A STEADY-STATE SATISFACTORY SOLUTION TO AN ENVIRONMENTAL GAME WITH PIECE-WISE DEFINED PAYOFFS

We model a pollution accumulation process through a nonlinear, nondifferentiable state equation and also as dependent on an environmental levy. Then the payoff function to an economic agent is defined piece-wise. However, for a simple demand and cost structure, the combined payoff function of all agents is diagonally strictly concave. This implies that a steady-state Nash equilibrium is unique and can be controlled by the levy. We analytically compute a steady-state Nash equilibrium solution for the agents, and use a Decision Support Tool to determine a satisfactory solution for the interactions between the agents and a legislator responsible for the levy.     

Nucleophilic Addition to a Triple Bond; Preliminary ab initio study

Preliminary ab initio, calculations (minimal basis set STO-3 G) suggest that the preferred direction of approach of a nucleophilic centre towards a CC triple bond makes an obtuse angle (～120°) with this bond. The stereoelectronic requirements for nucleophilic addition to triple bonds and to ketones are thus rather similar.     

Evidences for the relationship between surface structure and reactivity of goethite nanoparticles based on advanced molecular-probe methods

Surface properties of two goethites have been studied in order to compare the amount of acid surface sites and their distribution over the various surface domains. For this purpose, ammonia, pyridine and nitrogen were used as basic molecular probes. Calorimetry measurements of ammonia adsorption provided the image of the average surface acidity being moderate. This conclusion was supported by the moderate resistance of the adsorbed pyridine molecules to degassing conditions. Adsorption and desorption of pyridine prior to gaseous nitrogen adsorption resulting in masking/unmasking of acid surface sites on the goethite surface allowed confirmation of the acid character of the specific adsorption sites characterized by the high-energy adsorption of electron-donating molecular nitrogen. The amount of acid sites probed by nitrogen and ammonia were of the same order of magnitude but systematically higher for ammonia. The subsequent analysis of the argon and nitrogen derivatives of first-layer adsorption isotherm led to determine the distribution of {101} and {121} crystallographic faces and discuss the location of acid sites on these surface domains.     

o-nitrobenzyl photolabile protecting groups with red-shifted absorption: syntheses and uncaging cross-sections for one- and two-photon excitation

We evaluated the o-nitrobenzyl platform for designing photolabile protecting groups with red-shifted absorption that could be photolyzed upon one- and two-photon excitation. Several synthetic pathways to build different conjugated o-nitrobenzyl backbones, as well as to vary the benzylic position, are reported. Relative to the reference 4,5-dimethoxy-2-nitrobenzyl group, several o-nitrobenzyl derivatives exhibit a large and red-shifted one-photon absorption within the near-UV range. Uncaging after one-photon excitation was studied by measuring UV-visible absorption and steady-state fluorescence emission on model caged ethers and esters. In the whole series investigated, the caged substrates were released cleanly upon photolysis. Quantum yields of uncaging after one-photon absorption lie within the 0.1-1 % range. We observed that these drop as the maximum wavelength absorption of the o-nitrobenzyl protecting group is increased. A new method based on fluorescence correlation spectroscopy (FCS) after two-photon excitation was used to measure the action uncaging cross section for two-photon excitation. The series of o-nitrobenzyl caged fluorescent coumarins investigated exhibit values within the 0.1-0.01 Goeppert-Mayer (GM) range. Such results are in line with the low quantum yields of uncaging associated with cross-sections of 1-50 GM for two-photon absorption. Although the cross-sections for one- and two-photon absorption of o-nitrobenzyl photolabile protecting groups can be readily improved, we emphasize the difficulty in enlarging the corresponding action uncaging cross-sections in view of the observed trend of their quantum yield of uncaging.     

Superparamagnetic bimetallic cyanide-bridged coordination nanoparticles with TB = 9 K

Dispersible, nearly isolated 6 nm nanoparticles of the CsNiCr(CN)6 Prussian blue analogue coated with polyvinylpyrrolidone (PVP) show superparamagnetic behaviour with a relatively high blocking temperature TB = 9 K.     

