DFT Study on the Oxidative Addition of 4-Substituted Iodobenzenes on Pd ( 0 )-Phosphine Complexes

The oxidative addition of 4-substituted iodobenzenes on Pd(0)-PMe 3 complexes has been studied at the BP86 level of theory including dispersion correction and solvation effect, with tetrahydrofuran as solvent. The bisphosphine pathway was found to be barrierless, whereas themonophosphine route is hampered by the high dissociation energy of trimethylphosphine.The reaction free energy of this step shows linear correlationwith theHammett constants of the para substituents with themost electronwithdrawing groups being the most exergonic.


Introduction
Palladium-catalyzed cross-coupling reactions are the most prominent examples in the family of carbon-carbon bondforming reactions, which have gained enormous popularity in the last few decades [1,2] and are found in all areas of chemistry, from polymers to pharmaceuticals and agrochemicals [3].The Suzuki-Miyaura reaction is one of the most frequently used methods to form C-C bond in a catalytic way [4], but the number of applications employing Sonogashira coupling is drastically increased in the recent years as well [5].Other Pd-catalyzed cross-coupling reactions, such as Stille [6,7], Tamao et al. [8], and Baba and Negishi [9] couplings, have their important role in organic synthesis as well.
In general, the barriers of oxidative addition of aryl halides increase in the order of ArI < ArBr < ArCl consistent with the reactivity order reported by Fitton and Rick [27].Aryl halides with electron withdrawing groups give smaller barriers than those having electron donating groups [10].As a catalytically active complex, Pd(0)L 2 is usually considered as reference point due to its relative stability.The Pd(0)L 2 complex then reacts with the aryl halide in a concerted manner affording the complex Pd(II)X 2 L 2 (X = halide).Depending on the basicity, and the bulk of the phosphine, PdL complexes, formed after the dissociation of one phosphine ligand, should be considered as viable alternatives for active catalysts in some specific cases [18,19].The bisphosphine and monophosphine pathways are illustrated in Scheme 1.
The goal of this study is to explore how the substituents in para position influence the energetics of the oxidative addition of iodobenzenes on Pd(0)-PMe 3 complexes taking into consideration both the bisphosphine and monophosphine pathways.Our objective is also to get some insight about the electronic structure of Pd-PhI adducts which occur in both pathways.

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Scheme 1: Comparison of the bisphosphine and monophosphine pathways.

Computational Details
All structures were fully optimized at the DFT/BP86 level of theory [28,29] with ultrafine grids, assuming THF as solvent, employing the Gaussian 09 suite of programs [30].
The dispersion correction developed by Grimme et al. has been employed with Becke-Johnson damping and denoted by BP86-D3 [31].For palladium and iodine the def2-TZVP whereas for the other atoms the def2-SVP basis sets were used [32].Local minima were identified by the absence of the negative eigenvalues in the vibrational frequency analyses, whereas the Hessian matrix of transition states has only one negative eigenvalue.Gibbs free energies were calculated at 298.15 K. Intrinsic reaction coordinate (IRC) analyses [33] were carried out at the same level as the geometry optimizations in order to make sure that the corresponding local minima and transition states are smoothly connected to each other.The effect of the solvent was taken into account utilizing the SMD solvation model [34], introduced by Marenich et al., with the dielectric constant of  = 7.4257 for tetrahydrofuran.The SMD method is based on the charge density of a solute molecule interacting with the solvent represented as continuum.The full solute electron density is employed without the definition of partial atomic charges; therefore, "" stands for "density" in the abbreviation of the model.As in the previous SMx solvation models ( = 1-8) developed by the Minnesota group the solvent is represented as a dielectric medium with surface tension at the solute-solvent boundary.
For the QTAIM (Quantum Theory of Atoms In Molecules) calculations the AIMAll software package was utilized [35].

