Crystals and total positivity on orientable surfaces

We develop a combinatorial model of networks on orientable surfaces, and study weight and homology generating functions of paths and cycles in these networks. Network transformations preserving these generating functions are investigated. We describe in terms of our model the crystal structure and R-matrix of the affine geometric crystal of products of symmetric and dual symmetric powers of type A. Local realizations of the R-matrix and crystal actions are used to construct a double affine geometric crystal on a torus, generalizing the commutation result of Kajiwara et al. (Lett Math Phys, 60(3):211–219, 2002) and an observation of Berenstein and Kazhdan (MSJ Mem, 17:1–9, 2007). We show that our model on a cylinder gives a decomposition and parametrization of the totally non-negative part of the rational unipotent loop group of GL _n .     

A criterion for the existence of strong solutions for the 3D Navier–Stokes equations

In this note we provide a criterion for the existence of globally defined solutions for any regular initial data for the 3D Navier–Stokes system in Serrin’s classes.     

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.     

Facile access to a series of large polycondensed pyridazines and their utility for the supramolecular synthesis of coordination polymers

Domino cyclization of ketoenols and hydrazine leads to a series of polycondensed pyridazines, which reveal potential as rigid N-donor multidentate ligands for supramolecular synthesis of open coordination polymers.     

Crossed beam reactions of methylidyne [CH(X2Π)] with D2-acetylene [C2D2(X1Σg(+))] and of D1-methylidyne [CD(X2Π)] with acetylene [C2H2(X1Σg(+))

The crossed molecular beam reactions of ground state methylidyne, CH(X(2)Π), with D2-acetylene, C(2)D(2)(X(1)Σ(g)(+)), and of D1-methylidyne, CD(X(2)Π), with acetylene, C(2)H(2)(X(1)Σ(g)(+)), were conducted under single collision conditions at a collision energy of 17 kJ mol(-1). Four competing reaction channels were identified in each system following atomic 'hydrogen' (H/D) and molecular 'hydrogen' (H(2)/D(2)/HD) losses. The reaction dynamics were found to be indirect via complex formation and were initiated by two barrierless-addition pathways of methylidyne/D1-methylidyne to one and to both carbon atoms of the D2-acetylene/acetylene reactant yielding HCCDCD/DCCHCH and c-C(3)D(2)H/c-C(3)H(2)D collision complexes, respectively. The latter decomposed via atomic hydrogen/deuterium ejection to form the thermodynamically most stable cyclopropenylidene species (c-C(3)H(2), c-C(3)D(2), c-C(3)DH). On the other hand, the HCCDCD/DCCHCH adducts underwent hydrogen/deuterium shifts to form the propargyl radicals (HDCCCD, D(2)CCCH; HDCCCH, H(2)CCCD) followed by molecular 'hydrogen' losses within the rotational plane of the decomposing complex yielding l-C(3)H/l-C(3)D. Quantitatively, our crossed beam studies suggest a dominating atomic compared to molecular 'hydrogen' loss with fractions of 81 ± 23% vs. 19 ± 10% for the CD/C(2)H(2) and 87 ± 30% vs. 13 ± 4% for the CH/C(2)D(2) systems. The role of these reactions in the formation of interstellar isomers of C(3)H(2) and C(3)H is also discussed.     

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.     

A crossed beam and ab initio investigation of the reaction of boron monoxide ((11)BO; X(2)Σ+) with acetylene (C2H2; X(1)Σ(g)+)

The reaction dynamics of boron monoxide (BO; X(2)Σ(+)) with acetylene (C(2)H(2); X(1)Σ(g)(+)) were investigated under single collision conditions at a collision energy of 13 kJ mol(-1) employing the crossed molecular beam technique; electronic structure RRKM calculations were conducted to complement the experimental data. The reaction was found to have no entrance barrier and proceeded via indirect scattering dynamics initiated by an addition of the boron monoxide radical with its boron atom to the carbon-carbon triple bond forming the O(11)BHCCH intermediate. The latter decomposed via hydrogen atom emission to form the linear O(11)BCCH product through a tight exit transition state. The experimentally observed sideways scattering suggests that the hydrogen atom leaves perpendicularly to the rotational plane of the decomposing complex and almost parallel to the total angular momentum vector. RRKM calculations indicate that a minor micro channel could involve a hydrogen migration in the initial collision to form an O(11)BCCH(2) intermediate, which in turn can also emit atomic hydrogen. The overall reaction to form O(11)BCCH plus atomic hydrogen from the separated reactants was determined to be exoergic by 62 ± 8 kJ mol(-1). The reaction dynamics were also compared with the isoelectronic reaction of the cyano radical (CN; X(2)Σ(+)) with acetylene (C(2)H(2); X(1)Σ(g)(+)) studied earlier.     

Semiempirical UNO-CAS and UNO-CI: method and applications in nanoelectronics

Unrestricted Natural Orbital-Complete Active Space Configuration Interaction, abbreviated as UNO-CAS, has been implemented for NDDO-based semiempirical molecular-orbital (MO) theory. A computationally more economic technique, UNO-CIS, in which we use a configuration interaction (CI) calculation with only single excitations (CIS) to calculate excited states, has also been implemented and tested. The class of techniques in which unrestricted natural orbitals (UNOs) are used as the reference for CI calculations is denoted UNO-CI. Semiempirical UNO-CI gives good results for the optical band gaps of organic semiconductors such as polyynes and polyacenes, which are promising materials for nanoelectronics. The results of these semiempirical UNO-CI techniques are generally in better agreement with experiment than those obtained with the corresponding conventional semiempirical CI methods and comparable to or better than those obtained with far more computationally expensive methods such as time-dependent density-functional theory. We also show that symmetry breaking in semiempirical UHF calculations is very useful for predicting the diradical character of organic compounds in the singlet spin state.     

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.