DFT calculations of d0 M(NR)(CHtBu)(X)(Y) (M = Mo, W; R = CPh3, 2,6-iPr-C6H3; X and Y = CH2tBu, OtBu, OSi(OtBu)3) olefin metathesis catalysts: structural, spectroscopic and electronic properties

DFT(B3PW91) calculations have been carried out to rationalise the structural, electronic and spectroscopic properties of Mo and W imido M(NR1)(CHR2)(X)(Y) olefin metathesis catalysts by using either simplified or actual ligands of the experimental complexes. The calculated structures, energetics (preference for the syn isomer and alkylidene rotational barrier for the syn/anti interconversion), and spectroscopic properties (NMR J(C-H) coupling constants) are in good agreement with available experimental data. Additionally, the alkylidene nu(C-H) stretching frequencies, not available experimentally, have been calculated. These quasi-tetrahedral complexes have a linear imido group and a C-H alkylidene agostic interaction, which stabilizes the syn isomer. Whether looking at M(NR1)(CHR2)(X)(Y), M = Mo, W, or the isolobal Re complexes, Re(CR1)(CHR2)(X)(Y), a linear correlation is obtained between both the alkylidene nu(C-H) stretching frequencies and J(C-H) coupling constants with the calculated alkylidene C-H bond lengths. These correlations show that the strength of the alpha-C-H agostic interaction increases from alkylidyne Re to imido group 6 complexes and from Mo to W. The NBO and AIM Bader analyses show firstly that the imido and alkylidyne groups are both triply bonded to the metal, but that the triply bonded imido ligand is a weaker electron donor than the alkylidyne, hence the stronger alpha-C-H agostic interaction for group 6 imido complexes. Secondly, one of the pi bonds of the triply bonded ligand is weakened at the transition state of the alkylidene rotation: while no lone pair is formed, the metal-ligand triple bond is polarized. This is more favourable for an imido than for an alkylidyne ligand, hence the lower alkylidene rotational barrier for the former complexes. Conversely, the aryl imido is even less of an electron donor than the alkyl imido group, which in turn strengthens the alpha-C-H agostic interaction and lowers the alkylidene rotational barrier even more.     

Modulating spontaneous brain activity using repetitive transcranial magnetic stimulation

Background  

When no specific stimulus or task is presented, spontaneous fluctuations in brain activity occur. Brain regions showing such coherent fluctuations are thought to form organized networks known as 'resting-state' networks, a main representation of which is the default mode network. Spontaneous brain activity shows abnormalities in several neurological and psychiatric diseases that may reflect disturbances of ongoing thought processes. Information about the degree to which such spontaneous brain activity can be modulated may prove helpful in the development of treatment options. We investigated the effect of offline low-frequency rTMS on spontaneous neural activity, as measured with fMRI, using a sequential independent-component-analysis and regression approach to investigate local changes within the default mode network.     

Oganesson Is a Semiconductor: On the Relativistic Band‐Gap Narrowing in the Heaviest Noble‐Gas Solids

Oganesson (Og) is the most recent addition to Group 18. Investigations of its atomic electronic structure have unraveled a tremendous impact of relativistic effects, raising the question whether the heaviest noble gas lives up to its position in the periodic table. To address the issue, we explore the electronic structure of bulk Og by means of relativistic Kohn–Sham density functional theory and many‐body perturbation theory in the form of the GW method. Calculating the band structure of the noble‐gas solids from Ne to Og, we demonstrate excellent agreement for the band gaps of the experimentally known solids from Ne to Xe and provide values of 7.1 eV and 1.5 eV for the unknown solids of Rn and Og. While this is in line with periodic trends for Rn, the band gap of Og completely breaks with these trends. The surprisingly small band gap of Og moreover means that, in stark contrast to all other noble‐gas solids, the solid form of Og is a semiconductor.