Theoretical Studies of the b-Hydrogen Elimination from p-Allyl Palladium Complexes
Masato OSHIMA and Noriko INOUE
Organic synthetic reactions using allyl compounds with palladium catalyst were useful and many synthetic applications to construct the requisite carbon framework by C-C bond forming reactions were reported. As shown in Scheme 1, in most of these reactions, h3-allyl palladium intermediate was produced from allyl compounds with palladium(0) catalyst, then a succeeding nucleophilic attack of carbanion on the allylic moiety formed a new C-C bond. However, when the p-allyl ligand of the intermediate had b-hydrogen, the undesired diene product was sometimes obtained by b-hydrogen elimination.
b-Hydrogen elimination  is one of the fundamental reactions of organotransition metal complexes. Many examples about alkyl complexes were reported, nevertheless, the mechanism of b-hydrogen elimination for p-allyl complexes was not clarified.
In the case of the alkyl complexes, the reaction mechanism of b-hydrogen elimination is basically considered. In detail, the hydrogen at b-position interacts with metal centers, then the olefin eliminates via four centered transition states as shown in eq 1.
One representative example of b-elimination that has been studied kinetically is thermolysis of the iron alkyl complex (eq 2). Because the reaction was restrained by the additional PPh3 ligand, the first step of the reaction is the dissociation of PPh3 ligand to make a vacant coordination site on iron .
Most palladium(II) and platinum(II) complexes that have square planar shape are coordinatively unsaturated (16 electrons) stable complexes. The thermolysis mechanisms of cis-Pt(PPh3)2R2 have been studied in detail . The thermolysis of cis-Pt(PPh3)2Et2 in the absence of added tertiary phosphine proceeds by a dissociative mechanism, the rate-determining step being the formation of T-shaped dialkyl intermediate (Scheme 2, Path A). In the presence of added tertiary phosphine, the dissociative pathway is blocked, and the platinum dialkyl complex is compelled to decompose through five-coordinated intermediates (Path B).
In contrast to the platinum dialkyl complexes, thermolysis of trans-Pd(CH2CH3)2(PR3)2 is only slightly retarded by additional tertiary phosphine. Based on some experimental results, the thermolysis mechanism has been proposed as shown in Eq. 3 .
The transition state for b-hydrogen atom abstraction shown in Eq. 3 has been suggested on the basis of the extended Huckel MO calculations . For a b-hydrogen atom to be abstracted from an ethyl group, the two carbon atoms in the ethyl group, the b-hydrogen atom, and the metal atom must be coplanar. Furthermore, a bending of the M-C-C angle from its normal tetrahedral value of 109° may be required to bring the b-hydrogen atom into a region where it can interact with the d orbitals of the metal center. The bending of M-C-C angle from the normal tetrahedral angle has been found by ab initio calculation for a Ti-Et complex  and for a transition state in insertion of ethylene into a Rh-H bond in RhH2(Cl)(PH3)2 . The basic mechanism described above was established by subsequent theoretical studies .
Furthermore, in these mechanisms of alkyl complexes, because of the dynamic behavior, the b-hydrogen elimination of p-allyl complexes is complicated. Although the p-allyl ligand is observed as h3-form in the solid state by X-ray diffraction analysis, it can rapidly exchange from h3-allyl to h1-allyl in the solution (Eq. 4).
Researchers predict from this exchange, that the mechanism of b-hydrogen elimination of p-allyl ligand was that the geometry changes from h3-allyl to h1-allyl and a succeeding extraction of b-hydrogen produced diene product (Scheme 3). This idea is convenient because the reaction mechanism after the h1-allyl intermediate can be explained by the knowledge of alkyl complexes.
We can postulate the following seven pathways (Paths A-G) by considering the following alternatives. (1) b-Hydrogen elimination proceeds by h3-allyl or h1-allyl. (2) The reaction requires a vacant coordination site on palladium or not. (3) In case the b-hydrogen elimination proceeds h3-allyl, the extracted hydrogen is attached on either anti- or syn-carbon. (4) In case the b-hydrogen elimination proceeds h1-allyl, (5) an additional ligand assists in forming the h1-allyl intermediate or not. As shown in Scheme 4, 1,1-dimethyl-h3-allyl complex has two spectroscopically distinguishable kinds of b-hydrogen on anti- and syn-carbon. The fact suggests the following pathways.
