Relations among complementary and supplementary pairings of Saalschützian $${}_4F_3(1)$$ series

We investigate sums \(J(\vec {x})\) and \(L(\vec {x})\) of pairs of normalized Saalschützian \({}_4F_3(1)\) hypergeometric series, and develop a theory of relations among these J and L functions. The function \(L(\vec {x})\) has been studied extensively in the literature and has been shown to satisfy a number of two-term and three-term relations with respect to the variable \(\vec {x}\). More recent works have framed these relations in terms of Coxeter group actions on \(\vec {x}\) and have developed a similar theory of two-term and three-term relations for \(J(\vec {x})\). In this article, we derive “mixed” three-term relations, wherein any one of the L (respectively, J) functions arising in the above context may be expressed as a linear combination of two of the above J (respectively, L) functions. We show that, under the appropriate Coxeter group action, the resulting set of three-term relations (mixed and otherwise) among J and L functions partitions into eighteen orbits. We provide an explicit example of a relation from each orbit. We further classify the eighteen orbits into five types, with each type uniquely determined by the distances (under a certain natural metric) between the J and L functions in the relation. We show that the type of a relation dictates the complexity (in terms of both number of summands and number of factors in each summand) of the coefficients of the J and L functions therein.     

Ab initio X‐ray structural characterization of an inclusion compound with a compositionally disordered chiral guest: no prior knowledge of the crystal composition

The crystal structure and absolute configuration of a molecular host/guest/impurity inclusion complex were established unequivocally in spite of our having no prior knowledge of its chemical composition. The host (4R,5R)‐4,5‐bis(hydroxydiphenylmethyl)‐2,2‐dimethyl‐1,3‐dioxolane, (I), displays expected conformational features. The crystal‐disordered chiral guest 4,4a,5,6,7,8‐hexahydronaphthalen‐2(3H)‐one, (II), is present in the crystal 85.1 (4)% of the time. It shares a common site with 4a‐hydroperoxymethyl‐4,4a,5,6,7,8‐hexahydronaphthalen‐2(3H)‐one, (III), present 14.9 (4)% of the time, which is the product of autoxidation of (II). This minor peroxide impurity was isolated, and the results of nuclear magnetic resonance, mass spectrometry, and X‐ray fluorescence studies are consistent with the proposed structure of (III). The complete structure was therefore determined to be (4R,5R)‐4,5‐bis(hydroxydiphenylmethyl)‐2,2‐dimethyl‐1,3‐dioxolane–4,4a,5,6,7,8‐hexahydronaphthalen‐2(3H)‐one–4a‐hydroperoxymethyl‐4,4a,5,6,7,8‐hexahydronaphthalen‐2(3H)‐one (1/0.85/0.15), C₃₁H₃₀O₄·0.85C₁₀H₁₄O·0.15C₁₀H₁₄O₃, (IV). There are host–host, host–guest, and host–impurity hydrogen‐bonding interactions of types S and D in the solid state. We believe that the crystals of (IV) were originally prepared to establish the chirality of the guest (II) by means of X‐ray diffraction analysis of host/guest crystals obtained in the course of chiral resolution during cocrystallization of (II) with (I). In spite of the absence of `heavy' elements, the absolute configurations of all anomeric centres in the structure are assigned as R based on resonant scattering effects.     

Oligomerization of N‐Heterocyclic Silylene into Zwitterionic Silenes

N‐Heterocyclic carbenes (NHC's) are known to serve as efficient substrates for the stabilization of various transient species possessing low‐valent Group 14 elements and for the generation of double E=C bonds. Herein, we report that the thermal tri‐ and tetramerizations of pyridoannulated silylene 1 lead to the formation of remarkably stable silenes 2 and 3 featuring zwitterionic distribution of electron density. Co‐oligomerization of 1 and its germanium analogue gives a related tetrameric product 4 containing low‐valent germanium atom stabilized by binding with the partial carbene‐character C atom. Bonding situations in 2 – 4 are best described as silene or germene with the significant zwitterionic distribution of electron density. The singlet diradical electronic state of 2 is 10 kcal mol^?1 higher than the ground state configuration.     

