Toward inorganic electrides

Electrides are materials in which alkali metals (Li through Cs) ionize to form bound alkali cations and "excess" electrons. The electrons reside in large cavities or channels or both in the host lattice. We report here the first synthesis of thermally stable inorganic electrides with cation-to-electron ratios of 1:1 as in organic electrides. Although alkali metal adducts to alumino-silicate zeolites are well known, the cation-to-electron ratio is generally 3:1 or greater because these zeolites contain alkali cations prior to incorporation of the alkali metal. In this work, two pure silica zeolites, ITQ-4and ITQ-7, with pore diameters of approximately 7 A, absorb up to 40 wt % cesium from the vapor phase (even at room temperature). The other alkali metals (except Li) can also be introduced at elevated temperatures. The optical and magnetic properties of the cesium-loaded samples suggest ionization to form Cs+ and e- with substantial electron-spin pairing. The metal-loaded samples are stable to at least 100 degrees C and are able to reduce small aromatic molecules such as benzene and naphthalene to the radical anions within the pores of the zeolite.     

Some families of complete caps of quadrics and symplectic polarities over GF(8)

A cap on a quadric is a set of its points whose pairwise joins are all chords. A cap is complete if it is not part of a larger one. The only field for which all complete quadric caps are known is GF(2). Those caps are small; the biggest for each quadric is of order the dimension of the ambient space. Apart from information about ovoids in dimensions at most 7, little else is known. Here, the evidence is increased by providing caps over GF(2), odd, which, if >1, have size of order the dimension cubed. In particular, complete caps are obtained for the quadrics Q _2m (8), Q ₊ ^8k+7 (8), Q _- ^8k+3 (8), Q ₊ ^8k+1 (8) and Q _- ^8k+5 (8). These caps on Q ₊ ^8k+7 (8) and Q _- ^8k+3 (8) are complete on any Q _n(8) of which their quadrics are sections; so is that that of Q ₄₊₂(8) for any Q _2n (8) of which Q ₄₊₂(8) is a section with the same kernel. From the correspondence with Q _2n (8) complete caps are obtained for symplectic polarities over GF(8).     

Cyclic antiautomorphisms of directed triple systems

A transitive triple, (a,b,c), is defined to be the set {(a,b), (b,c), (a,c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D,β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of a Directed triple system, (D,β), is a permutation of D that maps β to β⁻¹, where β ⁻¹ = {(c,b,a)|(a,b,c) E β}. In this article we give necessary and sufficient conditions for the existence of a Directed triple system of order v admitting an antiautomorphism consisting of a single cycle of length d and having v − d fixed points. Further, we give a more general result for partial Directed triple systems in which the missing ordered pairs are precisely those containing two fixed points. © 1996 John Wiley & Sons, Inc.     

A note on “Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime”

In 2014, Wang et al. (2014) extended the model of Lou and Wang (2012) to incorporate the credit period dependent demand and default risk for deteriorating items with maximum lifetime. However, the rates of demand, default risk and deterioration in the model of Wang et al. (2014) are assumed to be specific functions of credit period which limits the contributions. In this note, we first generalize the theoretical results of Wang et al. (2014) under some certain conditions. Furthermore, we also present some structural results instead of a numerical analysis on variation of optimal replenishment and trade credit strategies with respect to key parameters.     

Reactivity of the hydrido/nitrosyl radical MHCl(NO)(CO)(P(i)Pr(3))(2), M = Ru, Os

