Non-Crossing Tableaux

In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example, standard Young tableaux, standard monomials, and standard bitableaux. We adopt a point of view that these standard objects are really non-nesting, and we find their non-crossing counterparts.     

Promotion and cyclic sieving via webs

We show that Schützenberger’s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon.     

Pattern selection during electropolishing due to double-layer effects

We extend our earlier study of nanoscale pattern formation during electropolishing [Nanotechnology 7, 360 (1996); Phys. Rev. B 56, 12 608 (1997)]. The patterns are attributed to preferential adsorption of organic molecules on the convex portion of the electrode due to its enhanced electric field. This local enhancement occurs because of the effect of surface curvature on the double-layer potential drop. By allowing for transport correction to the double-layer potential drop at thermodynamic equilibrium, we estimate this anodic overpotential to be in the realistic mV range and hence verify the Debye-Huckel approximation used in our model. This small anodic overpotential suggests that pattern formation is a generic electropolishing phenomenon whose only requirement is that the polarizability of the organic additive relative to water must lie within a range specified by our theory. We verify this prediction experimentally with a variety of electrolyte solutions. The voltage ranges for specific hexagonal and ridge patterns are well correlated by our model with only a single parameter. (c) 1999 American Institute of Physics.     

On the directed gas phase synthesis of the imidoborane molecule (HNBH)--an isoelectronic molecule of acetylene (HCCH)

The elementary reaction of ground state boron atoms, (B((2)P(j))), with ammonia (NH(3)(X(1)A(1))) was conducted under single collision conditions at a collision energy of 20.5 ± 0.4 kJ mol(-1) in a crossed molecular beams machine. Combined with electronic structure calculations, our experimental results suggested that the reaction was initiated by a barrier-less addition of the boron atom to the nonbonding electron pair of the nitrogen atom forming a weakly bound BNH(3) collision complex. This intermediate underwent a hydrogen shift to a doublet HBNH(2) radical that decomposed via atomic hydrogen loss to at least the imidoborane (HBNH(X(1)Σ(+)) molecule, an isoelectronic species of acetylene (HCCH(X(1)Σ(g)(+))). Our studies are also discussed in light of the isoelectronic C(2)H(3) potential energy surface accessed via the isoelectronic carbon-methyl system.     

A crossed beam and ab initio investigation on the formation of vinyl boron monoxide (C2H3BO; X1A') via reaction of boron monoxide (11BO; X2Σ+) with ethylene (C2H4; X1A(g))

The reaction dynamics of the boron monoxide radical ((11)BO; X(2)Σ(+)) with ethylene (C(2)H(4); X(1)A(g)) were investigated at a nominal collision energy of 12.2 kJ mol(-1) employing the crossed molecular beam technique and supported by ab initio and statistical (RRKM) calculations. The reaction is governed by indirect scattering dynamics with the boron monoxide radical attacking the carbon-carbon double bond of the ethylene molecule without entrance barrier with the boron atom. This addition leads to a doublet radical intermediate (O(11)BH(2)CCH(2)), which either undergoes unimolecular decomposition through hydrogen atom emission from the C1 atom via a tight transition state located about 13 kJ mol(-1) above the separated products or isomerizes via a hydrogen shift to the O(11)BHCCH(3) radical, which also can lose a hydrogen atom from the C1 atom. Both processes lead eventually to the formation of the vinyl boron monoxide molecule (C(2)H(3)BO; X(1)A'). The overall reaction was determined to be exoergic by about 40 kJ mol(-1). The reaction dynamics are also compared to the isoelectronic ethylene (C(2)H(4); X(1)A(g)) - cyano radical (CN; X(2)Σ(+)) system studied earlier.     

