Energetic and spectral properties of triple photon downconversion in a phase-matched KTiOPO4 crystal

We measured the spectrum and energy of infrared triple photons generated in a phase-matched KTiOPO4 crystal pumped by picosecond beams at 532 and 1662 nm. The experimental data are in good agreement with our model, taking into account the spectral linewidths of the incident beams as well as a parasitic Kerr effect.     

Reversible water uptake by a stable imine-based porous organic cage

A crystalline porous organic cage molecule, CC3, is shown to adsorb up to 20.1 wt% water reversibly. This was confirmed by both gravimetric sorption and by crystallographic analysis. Crystals of CC3 are stable in boiling water for at least 4 h. The surprising chemical and supramolecular stability of these imine-based molecular crystals suggests scope for practical applications in humid environments.     

Nash equilibrium based fairness

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ??Nash equilibrium based fair.?? We further define a ??Nash proportionately fair?? Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.     

N-Boc-Amides in Cross-Coupling Reactions

Since 2015, the use of amides as electrophilic partners in cross-coupling reactions has experienced exponential growth. Diverse amide derivatives have been studied and among them N-Boc-amides have shown good activities towards various cross-coupling reactions and presents, in our view, an important synthetic usefulness. This review describes the recent developments of these chemical transformations involving N-Boc-amides.     

Gravity and Signature Change

The use of proper time to describe classical spacetimes which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.     

New efficient construction of the ABC core of the taxoids via a sequence of consecutive cobalt(I)-mediated [2 + 2 + 2] and [4 + 2] cyclizations

[reaction: see text] A new and efficient sequence of two consecutive cyclizations, a cobalt(I)-mediated [2 + 2 + 2] cyclotrimerization and a Diels-Alder reaction, is proposed to allow the formation of the ABC core of the taxoids in 65% overall yield, starting from an acyclic polyunsaturated precursor.     

Structure‐Based Design and Synthesis of the First Weak Non‐Phosphate Inhibitors for IspF,an Enzyme in the Non‐Mevalonate Pathway of Isoprenoid Biosynthesis

In this paper, we describe the structure‐based design, synthesis, and biological evaluation of cytosine derivatives and analogues that inhibit IspF, an enzyme in the non‐mevalonate pathway of isoprenoid biosynthesis. This pathway is responsible for the biosynthesis of the C₅ precursors to isoprenoids, isopentenyl diphosphate (IPP, 1 ) and dimethylallyl diphosphate (DMAPP, 2 ; Scheme 1). The non‐mevalonate pathway is the sole source for 1 and 2 in the protozoan Plasmodium parasites. Since mammals exclusively utilize the alternative mevalonate pathway, the enzymes of the non‐mevalonate pathway have been identified as attractive new drug targets in the fight against malaria. Based on computer modeling (cf. Figs. 2 and 3), new cytosine derivatives and analogues (Fig. 1) were selected as potential drug‐like inhibitors of IspF protein, and synthesized (Schemes 2–5). Determination of the enzyme activity by ¹³C‐NMR spectroscopy in the presence of the new ligands showed inhibitory activities for some of the prepared cytosine and pyridine‐2,5‐diamine derivatives in the upper micromolar range (IC₅₀ values; Table). The data suggest that it is possible to inhibit IspF protein without binding to the polar diphosphate binding site and the side chain of Asp56′, which interacts with the ribose moiety of the substrate and substrate analogues. Furthermore, a new spacious sub‐pocket was discovered which accommodates aromatic spacers between cytosine derivatives or analogues (binding to ‘Pocket III’) and rings that occupy the flexible hydrophobic region of ‘Pocket II’. The proposed binding mode remains to be further validated by X‐ray crystallography.     

