Origin of the Relative Stereoselectivity of the β-Lactam Formation in the Staudinger Reaction

The relative (cis, trans) stereoselectivity of the β-lactam formation is one of the critical issues in the Staudinger reaction. Although many attempts have been made to explain and to predict the stereochemical outcomes, the origin of the stereoselectivity remains obscure. We are proposing a model that explains the relative stereoselectivity based on a kinetic analysis of the cis/trans ratios of reaction products. The results were derived from detailed Hammett analyses. Cyclic imines were employed to investigate the electronic effect of the ketene substituents, and it was found that the stereoselectivity could not be simply attributed to the torquoelectronic model. Based on our results, the origin of the relative stereoselectivity can be described as follows:  (1) the stereoselectivity is generated as a result of the competition between the direct ring closure and the isomerization of the imine moiety in the zwitterionic intermediate; (2) the ring closure step is most likely an intramolecular nucleophilic addition of the enolate to the imine moiety, which is obviously affected by the electronic effect of the ketene and imine substituents; (3) electron-donating ketene substituents and electron-withdrawing imine substituents accelerate the direct ring closure, leading to a preference for cis-β-lactam formation, while electron-withdrawing ketene substituents and electron-donating imine substituents slow the direct ring closure, leading to a preference for trans-β-lactam formation; and (4) the electronic effect of the substituents on the isomerization is a minor factor in influencing the stereoselectivity

Density Functional Theory Study of the Mechanism and Origins of Stereoselectivity in the Asymmetric Simmons–Smith Cyclopropanation with Charette Chiral Dioxaborolane Ligand

Asymmetric Simmons–Smith reaction using Charette chiral dioxaborolane ligand is a widely applied method for the construction of enantiomerically enriched cyclopropanes. The detailed mechanism and the origins of stereoselectivity of this important reaction were investigated using density functional theory (DFT) calculations. Our computational studies suggest that, in the traditional Simmons–Smith reaction conditions, the monomeric iodomethylzinc allyloxide generated in situ from the allylic alcohol and the zinc reagent has a strong tendency to form a dimer or a tetramer. The tetramer can easily undergo an intramolecular cyclopropanation to give the racemic cyclopropane product. However, when a stoichiometric amount of Charette chiral dioxaborolane ligand is employed, monomeric iodomethylzinc allyloxide is converted into an energetically more stable four-coordinated chiral zinc/ligand complex. The chiral complex has the zinc bonded to the CH2I group and coordinated by three oxygen atoms (one from the allylic alcohol and the other two oxygen atoms from the carbonyl oxygen and the ether oxygen in the dioxaborolane ligand), and it can undergo the cyclopropanation reaction easily. Three key factors influencing the enantioselectivity have been identified through examining the cyclopropanation transition states: (1) the torsional strain along the forming C–C bond, (2) the 1,3-allylic strain caused by the chain conformation, and (3) the ring strain generated in the transition states. In addition, the origin of the high anti diastereoselectivity for the substituent on the zinc reagent and the hydroxymethyl group of the allylic alcohol has been rationalized through analyzing the steric repulsion and the ring strain in the cyclopropanation transition states

Mechanisms of Cascade Reactions in the Syntheses of Camptothecin-Family Alkaloids: Intramolecular [4⁺ + 2] Reactions of <i>N</i>-Arylimidates and Alkynes

The key steps of cascade reactions employed in the syntheses of camptothecin-family alkaloids by Fortunak and Yao are intramolecular aza-Diels−Alder (IADA) reactions between in situ generated N-arylimidates and alkynes. The efficiencies of the IADA reactions are different but not well-understood. DFT calculations shown here provide insights into these two IADA reactions and well-rationalize why hexaphenyloxodiphosphonium triflate (Hendrickson reagent) as an amide-activating reagent is superior to trimethyloxonium fluoroborate

Why Is Copper(I) Complex More Competent Than Dirhodium(II) Complex in Catalytic Asymmetric O−H Insertion Reactions? A Computational Study of the Metal Carbenoid O−H Insertion into Water

Why Is Copper(I) Complex More Competent Than Dirhodium(II) Complex in Catalytic Asymmetric O−H Insertion Reactions? A Computational Study of the Metal Carbenoid O−H Insertion into Wate

The result of the literature.