A Spherically Shielded Triphenylamine and Its Persistent Radical Cation

This work reports the design and synthesis of a sterically protected triphenylamine scaffold which undergoes one-electron oxidation to form an amine-centered radical cation of remarkable stability. Several structural adjustments were made to tame the inherent reactivity of the radical cation. First, the parent propeller-shaped triphenylamine was planarized with sterically demanding bridging units and, second, protecting groups were deployed to block the reactive positions. The efficiently shielded triphenylamine core can be reversibly oxidized at moderate potentials (+0.38 V, vs. Fc/Fc⁺ in CH₂Cl₂). Spectroelectrochemistry and chemical oxidation studies were employed to monitor the evolution of characteristic photophysical features. To obtain a better understanding of the impact of one-electron oxidation on structural and electronic properties, joint experimental and computational studies were conducted, including X-ray structural analysis, electron paramagnetic resonance (EPR), and density functional theory (DFT) calculations. The sterically shielded radical cation combines various desirable attributes: A characteristic and unobstructed absorption in the visible region, high stability which enables storage for weeks without spectroscopically traceable degradation, and a reliable oxidation/re-reduction process due to effective screening of the planarized triphenylamine core from its environment.     

Copper(II) bromide and copper(II) acetate complexes of 4,4′‐(p‐phenylene)bipyridazine

4,4′‐(p‐Phenylene)bipyridazine, C₁₄H₁₀N₄, (I), and the coordination compounds catena‐poly[[dibromidocopper(II)]‐μ‐4,4′‐(p‐phenylene)bipyridazine‐κ²N²:N^2′], [CuBr₂(C₁₄H₁₀N₄)]_n, (II), and catena‐poly[[[tetrakis(μ‐acetato‐κ²O:O′)dicopper(II)]‐μ‐4,4′‐(p‐phenylene)bipyridazine‐κ²N¹:N^1′] chloroform disolvate], {[Cu₂(C₂H₃O₂)₄(C₁₄H₁₀N₄)]·2CHCl₃}_n, (III), contain a new extended bitopic ligand. The combination of the p‐phenylene spacer and the electron‐deficient pyridazine rings precludes C—H...π interactions between the lengthy aromatic molecules, which could be suited for the synthesis of open‐framework coordination polymers. In (I), the molecules are situated across a center of inversion and display a set of very weak intermolecular C—H...N hydrogen bonds [3.399 (3) and 3.608 (2) Å]. In (II) and (III), the ligand molecules are situated across a center of inversion and act as N²,N^2′‐bidentate [in (II)] and N¹,N^1′‐bidentate [in (III)] long‐distance bridges between the metal ions, leading to the formation of coordination chains [Cu—N = 2.005 (3) Å in (II) and 2.199 (2) Å in (III)]. In (II), the copper ion lies on a center of inversion and adopts CuN₂Br₄ (4+2)‐coordination involving two long axial Cu—Br bonds [3.2421 (4) Å]. In (III), the copper ion has a tetragonal pyramidal CuO₄N environment. The uncoordinated pyridazine N atom and two acetate O atoms provide a multiple acceptor site for accommodation of a chloroform solvent molecule by trifurcated hydrogen bonding [C—H...O(N) = 3.298 (5)–3.541 (4) Å].     

Crystal structure, coloring problem and magnetism of Gd(5-x)Zr(x)Si4

Ternary Gd(5-x)Zr(x)Si(4) silicides were synthesized by arc melting of the constituent elements and subsequent heat treatments. The Gd(5-x)Zr(x)Si(4) phases adopt the orthorhombic Gd(5)Si(4)-type (space group Pnma) structure for x≤ 0.25 and the tetragonal Zr(5)Si(4)-type (space group P4(1)2(1)2) structure for x≥ 1.0, respectively. The samples with intermediate compositions contain two phases. Single-crystal X-ray diffraction reveals a preferential site occupancy for Zr on the three metal sites in the order of M3 > M2 > M1. Size arguments based on the local coordination environments suggest that the larger Gd atoms preferentially occupy the larger M1 site, while the smaller Zr atoms tend to occupy the smaller metal sites, M2 and M3. Tight-binding linear-muffin-tin orbital calculations illustrate a role of the metal-silicon bonds in the metal site occupation. An increase in the valence electron concentration through the Zr substitution weakens the Si-Si interactions but enhances the metal-silicon and metal-metal interactions. The Curie temperature of Gd(5-x)Zr(x)Si(4) decreases gradually with the increasing Zr content.