What makes for a good catalytic cycle? A theoretical study of the role of an anionic palladium(0) complex in the cross-coupling of an aryl halide with an anionic nucleophile

The cross-coupling reaction Ar-X + Nu(-) -> Ar-Nu + X-, catalyzed by Pd(0) complexes, was studied theoretically by means of DFT calculations; Ph-Cl was used as a substrate and HS- as the nucleophile. The studied catalysts are the pristine Pd(0) complexes Pd-0-(PR3)(2) (1(R); R = H, vinyl, Ph), the corresponding anionic complexes Pd-0(PR3)(2)Cl- (1(R,Cl)), proposed by two of us (C.A. and A.J.), and the chelated complexes with diphosphine ligands PH2(CH2)(n)PH2 (2(H,n); n = 2-6). The full catalytic cycles were studied for 1(H), 1(H,Cl), 2(H,3), and 2(H,6). The efficiency of a catalytic cycle under turnover conditions is determined by the energetic span, the energy difference between the summit and trough of the cycle; the smaller the energy span, the higher the turnover frequency of the cycle. In this sense, the best Pd(0) catalyst was found to be the anionic 1(H,Cl) species. The DFT analysis shows that the anionic catalyst so formed is superior to the pristine species, since it "flattens" the energy landscape of the catalytic cycle by stabilizing the transition state for oxidative addition, the summit of the cycle, and at the same time "destabilizing" the nucleophilic addition product, the deepest point of the cycle. This is precisely the role deduced initially from experimental evidence. Thus, during substrate activation, the Cl- ion keeps a small P-Pd-P angle, which is a prerequisite for a low activation barrier to oxidative addition. During nucleophilic substitution, the Cl- additive is displaced by the nucleophile, and hence the stabilizing advantage is lost, thereby raising the substitution product complex relative to the onset of the reactants. After product release, Cl- returns to regenerate the anionic catalyst, Pd-0(PR3)(2)Cl-, which in turn binds the substrate and prevents its diffusive escape, thereby ensuring an efficient restart of the cycle.