In bold–the best performance.</p

Theoretical Elucidation of the Origins of Substituent and Strain Effects on the Rates of Diels–Alder Reactions of 1,2,4,5-Tetrazines

The Diels–Alder reactions of seven 1,2,4,5-tetrazines with unstrained and strained alkenes and alkynes were studied with quantum mechanical calculations (M06-2X density functional theory) and analyzed with the distortion/interaction model. The higher reactivities of alkenes compared to alkynes in the Diels–Alder reactions with tetrazines arise from the differences in both interaction and distortion energies. Alkenes have HOMO energies higher than those of alkynes and therefore stronger interaction energies in inverse-electron-demand Diels–Alder reactions with tetrazines. We have also found that the energies to distort alkenes into the Diels–Alder transition-state geometries are smaller than for alkynes in these reactions. The strained dienophiles, <i>trans</i>-cyclooctene and cyclooctyne, are much more reactive than unstrained <i>trans</i>-2-butene and 2-butyne, because they are predistorted toward the Diels–Alder transition structures. The reactivities of substituted tetrazines correlate with the electron-withdrawing abilities of the substituents. Electron-withdrawing groups lower the LUMO+1 of tetrazines, resulting in stronger interactions with the HOMO of dienophiles. Moreover, electron-withdrawing substituents destabilize the tetrazines, and this leads to smaller distortion energies in the Diels–Alder transition states

Mechanisms and Origins of Switchable Chemoselectivity of Ni-Catalyzed C(aryl)–O and C(acyl)–O Activation of Aryl Esters with Phosphine Ligands

Many experiments have shown that nickel with monodentate phosphine ligands favors the C­(aryl)–O activation over the C­(acyl)–O activation for aryl esters. However, Itami and co-workers recently discovered that nickel with bidentate phosphine ligands can selectively activate the C­(acyl)–O bond of aryl esters of aromatic carboxylic acids. The chemoselectivity with bidentate phosphine ligands can be switched back to C­(aryl)–O activation when aryl pivalates are employed. To understand the mechanisms and origins of this switchable chemoselectivity, density functional theory (DFT) calculations have been conducted. For aryl esters, nickel with bidentate phosphine ligands cleaves C­(acyl)–O and C­(aryl)–O bonds via three-centered transition states. The C­(acyl)–O activation is more favorable due to the lower bond dissociation energy (BDE) of C­(acyl)–O bond, which translates into a lower transition-state distortion energy. However, when monodentate phosphine ligands are used, a vacant coordination site on nickel creates an extra Ni–O bond in the five-centered C­(aryl)–O cleavage transition state. The additional interaction energy between the catalyst and substrate makes C­(aryl)–O activation favorable. In the case of aryl pivalates, nickel with bidentate phosphine ligands still favors the C­(acyl)–O activation over the C­(aryl)–O activation at the cleavage step. However, the subsequent decarbonylation generates a very unstable <i>t</i>Bu-Ni­(II) intermediate, and this unfavorable step greatly increases the overall barrier for generating the C­(acyl)–O activation products. Instead, the subsequent C–H activation of azoles and C–C coupling in the C­(aryl)–O activation pathway are much easier, leading to the observed C­(aryl)–O activation products

Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L_{1/2 +2} Regularization

<div><p>Cancer classification and feature (gene) selection plays an important role in knowledge discovery in genomic data. Although logistic regression is one of the most popular classification methods, it does not induce feature selection. In this paper, we presented a new hybrid L_{1/2 +2} regularization (HLR) function, a linear combination of L_1/2 and L₂ penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L_1/2 (sparsity) and L₂ (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding approach to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model. The empirical results and simulations indicate that the proposed method is highly competitive amongst several state-of-the-art methods.</p></div

Demand-side energy management under time-varying prices

Under time-varying electricity prices, an end-user may be stimulated to delay flexible demands that can be shifted over time. In this article, we study the problem where each end-user adopts an energy management system that helps time flexible demands fulfillments. Discomfort costs are incurred if demand is not satisfied immediately upon arrival. Energy storage and trading decisions are also considered. We model the problem as a finite horizon undiscounted Markov Decision Process, and outline a tractable approximate dynamic programming approach to overcome the curse of dimensionality. Specifically, we construct an approximation for the value-to-go function such that Bellman equations are converted into mixed-integer problems with structural properties. Finally, we numerically demonstrate that our approach achieves close performance to the exact approach, while dominating the myopic policy and no-control policy. Most importantly, the proposed approach can take advantage of the price differences and efficiently shift demands.</p