Under the usual conditions, the Pd-catalyzed arylation does not involve an electrophilic aromatic substitution reaction. On the basis of DFT calculations, we propose a mechanism for the Pd-catalyzed arylation that involves a proton abstraction by a carbonate or related ligand and that provides a satisfactory explanation for the experimental data.

A computational study with the Becke3LYP DFT functional is carried out on the cross-coupling reaction of vinyl bromide H 2 CdCHBr and vinylboronic acid H 2 CdCHB(OH) 2 catalyzed by palladium diphosphine [Pd(PH 3 ) 2 ] in the presence of an excess of base OH -. The full catalytic cycle is computed, starting from the separated reactants and the catalyst and finishing with the cross-coupled product and the regeneration of the catalyst. The different stages in the cycle (oxidative addition, isomerization, transmetalation, reductive elimination) are characterized through calculation of the corresponding intermediates and transition states. Different alternative mechanisms are considered, depending on the number of phosphine ligands at palladium, and on the cis or trans isomery around the metal center. The results indicate the existence of a number of competitive pathways of reasonably low energy.

The regioselectivity observed in the intramolecular palladium-catalyzed arylation of substituted bromobenzyldiarylmethanes as well as theoretical results demonstrate that the Pd-catalyzed arylation proceeds by a mechanism involving a proton abstraction by the carbonate, or a related basic ligand. The reaction is facilitated by electron-withdrawing substituents on the aromatic ring, which is inconsistent with an electrophilic aromatic-substitution mechanism. The more important directing effect is exerted by electron-withdrawing substituents ortho to the reacting site.

Palladium-catalyzed C-C cross-coupling reactions (Suzuki-Miyaura, Negishi, Stille, Sonogashira, etc.) are among the most useful reactions in modern organic synthesis because of their wide scope and selectivity under mild conditions. The many steps involved and the availability of competing pathways with similar energy barriers cause the mechanism to be quite complicated. In addition, the short-lived intermediates are difficult to detect, making it challenging to fully characterize the mechanism of these reactions using purely experimental techniques. Therefore, computational chemistry has proven crucial for elucidating the mechanism and shaping our current understanding of these processes. This mechanistic elucidation provides an opportunity to further expand these reactions to new substrates and to refine the selectivity of these reactions. During the past decade, we have applied computational chemistry, mostly using density functional theory (DFT), to the study of the mechanism of C-C cross-coupling reactions. This Account summarizes the results of our work, as well as significant contributions from others. Apart from a few studies on the general features of the catalytic cycles that have highlighted the existence of manifold competing pathways, most studies have focused on a specific reaction step, leading to the analysis of the oxidative addition, transmetalation, and reductive elimination steps of these processes. In oxidative addition, computational studies have clarified the connection between coordination number and selectivity. For transmetalation, computation has increased the understanding of different issues for the various named reactions: the role of the base in the Suzuki-Miyaura cross-coupling, the factors distinguishing the cyclic and open mechanisms in the Stille reaction, the identity of the active intermediates in the Negishi cross-coupling, and the different mechanistic alternatives in the Sonogashira reaction. We have also studied the closely related direct arylation process and highlighted the role of an external base as proton abstractor. Finally, we have also rationalized the effect of ligand substitution on the reductive elimination process. Computational chemistry has improved our understanding of palladium-catalyzed cross-coupling processes, allowing us to identify the mechanistic complexity of these reactions and, in a few selected cases, to fully clarify their mechanisms. Modern computational tools can deal with systems of the size and complexity involved in cross-coupling and have a continuing role in solving specific problems in this field.

The role of the base in the transmetalation step of the Suzuki-Miyaura cross-coupling reaction is analyzed computationally by means of DFT calculations with the Becke3LYP functional. The model system studied consists of Pd(CH=CH2)(PH3)2Br as the starting catalyst complex, CH2=CHB(OH)2 as the organoboronic acid, and OH- as the base. The two main mechanistic proposals, consisting of the base attacking first either the palladium complex or the organoboronic acid, are evaluated through geometry optimization of the corresponding intermediates and transition states. Supplementary calculations are carried out on the uncatalyzed reaction and on a process where the starting complex is Pd(CH=CH2)(PH3)2(OH). These calculations, considered together with available experimental data, strongly suggest that the main mechanism of transmetalation in the catalytic cycle starts with the reaction of the base and the organoboronic acid.

A DFT study of R-R reductive elimination (R = Me, Ph, vinyl) in plausible intermediates of Pd-catalyzed processes is reported. These include the square-planar tetracoordinated systems cis-[PdR(2)(PMe(3))(2)] themselves, possible intermediates cis-[PdR(2)(PMe(3))L] formed in solution or upon addition of coupling promoters (L = acetonitrile, ethylene, maleic anhydride (ma)), and tricoordinated intermediates cis-[PdR(2)(PMe(3))] (represented as L = empty). The activation energy ranges from 0.6 to 28.6 kcal/mol in the gas phase, increasing in the order vinyl-vinyl < Ph-Ph < Me-Me, depending on R, and ma < "empty" < ethylene < PMe(3) approximately MeCN, depending on L. The effect of added olefins was studied for a series of olefins, providing the following order of activation energy: p-benzoquinone < ma < trans-1,2-dicyanoethylene < 3,5-dimethylcyclopent-1-ene < 2,5-dihydrofuran < ethylene < trans-2-butene. Comparison of the calculated energies with experimental data for the coupling of cis-[PdMe(2)(PPh(3))(2)] in the presence of additives (PPh(3), p-benzoquinone, ma, trans-1,2-dicyanoethylene, 2,5-dihydrofuran, and 1-hexene) reveals that: (1) There is no universal coupling mechanism. (2) The coupling mechanism calculated for cis-[PdMe(2)(PMe(3))(2)] is direct, but PPh(3) retards the coupling for cis-[PdMe(2)(PPh(3))(2)], and DFT calculations support a switch of the coupling mechanism to dissociative for PPh(3). (3) Additives that would provide intermediates with coupling activation energies higher than a dissociative mechanism (e.g., common olefins) produce no effect on coupling. (4) Olefins with electron-withdrawing substituents facilitate the coupling through cis-[PdMe(2)(PR(3))(olefin)] intermediates with much lower activation energies than the starting complex or a tricoordinated intermediate. Practical consequences are discussed.

in which the nonlinear optical (NLO) response strikingly improved with double heteroaromatic rings. Herein, series of triphenylamine−dicyanovinylene based donor−π−acceptor dyes had been designed by structural tailoring of π-conjugated linkers and theoretical descriptions of their molecular NLO properties were reported. Density functional theory and timedependent density functional theory calculations were performed on optimized geometries to elucidate the electronic structures, absorption spectra, and NLO properties and also to shed light on how structural modification influences the NLO properties. The simulated absorption spectra results indicate that all of the dyes showed the maximum absorbance wavelength in the visible region. The lowest unoccupied molecular orbital−highest occupied molecular orbital energy gaps of all of the dyes have been found smaller, which results in large NLO response. Calculation of natural bond orbital analysis reveals that electrons successfully migrated from donor to acceptor via π-conjugated linkers and a charge separation state was formed. High NLO response revealed that this class of metal free organic dyes possess eye-catching and remarkably large first hyperpolarizability values, especially D8 with highest ⟨α⟩ and β tot computed to be 771.80 and 139 075.05 au, respectively. Our research presented a vital confirmation for controlling the kinds of π-conjugated linker that was a significant approach for the design of new appealing NLO compounds. This theoretical framework also highlighted the NLO properties of organic dyes that can be valuable for their uses in modern hi-tech applications.

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