On the combinatorics of the Pfaff identity

Recently, there has been a revival of interest in the Pfaff identity on hypergeometric series because of the specialization of Simons and a generalization of Munarini. We present combinatorial settings and interpretations of the specialization and the generalization; one is based on free Dyck paths and free Schröder paths, and the other relies on a correspondence of Foata and Labelle between the Meixner endofunctions and bicolored permutations, and an extension of the technique developed by Labelle and Yeh for the Pfaff identity. Applying the involution on weighted Schröder paths, we derive a formula for the Narayana numbers as an alternating sum of the Catalan numbers.     

Multistep energy and electron transfer processes in novel rotaxane donor–acceptor hybrids generating microsecond-lived charge separated states

A new set of [Cu(phen)₂]⁺ based rotaxanes, featuring [60]-fullerene as an electron acceptor and a variety of electron donating moieties, namely zinc porphyrin (ZnP), zinc phthalocyanine (ZnPc) and ferrocene (Fc), has been synthesized and fully characterized with respect to electrochemical and photophysical properties. The assembly of the rotaxanes has been achieved using a slight variation of our previously reported synthetic strategy that combines the Cu(i)-catalyzed azide–alkyne cycloaddition reaction (the “click” or CuAAC reaction) with Sauvage''s metal-template protocol. To underline our results, complementary model rotaxanes and catenanes have been prepared using the same strategy and their electrochemistry and photo-induced processes have been investigated. Insights into excited state interactions have been afforded from steady state and time resolved emission spectroscopy as well as transient absorption spectroscopy. It has been found that photo-excitation of the present rotaxanes triggers a cascade of multi-step energy and electron transfer events that ultimately leads to remarkably long-lived charge separated states featuring one-electron reduced C₆₀ radical anion (C₆₀˙^–) and either one-electron oxidized porphyrin (ZnP˙⁺) or one-electron oxidized ferrocene (Fc˙⁺) with lifetimes up to 61 microseconds. In addition, shorter-lived charge separated states involving one-electron oxidized copper complexes ([Cu(phen)₂]²⁺ (τ < 100 ns)), one-electron oxidized zinc phthalocyanine (ZnPc˙⁺; τ = 380–560 ns), or ZnP˙⁺ (τ = 2.3–8.4 μs), and C₆₀˙^– have been identified as intermediates during the sequence. Detailed energy diagrams illustrate the sequence and rate constants of the photophysical events occurring with the mechanically-linked chromophores. This work pioneers the exploration of mechanically-linked systems as platforms to position three distinct chromophores, which are able to absorb light over a very wide range of the visible region, triggering a cascade of short-range energy and electron transfer processes to afford long-lived charge separated states.     

Intramolecular d10-d10 interactions in heterometallic clusters of the transition metals

Weak attractive interactions between closed shell metal ions have been increasingly studied in the last few years and are generally designated as metallophilic interactions. They are best evidenced in the solid state where structural data obtained by X-ray diffraction provide precise information about the distance between the metals involved. The strength of such metal-metal interactions has been compared to that of hydrogen bonding (ca. 7-11 kcal mol(-1)) and is clearly sufficient to bring about novel bonding and structural features and confer interesting physical properties such as luminescence, polychromism, magnetism or one-dimensional electrical conductivity. The Cu(I)-Cu(I), Ag(I)-Ag(I) and Au(I)-Au(I) interactions have been increasingly observed and the latter have certainly been the most studied. Early qualitative analyses of the aurophilic attraction focused on Au-Au bonding originating from 6s, 6p and 5d orbital mixing. Numerous theoretical studies on metallophilic interactions continue to be carried out at various levels of sophistication which take into account relativistic and correlation effects to describe these van der Waals-type interactions. In this critical review, we would like to focus on the synthesis and structures of heterometallic clusters of the transition metals in which intra- rather than intermolecular d(10)-d(10) interactions are at work, in order to limit the role of packing effects. We wish to provide the reader with a comparative overview of the metal core structures resulting from or favoring metallophilic interactions but do not intend to provide a comprehensive coverage of the literature. We will first examine heterometallic clusters displaying homometallic and then heterometallic d(10)-d(10) interactions. Although the focus of this review is on d(10)-d(10) interactions involving metals from the group 11, we shall also briefly examine for comparison some complexes displaying intramolecular d(10)-d(10) interactions involving metals from other groups (188 references).     

Influence of microgel architecture and oil polarity on stabilization of emulsions by stimuli-sensitive core-shell poly(N-isopropylacrylamide-co-methacrylic acid) microgels: Mickering versus Pickering behavior?

Charged poly(N-isopropylacrylamide-co-methacrylic acid) [P(NiPAM-co-MAA)] microgels can stabilize thermo- and pH-sensitive emulsions. By placing charged units at different locations in the microgels and comparing the emulsion properties, we demonstrate that their behaviors as emulsion stabilizers are very different from molecular surfactants and rigid Pickering stabilizers. The results show that the stabilization of the emulsions is independent of electrostatic repulsion although the presence and location of charges are relevant. Apparently, the charges facilitate emulsion stabilization via the extent of swelling and deformability of the microgels. The stabilization of these emulsions is linked to the swelling and structure of the microgels at the oil-water interface, which depends not only on the presence of charged moieties and on solvent polarity but also on the microgel (core-shell) morphology. Therefore, the internal soft and porous structure of microgels is important, and these features make microgel-stabilized emulsions characteristically different from classical, rigid-particle-stabilized Pickering emulsions, the stability of which depends on the surface properties of the particles.     

