The addition of an allylic metal reagent to an olefin (eq 1) is isoelectronic with the aldol reaction between an enolate and a carbonyl compound, yet it has attracted far less attention than the latter because of intrinsic difficulty to carry out the reaction (note that the former is less exothermic than the latter). The reaction however is no less interesting than the aldol reaction from stereochemical and synthetic points of view, as it creates three contiguous chiral centers in one operation. The factors to be controlled are, however, more complicated than those in the aldol reaction. In order for this reaction to become useful for synthesis of diastereomerically and enantiomerically pure molecules, the reaction must show high levels of SE2'-regioselectivity for the allylic metal reagent, 1,2-simple diastereoselectivity in regard of the forming C3- C4 bond, and enantiotopos selectivity with respect to the acceptor olefinic face. We started sometime ago to investigate the control of these issues in the allylzincation of cyclopropenone acetals and reported that proper choice of neutral and anionic ligands on the metal atom allows us to achieve very high levels of control of the diastereoselectivity (as well to achieve as enhancement of reactivity).
Extension of these findings subsequently led us to find that an allylic zinc reagent bearing an anionic bis-oxazoline ligand takes place with excellent enantioselectivity (eq 2). For instance, the reaction of the cyclopropenone acetal 3 with an allylic zinc bromide in the presence of one equivalent of the anionic bis-oxazoline ligand 2a proceeded smoothly at room temperature to afford the cyclopropanone acetal 4 in high yield with the enantioselectivity better than 98% ee. On the other hand, in the reaction of substituted allylic zinc reagents, e.g., cinnamylzinc reagent, both the enantioselectivity and the 1,2-diastereoselectivity for the newly formed C-C bond eroded rather mysteriously. Interpretation of the mixed success and the resolution of these problems by analysis with pencil and paper appeared to be difficult since very little was known for the nature of the olefin carbometalation reactions. We thus felt it necessary to obtain molecular-level understanding of the stereochemistry of allylmetalation of olefins by computational analysis. By following the protocol we have established previously for carbometalation reaction with organolithium and copper reagents, we first analyzed the reaction with ab initio calculations for simple models, and then with semiempirical methods for larger systems. By taking advantage of the capability of electronic publication to handle 3D pictures, we present herein our the computational studies with 3D molecular pictures of various transition structures of olefin allylmetalation reactions.
Before describing our computational work, summary of the experimental results of the enantioselective allylzincation of cyclopropenone acetal will be presented first. Asymmetric allyl- and prenylzincation reactions of CPA3 were first examined by using chiral bis-oxazoline ligand 2a (eq 2). The allylation reaction proceeded smoothly at room temperature to afford 4 in 89% yield with 98% ee. Addition of prenylzinc reagent to CPA 3 also proceeded in the presence of a ligand 2a with exclusive SE' selectivity to give allylation product 5 in 90% yield with high enantioselectivity (93% ee). Enantioselective allylation and prenylation of 3 in the presence of the anionic ligand 2b afforded allylzincation product 7 and 8 in good yield with comparable enantioselectivity to those of ligand 2a (eq 3). Both the isopropyl-substituted and the phenyl-substituted ligands 2a and 2b can be recovered after the allylzincation reaction.
The addition of a substituted allylic zinc reagent creates an issue of mutual face selection for the two olefinic faces of both reactants, that is, 1,2-diastereoselectivity concerning the newly formed C-C bond. The reaction of substituted allylic zinc reagents 9, 10 and 11 were thus examined in the presence of anionic bis-oxazoline ligand (2a or 2c) as shown in eq 4. As summarized in Table 1, the diastereoselectivity for crotylzinc reagent 9, cinnamyl reagent 10 and perhydrocinnamyl reagent 11 was moderate and 72:28, 73:27 and 83:17, respectively, and when the anionic bis-oxazoline ligands 2a and 2c was used. The use of t-butyl substituted ligand as in 11 did not improved the 1,2-diastereoselectivity (entries 3 and 4) while it greatly improved the enantioselectivity from 62 to 97%.
