EBC-232 and 323: A Structural Conundrum Necessitating Unification of Five In Silico Prediction and Elucidation Methods

Structurally unique halimanes EBC-232 and EBC-323, isolated from the Australian rainforest plant Croton insularis, proved considerably difficult to elucidate. The two diastereomers, which consist an unusual oxo-6,7-spiro ring system fused to a dihydrofuran, were solved by unification and consultation of five in silico NMR elucidation and prediction methods [i.e., ACDLabs, olefin strain energy (OSE), DP4, DU8+ and TD DFT CD]. Structure elucidation challenges of this nature are prime test case examples for empowering future AI learning in structure elucidation.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure

Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness.

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Résumé On dérive des limites supérieures et inférieures des contraintes tangentielles suivant la théorie de la flexion de Saint-Venant, que l'on utilise aux fins d'établir le caractère asymptotique de la formule de la Résistance des Matériaux dans le cas limite d'une épaisseur extrêmement petite.

     

Modeling of in-situ biorestoration of organic compounds in groundwater

A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.     

A three-dimensional inverse problem for inhomogeneities in elastic solids

The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases.     

Enhancing the Value of Free Metals in the Synthesis of Lanthanoid Formamidinates: Is a Co‐oxidant Needed?

Treatment of N,N′‐bis(aryl)formamidines (ArFormH), N,N′‐bis(2,6‐difluorophenyl)formamidine (DFFormH) or N,N′‐bis(2,6‐diisopropylphenyl)formamidine (DippFormH), with europium metal in CH₃CN is an efficient synthesis of the divalent complexes: [{Eu(DFForm)₂(CH₃CN)₂}₂] ( Eu1 ) or [Eu(DippForm)₂(CH₃CN)₄] ( Eu2 ). The synthetic method was extended to ytterbium, but the metal required activation by addition of Hg⁰. With DFFormH in CH₃CN, [{Yb(DFForm)₂(CH₃CN)}₂] ( Yb1 ) was obtained in good yield, and [Yb(DFForm)₂(thf)₃] ( Yb3 ) was obtained from a synthesis in CH₃CN/THF. Thus, this synthetic method completely circumvents the use of either salt metathesis, or redox transmetallation/protolysis (RTP) protocols to prepare divalent rare‐earth formamidinates. Heating Yb1 in PhMe/C₆D₆ resulted in decomposition to trivalent products, including one from a CH₃CN activation process. For a synthetic comparison, divalent ytterbium DFForm and DippForm complexes were synthesised by RTP reactions between Yb⁰, Hg(R)₂ (R=Ph, C₆F₅), and ArFormH in THF, leading to the isolation of either [Yb(DFForm)₂(thf)₃] ( Yb3 ), or the first five coordinate rare‐earth formamidinate complex [Yb(DippForm)₂(thf)] ( Yb4 b ), and, from adjustment of the stoichiometry, trivalent [Yb(DFForm)₃(thf)] ( Yb6 ). Oxidation of Yb3 with benzophenone (bp), or halogenating agents (TiCl₄(thf)₂, Ph₃CCl, C₂Cl₆) gave [Yb(DFForm)₃(bp)] or [Yb(DFForm)₂Cl(thf)₂], respectively. Furthermore, the structural chemistry of divalent ArForm complexes has been substantially broadened. Not only have the highest and lowest coordination numbers for divalent rare‐earth ArForm complexes been achieved in Eu2 and Yb4 b , respectively, but also dimeric Eu1 and Yb1 have highly unusual ArForm bridging coordination modes, either perpendicular μ‐1κ(N:N′):2κ(N:N′) in Eu1 , or the twisted μ‐1κ(N:N′):2κ(N′:F′) DFForm coordination in Yb1 , both unprecedented in divalent rare‐earth ArForm chemistry and in the wider divalent rare‐earth amidinate field.     

Theoretical study on the origin of enantioselectivity in the primary amine–Brønsted acid catalyzed epoxidation of cyclic enones

Computational studies to determine the origin of enantioselectivity in the (1R,2R)-1,2-diphenylethane-1,2-diamine (DEPN)–Brønsted acid catalyzed epoxidation of 2-cyclohexen-1-one have been performed using density functional theory. Transition states for conjugate addition and ring closure steps of the epoxidations catalyzed by three different catalyst systems were characterized. Our calculations show that the C_sp2H?O H-bond interaction between the benzene ring of the catalyst and H₂O is mainly responsible for the chiral discrimination observed. The Brønsted acid counterion plays a very important role in ensuring high enantioselectivity by improving the rigidity of the transition state structures to allow the efficient formation of the C_sp2H?O H-bond. Moreover, we explain why these two diamine catalysts (1S,2S)-DACH and (1R,2R)-DPEN display consistent enantioselectivities in the catalytic epoxidation of 2-cyclohexen-1-one when combining with three different cocatalysts; achiral TFA, and chiral (R)- and (S)-TRIP.