Elucidating the origin of diastereoselectivity in a self-replicating system: selfishness versus altruism

We have investigated a diastereoselective self‐replicating system based on a cycloaddition of a fulvene derivative and a maleimide using a two‐pronged approach of combining NMR spectroscopy with computational modelling. Two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, one diastereomer takes over the resources as a “selfish” autocatalyst, while exploiting the competitor as a weak “altruist”, resulting in a diastereoselectivity of 16:1. We applied 1D and 2D NMR spectroscopic techniques supported by ab initio chemical shifts as well as ab initio molecular dynamics simulations to study the structure and dynamics of the underlying network. This powerful combination allowed us to decipher the energetic and structural rationale behind the observed behaviour, while static computational methods currently used in the field did not.     

Diversity through a branched reaction pathway: generation of multicyclic scaffolds and identification of antimigratory agents

A library of 91 heterocyclic compounds composed of 16 distinct scaffolds has been synthesized through a sequence of phosphine-catalyzed ring-forming reactions, Tebbe reactions, Diels-Alder reactions, and, in some cases, hydrolysis. This effort in diversity-oriented synthesis produced a collection of compounds that exhibited high levels of structural variation both in terms of stereochemistry and the range of scaffolds represented. A simple but powerful sequence of reactions thus led to a high-diversity library of relatively modest size with which to explore biologically relevant regions of chemical space. From this library, several molecules were identified that inhibit the migration and invasion of breast cancer cells and may serve as leads for the development of antimetastatic agents.     

MRI-guided neutron capture therapy by use of a dual gadolinium/boron agent targeted at tumour cells through upregulated low-density lipoprotein transporters

The upregulation of low-density lipoprotein (LDL) transporters in tumour cells has been exploited to deliver a sufficient amount of gadolinium/boron/ligand (Gd/B/L) probes for neutron capture therapy, a binary chemio-radiotherapy for cancer treatment. The Gd/B/L probe consists of a carborane unit (ten B atoms) bearing an aliphatic chain on one side (to bind LDL particles), and a Gd(III)/1,4,7,10-tetraazacyclododecane monoamide complex on the other (for detection by magnetic resonance imaging (MRI)). Up to 190 Gd/B/L probes were loaded per LDL particle. The uptake from tumour cells was initially assessed on cell cultures of human hepatoma (HepG2), murine melanoma (B16), and human glioblastoma (U87). The MRI assessment of the amount of Gd/B/L taken up by tumour cells was validated by inductively coupled plasma-mass-spectrometric measurements of the Gd and B content. Measurements were undertaken in vivo on mice bearing tumours in which B16 tumour cells were inoculated at the base of the neck. From the acquisition of magnetic resonance images, it was established that after 4-6 hours from the administration of the Gd/B/L-LDL particles (0.1 and 1 mmol kg(-1) of Gd and (10)B, respectively) the amount of boron taken up in the tumour region is above the threshold required for successful NCT treatment. After neutron irradiation, tumour growth was followed for 20 days by MRI. The group of treated mice showed markedly lower tumour growth with respect to the control group.     

Atomistic surface erosion and thin film growth modelled over realistic time scales

We present results of atomistic modelling of surface growth and sputtering using a multi-time scale molecular dynamics-on-the-fly kinetic Monte Carlo scheme which allows simulations to be carried out over realistic experimental times. The method uses molecular dynamics to model the fast processes and then calculates the diffusion barriers for the slow processes on-the-fly, without any preconceptions about what transitions might occur. The method is applied to the growth of metal and oxide materials at impact energies typical for both vapour deposition and magnetron sputtering. The method can be used to explain growth processes, such as the filling of vacancies and the formation of stacking faults. By tuning the variable experimental parameters on the computer, a parameter set for optimum crystalline growth can be determined. The method can also be used to model sputtering where the particle interactions with the surface occur at a higher energy. It is shown how a steady state can arise in which interstitial clusters are continuously being formed below the surface during an atom impact event which also recombine or diffuse to the surface between impact events. For fcc metals the near surface region remains basically crystalline during the erosion process with a pitted topography which soon attains a steady state roughness.     

2-difluoromethylene-4-methylenepentanoic acid, a paradoxical probe able to mimic the signaling role of 2-oxoglutaric acid in cyanobacteria

2-Difluoromethylene-4-methylenepentanoic acid (DFMPA), a seemingly deviated analog of 2-oxoglutaric acid (2-OG), could surprisingly mimic its signaling function in cyanobacteria. Computer modeling revealed the favorable binding of DFMPA toward the 2-OG receptor, NtcA, via mutual conformational changes, suggesting that structural alteration of 2-OG is tolerated for it to exercise its signaling role. This extremely useful finding could be exploited for the design of affinity probes with which to study new 2-OG receptors in related signaling pathways.