The 1,2-diastereoselectivity of the addition of a metal enolate or an allylic metal reagent to a carbonyl group conventionally calls for chair and boat transition states. On the other hand, we have reported previously in a preliminary form that the allylmetalation of isolated C-C double bond and triple bond may proceeds through a single half chair transition state. We thus suspected that the flexibility of the half chair transition state may be the reason for the erosion of the selectivity, and started to investigate the details of the transition state first at the ab initio level for simplified model systems and then at the semiempirical level for more realistic models.
Calculations were performed with a GAUSSIAN 92 program and MOPAC ver 6.0 for the ab initio and MNDO calculations, respectively. The transition structures were optimized with the Hartree-Fock method. In ab initio calculations, for the zinc atom, the inner-shell (from 1s to 3d) electrons were replaced by an effective core potential (ECP). The potential parameters employed in out calculations are those given by Hay and Wadt. The remaining electrons were described by basis functions of double-ζ quality. For all other atoms, the 3-21G basis set was used for geometry optimizations.
Simplified models: Ab initio calculation of allylzincation of cyclopropene
In the prototypical reaction of allylzinc chloride with cyclopropene without any extra ligand, we could locate two (and only two) diastereomeric transition structures TS A and TS B (Figure 1), which differ from each other with respect to the relative arrangement of the cyclopropene ring and the allylic moiety. Both TSs have half-chair conformation owing to the requirement of planar arrangement of C3-C4-C5-Zn to maximize the orbital interaction. The energy difference is rather small (0.76 kcal) in spite of the fact that the C3-C4 eclipsed conformation in TS A provides seemingly disadvantageous steric effects which is not present in the staggered conformation in TS B. The long distance between C3 and C4 (2.5 angstrom) likely lessens the C- H/C- H torsional strain.
Solvent effects were then investigated by adding one molecule of water (a model for an ethereal solvent) on the metal so that coordinative saturation is achieved (Figure 2). It is notable that solvation does not affect much the gross molecular geometry of the TSs, only elongating the forming C4-C5 and C1-Zn bond by 1-2%. Apparently, the electronic background that determines the basic half chair conformation (vide supra) is strong enough not to allow large structural perturbation by a solvent molecule. The relative energy of the two TSs was however raised slightly to 1.29 kcal/mol, suggesting that solvation may significantly affect the stereoselectivity..
Finally, the reaction of water-solvated crotylzinc chloride with cyclopropene was studied. We also found two TSs of nearly equal energy as shown in Figure 3. The calculated energy difference (0.369 kcal/mol) at this level of approximation of solution reactions should be viewed as negligible, yet some important characteristics were noted. First, only the half-chair TSs are available for the reaction as in the previous models. Second, there may occur some torsional strain for the forming C3- C4 bond in TS E (indicated by an arrow) which may slightly destabilize this transition structure. In TS F, on the other hand, the short distance (2.593 angstrom) between the two asterisked hydrogens suggests that TS F would be significantly destabilized if H** is replaced by an alkoxy group as in our actual substrates CPA 3.
Computational analysis of the enantioselectivity by MNDO calculations.
We next examined the origin of enantioselectivity in the addition of allylzinc reagent with the anionic bis-oxazoline ligand to cyclopropenone propanediyl acetal. The reactants in this model reaction differ from the reality only for the omission of the gem-dimethyl groups in the acetal. Since the bis-oxazoline ligand is too large to be optimized by the ab initio calculations, we employed the MNDO hamiltonian for these calculations. We first made comparison between the HF/3-21G and the MNDO methods for the transition structure of allylzinc addition to cyclopropene to find that the latter reproduced the former with acceptable level of precision (with slight underestimation of the forming C-C and C-Zn bond lengths as indicated in Figure 4). We found that the PM3 parameters in MOPAC ver 6.0 gave totally incorrect geometry for Zn-containing TSs.