Results and Discussion
It is known that increasing the phosphine basicity is advantageous to the activity of the catalytic system.It was also shown that sterically more demanding phosphines tend to turn the monoligated pathway as the preferred one.For this study the less bulky, yet strongly basic trimethylphosphine has been selected.For catalytically active complexes both Pd(PMe 3 ) 2 (1) and Pd(PMe 3 ) (2) have been taken into consideration in order to decide whether the monoligated or the bisligated pathways are dominating for the various substituted iodobenzenes at the BP86/SMD level of theory including dispersion correction.
The dissociation of one PMe 3 from complex (1) undergoes with a free energy of 31.2 kcal/mol, which is notably higher than that obtained by Lam and coworkers (20.5 kcal/mol) at B3LYP level with double- basis set, without solvation corrections [19].As expected, the remaining PMe 3 is bound stronger to Pd, which is reflected in the shorter Pd-P bond distance (2.163 Å) as opposed to that in complex 1 (2.282Å) (Figure 1).
In order to unravel the strong dependence of the dissociation free energy (Δ diss ) of trimethylphosphine from 1 the reaction free energy for the 1 → 2 + PMe 3 process has been recomputed with the BP86 functional investigating the effect of solvation and dispersion corrections.Surprisingly, the neglect of solvent effects resulted in a Δ diss being only slightly higher than the original value (32.2 kcal/mol), whereas at the BP86/SMD level (without D3 correction) 24.7 kcal/mol has been obtained, being fairly close to Δ diss = 20.5 kcal/mol achieved with the B3LYP functional [19].
For the pathway involving complex (1) iodobenzene coordinates with the palladium center in a  2 -like manner (Figure 2) resulting in the adduct 4a.The coordination causes a slight increase in Pd-P bond length, as well as in the distance of the coordinating carbon atoms going from 1.407 Å to 1.462 Å.The coordination is exergonic by −7.3 kcal/mol.
The oxidative addition step itself is very facile.The free energy difference between 4a and transition state 5TSa is 6.7 kcal/mol, meaning that the overall activation free energy is −0.6 kcal/mol; thus, it is below the sum of the free energies of the separated reactants.As a result of this process a somewhat distorted square planar Pd(II)-iodo-phenyl complex is formed (6a) where the phenyl group is perpendicular to the plane spanned by the phosphines and the iodo ligand.The formation of 6a is exergonic by −36.7 kcal/mol with respect to the summed free energies of 1 and 3a.
The dissociative pathway starts with the dissociation of one PMe 3 with a bond dissociation free energy of 31.2 kcal/mol (vide supra) giving rise to the monoligated complex Pd(PMe 3 ) (2).The coordination of iodobenzene (3a) is notably more exergonic (−17.8 kcal/mol) in comparison to that of the more saturated complex (1).The coordination type is, however, more like  1 -C, compared to  2 -(C,C) according to the significant difference in bond lengths between palladium and the coordinating carbon atoms.The oxidative addition step then proceeds via transition state 8TSa with a barrier of 0.8 kcal.The formation of the T-shaped Pd(II) complex 9a is endergonic by 27.3 kcal/mol.The closing step of the dissociative oxidative addition pathway is the  coordination of PMe 3 to the vacant site on Pd resulting in 6a.The free energy associated with this process is −13.1 kcal/mol, meaning that trimethylphosphine is much less weakly bound in 6a than in 1.
The concerted and the dissociative pathways are compared in Figure 3.A clear preference for the former one is predicted at the BP86-D3 level of theory with virtually no barrier due to the relatively high stability of the transition state 5TSa.
In order to get more insight into the electronic structure of iodobenzene adducts and the oxidative addition transition state, QTAIM calculations [36] have been performed and the Laplacians of the electron densities are depicted in Figure 4.The visual inspection of the Laplacian distribution of 4a shows a close resemblance to that of olefin complexes, for instance, in W(CO) 5 (C 2 H 4 ) [37], where the distortion in electron density distribution also emphasizes the presence of a donor interaction.The existence of bond paths between Pd and two carbons in iodobenzene suggests that the coordination mode is indeed  2 -(C,C).On the other hand, the corresponding carbon atoms in 7a show difference not only in the distance to Pd, but also in the lack of the second Pd-C bond path, and much less distortion in the density distribution of the second carbon.Hence, the coordination mode in the more unsaturated Pd-iodobenzene complex is undoubtedly of  1 -C type.
The Laplacian distribution of transition state 5TSa reveals the presence of a three-center Pd-C-I bond with bond paths between these three atoms.The electron density distribution around the carbon atom shows significant distortion towards the iodine, which may be responsible for the high relative stability of 5TSa in terms of free energy.
The substituent effect for the oxidative addition of 4substituted iodobenzenes was investigated with some representative functional groups spanning the range of Hammett  para constants between −0.83 and 0.78.The free energies of the iodobenzene coordination, the oxidative addition, and the activation free energies were collected in Table 1 for the bisphosphine pathways and in Table 2 for the monophosphine pathways.
In terms of the bond free energy between the iodobenzenes and the palladium containing fragment the substituents show a quite strong dependence on   .For the electron donor groups, such as OMe, and Me the coordination strength is rather weak.Moreover, the iodobenzene coordination and dissociation are almost in equilibrium in the case of the NMe 2 substituent.On the other hand, for the strongly electron withdrawing groups CN and NO 2 the free energy of coordination exceeds −10 kcal/mol.
Interestingly, the free energy difference between the adducts (4) and the transition states (5TS) shows notable difference only for the most electron donating substituents.For NMe 2 , and OMe, this difference is only 1.7 and 2.0 kcal/mol, respectively.On the other hand, it is 5.0 kcal/mol for the methyl group and 6.2 kcal/mol for the nitro group, and difference in free energies falls in this range for all the  (4a) (5TSa) (7a) other substituents.It is important to emphasize, however, that the oxidative addition is very facile in the case of the bisphosphine pathway, regardless of the substituents on iodobenzene, and can be considered as barrierless.This is in contrast with the experimental [13] and theoretical [20] findings with basic, but bulky, phosphines, where the free energy barrier for the oxidative addition of PhI was found as 24.6 and 28.4 kcal/mol, respectively, emphasizing the key role of the ligand bulk upon the reaction mechanism.The reaction free energies for the oxidative addition, following the bisphosphine pathway, however, reveal strong dependence on the Hammett para constants.A reasonable linear correlation  2 = 0.954 has been obtained between Δ and   .The correlation diagram is depicted in Figure 5.The free energy of coordination of iodobenzenes to the highly unsaturated complex 2 shows a peculiar dependence upon the substituent constant (see Table 2).For the electron donating groups, NMe 2 , OMe, and CH 3 , more stable  1 -C complexes are formed with free energies of only 3.5-5.8kcal/mol above that of the sum of 2 and 3. Neutral and electron withdrawing substituents, however, fall into another category with relative free energies over 10 kcal/mol with respect to 2 + 3. Interestingly, the relative stability of transition states 8TS shows an opposite trend revealing the highest barrier (15.8 kcal/mol) for the methoxy group and the lowest barrier (11.7 kcal/mol) for the cyano group.On the other hand, the relative free energies of the threecoordinate complexes 9 show no obvious dependence on   .For all substituents the barriers exceed those obtained for the bisphosphine pathway; thus, the monophosphine route (i.e., the dissociative mechanism) is disfavored in all cases.