On the Erdelyi-Magnus-Nevai Conjecture for Jacobi Polynomials

T. Erdelyi, A.P. Magnus and P. Nevai conjectured that for the orthonormal Jacobi polynomials satisfy the inequality

Diastereoselective Synthesis of Cyclopropanes from Carbon Pronucleophiles and Alkenes

Cyclopropanes are desirable structural motifs with valuable applications in drug discovery and beyond. Established alkene cyclopropanation methods give rise to cyclopropanes with a limited array of substituents, are difficult to scale, or both. Herein, we disclose a new cyclopropane synthesis through the formal coupling of abundant carbon pronucleophiles and unactivated alkenes. This strategy exploits dicationic adducts derived from electrolysis of thianthrene in the presence of alkene substrates. We find that these dielectrophiles undergo cyclopropanation with methylene pronucleophiles via alkenyl thianthrenium intermediates. This protocol is scalable, proceeds with high diastereoselectivity, and tolerates diverse functional groups on both the alkene and pronucleophile coupling partners. To validate the utility of this new procedure, we prepared an array of substituted analogs of an established cyclopropane that is en route to multiple pharmaceuticals.     

Platinum-Iron(II) Oxide Sites Directly Responsible for Preferential Carbon Monoxide Oxidation at Ambient Temperature: An Operando X-ray Absorption Spectroscopy Study**

Operando X-ray absorption spectroscopy identified that the concentration of Fe²⁺ species in the working state-of-the-art Pt−FeO_x catalysts quantitatively correlates to their preferential carbon monoxide oxidation steady-state reaction rate at ambient temperature. Deactivation of such catalysts with time on stream originates from irreversible oxidation of active Fe²⁺ sites. The active Fe²⁺ species are presumably Fe⁺²O⁻² clusters in contact with platinum nanoparticles; they coexist with spectator trivalent oxidic iron (Fe³⁺) and metallic iron (Fe⁰) partially alloyed with platinum. The concentration of active sites and, therefore, the catalyst activity strongly depends on the pretreatment conditions. Fe²⁺ is the resting state of the active sites in the preferential carbon monoxide oxidation cycle.     

Crystallographic characterization of helical secondary structures in alpha/beta-peptides with 1:1 residue alternation

Oligomers that contain both alpha- and beta-amino acid residues in a 1:1 alternating pattern have recently been shown by several groups to adopt helical secondary structures in solution. The beta-residue substitution pattern has a profound effect on the type of helix formed and the stability of the helical conformation. On the basis of two-dimensional NMR data, we have previously proposed that beta-residues with a five-membered ring constraint promote two different types of alpha/beta-peptide helix. The "11-helix" contains i, i+3 CO...H-N hydrogen bonds between backbone amide groups; these hydrogen bonds occur in 11-atom rings. The alpha/beta-peptide "14/15-helix" contains i, i+4 CO...H-N hydrogen bonds, which occur in alternating 14- and 15-atom rings. Here we provide crystallographic data for 14 alpha/beta-peptides that form the 11-helix and/or the 14/15-helix. These results were obtained for a series of oligomers containing beta-residues derived from ( S,S)- trans-2-aminocyclopentanecarboxylic acid (ACPC) and alpha-residues derived from alpha-aminoisobutyric acid (Aib) or l-alanine (Ala). The crystallized alpha/beta-peptides range in length from 4 to 10 residues. Nine of the alpha/beta-peptides display the 11-helix in the solid state, three display the 14/15-helix, and two display conformations that contain both i, i+3 and i, i+4 CO...H-N hydrogen bonds, but not bifurcated hydrogen bonds. Only 3 of the 14 crystal structures presented here have been previously described. These results suggest that longer alpha/beta-peptides prefer the 14/15-helix over the 11-helix, a conclusion that is consistent with previously reported NMR data obtained in solution.     

Designing ionic liquids with boron cluster anions: alkylpyridinium and imidazolium [nido-C(2)B(9)H(11)] and [closo-CB(11)H(12)] carborane salts

A range of new alkylpyridinium and imidazolium carborane salts with [nido-C(2)B(9)H(12)](-), [closo-CB(11)H(12)](-), and [RC(2)B(11)H(11)](-) (R = methyl or butyl) anions have been prepared and characterized by physical and thermal methods, including the solid state structures of five of the salts determined by single crystal X-ray diffraction. The tendency of the salts to form low-melting ionic liquids has been assessed; all the salts studied with [nido-C(2)B(9)H(12)](-) anions melted below 100 degrees C and, significantly, have melting points that are 25-85 degrees C lower than those of the corresponding [closo-CB(11)H(12)](-) analogs, demonstrating that a wider range of boron-rich ionic liquid materials can be readily accessed.