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Modern density functional theory and powerful contemporary computers have made it possible to explore complex reactions of value in organic synthesis. We describe recent explorations of mechanisms and origins of stereoselectivities with density functional theory calculations. The specific functionals and basis sets that are routinely used in computational studies of stereoselectivities of organic and organometallic reactions in our group are described, followed by our recent studies that uncovered the origins of stereocontrol in reactions catalyzed by (1) vicinal diamines, including cinchona alkaloid-derived primary amines, (2) vicinal amidophosphines, and (3) organo-transition-metal complexes. Two common cyclic models account for the stereoselectivity of aldol reactions of metal enolates (Zimmerman-Traxler) or those catalyzed by the organocatalyst proline (Houk-List). Three other models were derived from computational studies described in this Account. Cinchona alkaloid-derived primary amines and other vicinal diamines are venerable asymmetric organocatalysts. For α-fluorinations and a variety of aldol reactions, vicinal diamines form enamines at one terminal amine and activate electrophilically with NH(+) or NF(+) at the other. We found that the stereocontrolling transition states are cyclic and that their conformational preferences are responsible for the observed stereoselectivity. In fluorinations, the chair seven-membered cyclic transition states is highly favored, just as the Zimmerman-Traxler chair six-membered aldol transition state controls stereoselectivity. In aldol reactions with vicinal diamine catalysts, the crown transition states are favored, both in the prototype and in an experimental example, shown in the graphic. We found that low-energy conformations of cyclic transition states occur and control stereoselectivities in these reactions. Another class of bifunctional organocatalysts, the vicinal amidophosphines, catalyzes the (3 + 2) annulation reaction of allenes with activated olefins. Stereocontrol here is due to an intermolecular hydrogen bond that activates the electrophilic partner in this reaction. We have also studied complex organometallic catalysts. Krische's ruthenium-catalyzed asymmetric hydrohydroxyalkylation of butadiene involves two chiral ligands at Ru, a chiral diphosphine and a chiral phosphate. The size of this combination strains the limits of modern computations with over 160 atoms, multiple significant steps, and a variety of ligand coordinations and conformations possible. We found that carbon-carbon bond formation occurs via a chair Zimmerman-Traxler-type transition structure and that a formyl CH···O hydrogen bond from aldehyde CH to phosphate oxygen, as well as steric interactions of the two chiral ligands, control the stereoselectivity.

The mechanisms and selectivities of the cycloadditions of tropone to dimethylfulvene have been investigated with M06-2X and B3LYP-D3 density functional theory (DFT) calculations and quasi-classical direct molecular dynamics simulations. The originally proposed reaction mechanism (Houk) involves a highly peri-, regio-, and stereoselective [6 + 4] cycloaddition of tropone [4π] to dimethylfulvene [6π], followed by a [1,5] hydrogen shift, and, finally, a second [6 + 4] cycloaddition of tropone [6π] to the cyclopentadiene moiety [4π]. Paddon-Row and Warrener proposed an alternative mechanism: the initial cycloaddition involves a different [6 + 4] cycloaddition in which fulvene acts as the 4π component, and a subsequent Cope rearrangement produces the formal [6 + 4] adduct. Computations now demonstrate that the initial cycloaddition proceeds via an ambimodal transition state that can lead to both of the proposed [6 + 4] adducts. These adducts can interconvert through a [3,3] sigmatropic shift (Cope rearrangement). Molecular dynamics simulations reveal the initial distribution of products and provide insights into the time-resolved mechanism of this ambimodal cycloaddition. Competing [4 + 2] cycloadditions and various sigmatropic shifts are also explored.

Accessing hindered amines, particularly primary amines α to a fully substituted carbon center, is synthetically challenging. We report an electrochemical method to access such hindered amines starting from benchtop-stable iminium salts and cyano­heteroarenes. A wide variety of substituted heterocycles (pyridine, pyrimidine, pyrazine, purine, azaindole) can be utilized in the cross-coupling reaction, including those substituted with a halide, trifluoromethyl, ester, amide, or ether group, a heterocycle, or an unprotected alcohol or alkyne. Mechanistic insight based on DFT data, as well as cyclic voltammetry and NMR spectroscopy, suggests that a proton-coupled electron-transfer mechanism is operational as part of a hetero-biradical cross-coupling of α-amino radicals and radicals derived from cyano­heteroarenes.