The model reaction studied by the MNDO method is the allylzincation of cyclopropenone acetal 16, lacking the gem-dimethyl groups in 3, which gives rise to two enantiomers 17 (experimental major enantiomer) and 18 (minor isomer ) (eq 5). Two conformationally isomeric TSs are available for each enantiomer, and in Figures 5a and 5b are shown these four possible TSs. The TSs are fully optimized by the MNDO method without any structural restriction. The values in the parentheses refer to the computed relative heat of formation (Figure 5a). TS G and TS H differ from each other for the orientation of the allylic moiety relative to the ligand and produces the enantiomer 17. Similarly, TS J and TS I lead to the minor isomer 18. TS G and TS H are found to be ca. 1 kcal/mol preferred than TS I and TS J. The calculated enantioselectivity from the energy difference is 91:9 at 20 degree and this result reproduces the experimental trend (>99:1). Topological relationship between the ligand isopropyl groups and the acetal group is schematized in Scheme 2, illustrating that the enantioselectivity with respect to the cyclopropenone acetal olefin is determined by steric interaction between the bis-oxazoline substituents and the bulky acetal group. In other way of viewing the matter, one may perceive that the six-centered TS of the allylzincation is recognized by the chiral "cleft" formed by the two isopropyl groups.
One notable structural feature in these TSs is the tetrahedral coordination geometry for the metal, which is well protected by the bulky ligand. The lack of chelation between the metal and the acetal oxygen is noteworthy. These structural features agree well with the experimental observations that the solvent basicity (e.g., THF vs. CH2Cl2) or the presence of very basic ligand (e.g., HMPA) did not affect much the selectivity. This latter observations stand in contrast to the fact that stereochemistry of the simpler allylic zinc reagents (e.g., allylzinc bromide) is highly susceptible to solvent effects. 
With a substituted allylic zinc reagent such as cinnamylzinc reagent, the degeneracy of the product in Figure 5 disappears and each four TSs lead to four different products, two enantiomeric and two diastereomeric pairs. In Figure 6 are shown the four possible transition structures of the reaction of CPA 16 with a cinnamylzinc possessing chiral ligand 2a (eq 6).
Each TS G', H', I' and J' gives corresponding four different cyclopropylzinc product 19, 20, 21 and 22, respectively. The energy difference corresponds to the product ratio of 85.7:8:6:0.3 at 20 degree. The enantiotopos selectivity and relative diastereoselectivity expected from the calculated difference of heat of formation is 94:6 and 92:8, respectively. Although these ratios are much higher than those obtained experimentally (i.e., 78:22, 73:27), the computational result correctly predicts the formation of 19 as a major diastereomer and the formation of the minor diastereomers 21 and 22 derived from TS H' and TS J'.
In TS G', one can observe the minimum steric interactions among the isopropyl group of ligand 2a, the phenyl substituent of the cinnamyl zinc moiety, and the acetal moiety of 16. In contrast, significant steric repulsion among the acetal moiety of 16, phenyl substituent of cinnamyl moiety and isopropyl group of the chiral ligand is observed in TS J', thus the increment of the steric hindrance in TS caused the larger energy difference (3.27 kcal/mol) than that of the allylzinc addition case. (The steric interactions discussed above will be readily understood, if the readers take a look at the space-filling 3D models linked to Fig. 6, which are to be clicked once.) The heat of formation of TS H' is now higher than TS I' in spite of the favorable orientation of CPA. The inversion of the order of stability indicated the lowering of optical purity of major diastereomer, which was indeed observed experimentally.
In summary, the ab initio calculations indicated that the allylmetalation of cyclopropene proceeds via two diastereomeric half chair transition states of similar energies. The MNDO calculations, which reproduce the essential feature of the ab initio structures for the simplified model TS, offered us not only pictorial but energetic understanding of the experimental selectivities. The accuracy of the MNDO calculations was found to be high enough to predict the sense of the selectivities but is not enough to predict the degree of the selectivities. In addition, the lack of suitable theoretical method in the semiempirical calculations did not allow us to understand the background reasons for the selectivities. We would hope that some future advances in theory  will allow us not only to predict the experimental data but also to achieve theoretical understanding of the prediction.
We thank the Ministry of Education, Science and Culture, Japan for financial support, and the Institute for Molecular Science, Japan for computational time.