It looks easy to distinguish these two pathways by experiment using the p-allyl complexes in which one of the methyl substitutent was labeled with deuterium atoms. Unfortunately, the anti-methyl and the syn-methyl groups can exchange smoothly at room temperature by another common dynamic behavior of p-allyl palladium complexes which is called p-s-p interconversion as shown in Eq. 5.
Because of the dynamic behaviors described above, it is impossible to clarify the detailed mechanism of b-hydrogen elimination of p-allyl ligand and only theoretical study can ascertain the detailed pathway. Herein, we wish to report a systematic theoretical study of b-hydrogen elimination of p-allylpalladium complexes.
2 Calculation Details
Assuming that the reaction proceeds in h3-allyl form with vacant coordination site, the phosphine ligand eliminates from palladium, and then succeeding extraction of b-hydrogen on anti- or syn-carbon occurs to produce diene intermediates. (Paths A and B in Scheme 5)
In case the b-elimination does not require a vacant coordination site, following two pathways via five coordinated transition states TS3 and TS4 could be considered. (Paths C and D in Scheme 6)
Two kinds of transition states can be considered in which the b-hydrogen elimination proceeds from h1-allyl intermediate. One passes through the four centered transition states TS5 from 7 that has h1-allyl ligand with agnostic interaction. Another pathway is via five centered transition states TS6.
Based on our previous calculations, coordinatively unsaturated h1-allyl species 11 could not converge as an intermediate, and then we did not calculate reaction pathways via 11. Two pathways could be assumed from complex 1 to intermediate 7. One was that a b-hydrogen atom close to palladium like TS7 and a C=C moiety of allyl ligand dissociated from palladium with transformation from h3-allyl to h1-allyl at the same time (Path E in Scheme 8). The other was that h1-allyl intermediate 9 was produced by the coordination of an additional phosphine ligand and then a b-hydrogen atom close to palladium like TS9, with dissociation of phosphine ligand (Path F). From intermediate 9, the pathway via five coordinate TS6 to 10 with liberating diene was possible (Path G).
3 Computational Methods
All geometry optimizations, vibrational frequencies, and energy calculations were carried out with density functional theory (DFT)  at the B3LYP level  with mixed basis set in Gaussian98 program  and verified to be either minima or transition states from their Hessian matrices for all reactions: minima for all positive eigenvalues and transition states for only one negative eigenvalue. The mixed basis set contains LANL2DZ  for palladium, carbon, and hydrogen atoms and LANL2DZ with diffuse function for phosphorus atom .
4 Results and Discussion
We had calculated all pathways and explored transition states TS1-9. Different from the neutral dialkyl palladium complexes, five coordinate transition states for b-hydrogen elimination, such as TS3, TS4, and TS6 did not converge. In TS3 and TS4 cases, as the b-hydrogen approached to palladium, h3-allyl changed to h1-allyl form, and it seem to became TS5. In spite of several tries, we could not find TS6 and TS7. In the calculations for TS6 and TS7, these species showed over 40 kcal/mol higher potential energy at SCF level than each precursor. From these results, we concluded the Paths C, D, E, and G were unreal. Although we also could not find out TS8 and TS9, it could be understood that there were no transition states between 1 to 9 and 9 to 7 for the following reasons. When the calculations for the exploring TS8 were performed while bringing a phosphine ligand close to the palladium atom of 1, their potential energies smoothly became higher without any maximum of the energy and 9 was obtained. Similarly, the calculations assuming a phosphine ligand was close to the palladium atom of 7 were finally to give 9 with smooth dissociating of the b-hydrogen without any maximum potential energy.
The potential energies that were calculated from zero point energies of all intermediates and transition states in Paths A and B are shown in Figure 1. Coordinatively unsaturated intermediate 2 had 24.57 kcal/mol higher potential energy than 1. In previous calculations, we confirmed that there was no transition state between 1 and 2. The structures of 1 and 2 with selected bond lengths (A) and angles (°) are shown in Figure 2. By the dissociation of the phosphine ligand of 1, Pd1-C2 of 2 was shorter than that of 1 and the other side of h3-allyl ligand (C4) was leaving the palladium center. The remaining phosphine ligand of 2 was moved to vacant side and the angle of C2-Pd1-P was changed from 94.9° to 163.7°.
