Diels-Alder reaction between butadiene and ethylene. The transition state is shown in Fig. 2.15. Note that the orbitals of the basis sets are... 

Fig. 8.5 The calculated transition-state structure for the reaction of acrolein with butadiene leading to carbo-Diels-Alder adduct catalyzed by BH3 using a RHF/3-21G basis set [6]...

Individual activation energies from BP, BLYP, EDFl and B3LYP density functional models are similar (and different from those of Hartree-Fock and local density models). They are both smaller and larger than standard values, but typically deviate by only a few kcal/mol. The most conspicuous exception is for Diels-Alder cycloaddition of cyclopentadiene and ethylene. Density functional models show activation energies around 20 kcaPmol, consistent with the experimental estimate for the reaction but significantly larger than the 9 kcal/mol value obtained from MP2/6-311+G calculations. Overall, density functional models appear to provide an acceptable account of activation energies, and are recommended for use. Results from 6-3IG and 6-311+G basis sets are very similar, and it is difficult to justify use of the latter. 

---