Bis- through Tetrakis-Adducts of C60 by Reversible Tether-Directed Remote Functionalization and systematic investigation of the changes in fullerene properties as a function of degree,pattern, and nature of functionalization

By the tether-directed remote functionalization method, a series of bis- to hexakis-adducts of C₆₀, i.e., 1 – 7 (Fig. 1), had previously been prepared with high regioselectivity. An efficient method for the removal of the tether-reactive-group conjugate was now developed and its utility demonstrated in the regioselective synthesis of bis- to tetrakis(methano)fullerenes ( = di- to tetracyclopropafullerenes-C₆₀-I_h) 9 – 11 starting from 4, 5, and 7, respectively (Schemes 2, 4, and 5). This versatile protocol consists of a ¹O₂ ene reaction with the two cyclohexene rings in the starting materials, reduction of the formed mixture of isomeric allylic hydroperoxides to the corresponding alcohols, acid-promoted elimination of H₂O to cyclohexa-1,3-dienes, Diels-Alder addition of dimethyl acetylenedicarboxylate, retro-Diels-Alder addition, and, ultimately, transesterification. In the series 9 – 11 , all methano moieties are attached along an equatorial belt of the fullerene. Starting from C_2v-symmetrical tetrakis-adduct 15 , transesterification with dodecan-1-ol or octan-1-ol yielded the octaesters 16 and 17 , respectively, as noncrystalline fullerene derivatives (Scheme 3). The X-ray crystal structure of a CHCl₃ solvate of 11 (Fig. 3) showed that the residual conjugated π-chromophore of the C-sphere is reduced to two tetrabenzopyracylene substructures connected by four biphenyl-type bonds (Fig. 5). In the eight six-membered rings surrounding the two pyracylene (= cyclopent[fg]acenaphthylene) moieties, 6–6 and 6–5 bond-length alteration (0.05 Å) was reduced by ca. 0.01 Å as compared to the free C₆₀ skeleton (0.06 Å) (Fig. 4). The crystal packing (Fig. 6) revealed short contacts between Cl-atoms of the solvent molecule and sp²- and sp³-C-atoms of the C-sphere, as well as short contacts between Cl-atoms and O-atoms of the EtOOC groups attached to the methano moieties of 11 . The physical properties and chemical reactivity of compounds 1 - 11 were comprehensively investigated as a function of degree and pattern of addition and the nature of the addends. Methods applied to this study were UV/VIS (Figs. 7–11), IR, and NMR spectroscopy (Table 2), cyclic (CV) and steady-state (SSV) voltammetry (Table 1), calculations of the energies of the lowest uunoccupied mmolecular orbitals (LUMOs) and electron affinities (Figs. 12 and 13), and evaluation of chemical reactivity in competition experiments. It was found that the properties of the fullerene derivatives were not only affected by the degree and pattern of addition but also, in a remarkable way, by the nature of the addends (methano vs. but-2-ene-1, 4-diyl) anellated to the C-sphere. Attachment of multiple thano moieties along an equatorial belt as in the series 8 – 11 induces only a small perturbation of the original fullerene π-chromophore. In general, with increasing attenuation of the conjugated fullerene π-chromophore, the optical (HOMO-LUMO) gap in the UV/VIS spectrum is shifted to higher energy, the number of reversible one-electron reductions decreases, and the first reduction potential becomes increasingly negative, the computed LUMO energy increases and the electron affinity decreases, and the reactivity of the fullerene towards nucleophiles and carbenes and as dienophile in cycloadditions decreases.     

Thermodynamic origin of the chiral recognition of tryptophan on teicoplanin and teicoplanin aglycone stationary phases

The D-, L-tryptophan binding and the chiral recognition properties of the teicoplanin and teicoplanin aglycone (TAG) chiral stationary phase (CSPs) were compared at various column temperatures. The solute adsorption isotherms (bi-Langmuir model) were determined for both the two CSPs using the perturbation method. It was demonstrated that the sugar units were involved in the reduction of the apparent enantioselectivity through two phenomena: (i) the inhibition of some enantioselective contacts with low-affinity binding regions of the aglycone and (ii) a decrease in the stereoselective properties of the aglycone high-affinity binding pocket. The phenomenon (ii) was governed by both a decrease in the ratio of the enantiomer adsorption constant and a strong reduction of the site accessibility for D- and L-tryptophan. In addition, a temperature effect study was performed to investigate the chiral recognition mechanism at the aglycone high-affinity pocket. An enthalpy-entropy compensation analysis derived from the Grunwald model as well as the comparison with the literature data demonstrated that the enantioselective binding mode was dependent on an interface dehydration process. The change in the enantioselective process observed between the TAG and teicoplanin CSP was characterized by a difference of ca. 2-3 ordered water molecules released from the species interface.