Starting from 2, two transition states TS1 and TS2 that had one imaginary frequency with 633.0i and 683.6i, respectively, were found and these structures are shown in Figure 2 with selected bond lengths (A) and angles (°). The transition state TS1 corresponded to the one where the b-hydrogen (H16) on syn-carbon (C13) was extracted by palladium. On the other hand, the transition state that the b-hydrogen (H17) on anti-carbon (C5) was extracted was found as TS2. The diene intermediates 3 and 4 were obtained from 2 via TS1 and TS2 with 23.64 and 25.46 kcal/mol of activation energies, respectively. For the b-hydrogen to be abstracted, the four atoms of Pd1, C4, C13, and H16 in TS1, and of Pd1, C4, C5, and H17 in TS2 must be coplanar. The sums of the interior angels of the each quadrangle that composed by four atoms were 356.5° for TS1 and 352.2° for TS2, respectively. It was indicated that the central four atoms at the transition state of TS1 were near to coplanar than those of TS2, and then the activation energy of Path A was lower than that of Path B. To make sure of the difference of the activation energy between TS1 and TS2, the calculations of TS1 and TS2 using P(CH3)3 instead of PH3 were performed, and then the activation energies 22.88 kcal/mol for TS1 and 24.72 kcal/mol for TS2 were obtained with the similar tendency. These results suggested that the elimination of b-hydrogen on syn-carbon (Path A) proceeded faster than that on anti-carbon (Path B).
Figure 1. Potential energies of Paths A and B. All energies were calculated from zero point energies [kcal/mol].
Figure 2. The structures of 1, 2, TS1, and TS2 with selected bond lengths (A) and angles (°).
The potential energy diagram of Path F that passed through the h1-allyl intermediate is shown in Figure 3. The h1-allyl intermediate 9 was produced by the coordination of additional PH3 to 1 without transition state, and then by exchanging one of the phosphine ligand for the b-hydrogen to give 7. The b-hydrogen elimination smoothly proceed from 7 via TS5 that had 404.3i of imaginary frequency with a low barrier (9.76 kcal/mol) to form diene-hydrido intermediate 5. The detailed structures of 5, 7, 9, and TS5 are shown in Figure 4.
The intermediate 9 was almost a square planar structure and the C2=C3 double bond moiety of allylic ligand was completely dissociated from the palladium atom. The intermediate 7 had a distorted square planar structure and C13-H16 bond (1.1567 A) was became elongated by the effect of the agnostic interaction between H16 and Pd1. Based on the sum of the interior angles of each quadrangle that was composed by the four atoms of Pd1, C4, C13, and H16 in TS5 was 359.3°, these atoms were almost located perfectly coplanar. Due to the stronger trans influence of hydrido ligand than that of olefinic ligand, greater elongation of Pd1-P20 than of Pd1-P6 were observed in both TS5 and 5.
Figure 3. Potential energies of Path F. All energies were calculated from zero point energies [kcal/mol].
Figure 4. The structures of 5, 7, 9, and TS5 with selected bond lengths (A) and angles (°).
It is obvious that Path F was smooth and more plausible than Path A in the presence of additional phosphine ligand, because of the large energy barrier of the beginning step in Path A due to the dissociation of a phosphine ligand from 1 to form 2. This result corresponded to the following fact. When there was much phosphine ligand in the reaction, a lot of by-product dienes tended to be produced. Because the reaction conditions suggest that mainly to generate dienes is undesirable for the investigation of palladium-catalyzed reaction, there is no systematic study for the producing dienes, but most of the researchers in this field have vaguely noticed the tendency.
The reaction pathways after the intermediate 3, 4, and 5 were not discussed in this study. On the basis of the knowledge about organometallic chemistry, it can be speculated that the diene moiety of these intermediates will release by some ligand exchange.
This work was partially supported by the "Academic Frontier" Project for Private Universities (2006-2008), matching fund subsidy from the Ministry of Education, Culture, Sports Science and Technology.
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