The reaction of equimolar NO with the 16 electron molecule RuHCl(CO)L(2) (L = P(i)Pr(3)) proceeds, via a radical adduct RuHCl(CO)(NO) L(2), onward to form RuCl(NO)(CO)L(2) (X-ray structure determination) and RuHCl(HNO)(CO)L(2), in a 1:1 mole ratio. The HNO ligand, bound by N and trans to hydride, is rapidly degraded by excess NO. The osmium complex behaves analogously, but the adduct has a higher formation constant, permitting determination of its IR spectrum; both MHCl(CO)(NO)L(2) radicals are characterized by EPR spectroscopy, and DFT calculations on the Ru system show it to have a "half-bent" Ru-N-O unit with the spin density mainly on nitrogen. DFT (PBE) energies rule out certain possible mechanistic steps for forming the two products. A survey of the literature leads to the hypothesis that NO should generally be considered as a (neutral) Lewis base (2-electron donor) when it binds to a 16 electron complex which is resistant to oxidation or reduction, and that the resulting N-centered radical has a M-N-O angle of approximately 140 degrees, which distinguishes it from NO(-) (bent at <140 degrees ) and from NO(+) (>170 degrees ).     

Barium azacryptand sodide,the first alkalide with an alkaline Earth cation,also contains a novel dimer, (Na(2))(2-)

The first barium sodide, with stoichiometry Ba(2+)(H(5)Azacryptand[2.2.2](-))Na(-).2MeNH(2), was synthesized by the reaction of Ba, Na, and H(6)Azacryptand[2.2.2] in NH(3)-MeNH(2) solution. It was characterized by X-ray crystallography, (23)Na MAS NMR, hydrogen evolution, DSC, optical spectroscopy, and magnetic susceptibility. This is the first sodide in which the sodium anions form (Na(2))(2)(-) dimers. Previous theoretical predictions were verified by a calculation of the potential energy curve for the dimer in the field of the surrounding charges, whose positions were determined from the crystal structure.     

Gating the mechanistic pathway to the elusive 4-membered ring azeteoporphyrin

Photolysis of metalated (Cu and Ni) and free base 2-diazo-3-oxochlorins within a frozen matrix (λ = 457.9 nm, toluene, 80 K) generates a single photointermediate with a hypsochromically shifted electronic absorption spectrum relative to the starting diazochlorins. The appearance of ketene (~2131 cm(-1)) and azete (~1670 cm(-1)) vibrations in infrared absorption and Raman spectra, respectively, identifies this intermediate as resulting from the Wolff rearrangement of the diazochlorins upon N(2) loss. Computational modeling of the vibrational spectra and TDDFT simulation of the electronic transitions of potential photointermediates corroborate this assignment. Isolation and analysis of photoproducts of these diazochlorins formed within n-butanol-doped frozen toluene matrices indicate near exclusive formation of azeteoporphyrins. In sharp contrast, room temperature laser photolysis of these materials yields a mixture of photoproducts deriving from the presence of both carbene and ketene intermediates. Computational modeling of the intramolecular reactivity of the proposed sp(2) carbene intermediate shows exclusive bond insertion to the adjacent phenyl group, and no evidence of Wolff rearrangement. Computational reaction profile analyses reveal that the barrierless Wolff rearrangement proceeds via an out-of-plane carbene electronic configuration that is generated directly during the loss of N(2). The formation of out-of-plane carbene, resulting in the exclusive formation of the observed ketene photointermediate at low temperatures, is consistent with orbital symmetry considerations and by the geometric constraints imposed by the frozen matrix. Combined, this leads to a model showing that azeteoporphyrin formation via the Wolff rearrangement is dependent upon the structural disposition of the adjacent framework, and the specific reaction intermediate formed is very sensitive to this feature.     

Masking-level differences for trains of clicks

Masking-level differences (MLDs) were measured for trains of 2000-Hz bandpass clicks as a function of the interclick interval (ICI) and the number of clicks in the train. The magnitude of the MLD grew as the number of clicks in the train was increased from 1 to 32. While the MLDs tended to be larger at longer ICIs, the effect was mediated by changes in detectability in the homophasic conditions. For click trains consisting of 4-32 clicks, the improvement in detectability in the antiphasic conditions with increases in the number of clicks appears to be the result of integration of acoustic power, as is the case for the homophasic conditions. The absence of MLDs for short trains of high-frequency transients remains quite puzzling, since large MLDs are found with single, low-frequency transients.