Conclusion
A DFT study employing the BP86-D3 theory was carried out utilizing the SMD solvation model with THF as solvent in order to shed some light on the mechanism of the oxidative addition of 4-substituted iodobenzenes on Pd(0)-PMe 3 complexes.The bisphosphine pathway starting from complex Pd(PMe 3 ) 2 (1) is compared with the monophosphine route, where the addition of iodobenzenes is preceded by the dissociation of the PMe 3 ligand resulting in complex 2, as catalyst.
It can be concluded that this elementary step, with PMe 3 , as ligand, is expected to take place in a very fast reaction.The bisphosphine pathway is predicted to be the viable route regardless of the para substituents for two reasons: (i) the very facile addition of 3a-h to 1 and (ii) the high dissociation free energy of the PMe 3 ligand, which results in an overall barrier of 31.2 kcal/mol for the monophosphine pathways.The reaction free energy of the oxidative addition shows linear correlation with the Hammett constant of the para substituent, with the most electron withdrawing groups being the most exergonic.
These results suggest that, in accord with previous findings, palladium complexes with basic and sterically not demanding phosphines may serve as highly active catalyst for cross-coupling reactions where oxidative addition is ratedetermining.The strong preference for the bisphosphine pathway, however, emphasizes that the phosphine should be employed at least in a 2 : 1 ratio with respect to palladium, when the catalyst is formed "in situ."

Figure 2 :
Figure 2: Computed structures of the intermediates and transition states associated with the oxidative addition step.Bond distances are given in Å.

Figure 3 :
Figure 3: Gibbs free energy diagram of the oxidative addition for the concerted (black) and the dissociative (grey) pathways.

Table 1 :
Computed activation free energies and reaction free energies (in kcal/mol) for the oxidative addition of 4-substituted iodobenzenes following the bisphosphine pathway.The gibbs free energy of activation.

Table 2 :
Computed activation free energies and reaction free energies (in kcal/mol) for the oxidative addition of 4-substituted iodobenzenes following the dissociated pathway.The opening step that is the dissociation of one trimethylphosphine needs a free energy of 31.2 kcal/mol.Free energy values are relative to the sum of those of Pd(PMe 3 ) 2 and the corresponding iodobenzenes.