Frobenius formula for the characters of hecke algebras of type An−1 at roots of unity

A Frobenius formula is found for the (m, k)-standard characters φ^σ _ρ, of the Hecke algebras H_n(q) of type A_n-1, where q is a primitive pth root of unity, with p=m+k.     

Hydrodynamic and interparticle potential effects on aggregation of colloidal particles

The effects of both hydrodynamic interaction and the form of the interparticle potential on the aggregation process for dispersed spherical particles are investigated by computational simulation. The simulation methods of Brownian Dynamics (BD) and Stokesian Dynamics (SD) are applied, over a range of solid volume fraction of $0.04???0.12$. The interparticle potential is a combination of a generalized Lennard-Jones form and a Yukawa potential, the latter of which describes a screened electrostatic repulsion at longer range. The combined potential is parameterized to include a roughly constant primary minimum near contact, along with a variable repulsive barrier at slightly larger separation. The microstructure is characterized through the pair distribution function, g(r), and the static structure factor. The repulsive barrier reduces the rate of aggregation and is also seen to affect the structure, with a large repulsion associated with a more tenuous structure. This is reflected in the potential having a strong effect on the evolution of ‘bonds’ per particle. Hydrodynamic interactions were found to reduce the solid fraction required for percolation, with the influence depending upon the form of the potential; the difference in percolation threshold was significant, with ${?}_{c\text{,}\mathit{SD}}?0.06$ and ${?}_{c\text{,}\mathit{BD}}?0.08$ a typical difference for moderate repulsion barriers. These results are for 864 particles in a cubic unit cell. To address the mechanism for this influence of hydrodynamic interactions, a complementary analysis of the evolution of numerous independent three-particle aggregates was performed. The analysis shows that hydrodynamic interaction slows the evolution toward a condensed aggregate of lowest potential energy in a way which cannot be explained by a simple rescaling of the drag due to uncorrelated particle motions.     

Six-coordinate uranium complexes featuring a bidentate anilide ligand

The synthesis of a new bidentate anilide ligand and four uranium amide complexes utilizing the ligand are reported. The secondary aniline HN[R]Ar_MeL (R = C(CD₃)₂CH₃, Ar_MeL = 2-NMe₂-5-MeC₆H₃) is prepared by condensation of H₂NAr_MeL and acetone-d₆ followed by alkylation of the resulting imine with MeLi. The ligand precursors (Et₂O)Li(N[R]Ar_MeL) and K(N[R]Ar_MeL) are prepared through deprotonation of HN[R]Ar_MeL with n-BuLi and KH, respectively. Treatment of UI₃(THF)₄ with (Et₂O)Li(N[R]Ar_MeL) (2 equiv) provides the uranium(III) -ate complex Li[I₂U(N[R]Ar_MeL)₂] (Li[1]), while treatment of UI₃ with three equiv. of K(N[R]Ar_MeL) provides the neutral uranium(III) complex U(N[R]Ar_MeL)₃ (2). Both uranium(III) complexes are susceptible to 1e oxidation, as is demonstrated by the syntheses of the uranium(IV) derivatives I₂U(N[R]Ar_MeL)₂ (1) and [U(N[R]Ar_MeL)₃][OTf] ([2][OTf]; OTf = CF₃SO₃). The spectroscopic and X-ray structural characterization of all four uranium complexes is described. The structures of 2 and [2][OTf] exhibit a large degree of steric pressure about the uranium center, effectively preventing the [2]⁺ ion from achieving a seven-coordinate structure.     

A highly reduced cyanogen ligand derived from cyanide reductive coupling

The synthesis, structure, and spectroscopic features of a bimetallic cyanogen complex obtained from the reductive coupling of cyanide by a niobium(IV) precursor are described, and a mechanism for the coupling reaction is proposed based on DFT calculations.     

Terminal, anionic carbide, nitride, and phosphide transition-metal complexes as synthetic entries to low-coordinate phosphorus derivatives

Anionic terminal one-atom nitride, phosphide, and carbide complexes are excellent starting materials for the synthesis of ligands containing low-coordinate phosphorus centers in the protecting coordination sphere of the metal complex. Salt-elimination reactions with chlorophosphanes lead to phosphaisocyanide, iminophosphinimide, and diorganophosphanylphosphinidene complexes in which the unusual phosphorus ligands are stabilized by coordination. X-ray structure analyses and density-functional calculations illuminate the bonding in these compounds.     

A nitridoniobium(V) reagent that effects acid chloride to organic nitrile conversion: synthesis via heterodinuclear (Nb/Mo) dinitrogen cleavage, mechanistic insights, and recycling

The transformation of acid chlorides (RC(O)Cl) to organic nitriles (RC[triple bond]N) by the terminal niobium nitride anion [N[triple bond]Nb(N[Np]Ar)3]- ([1a-N]-, where Np = neopentyl and Ar = 3,5-Me2C6H3) via isovalent N for O(Cl) metathetical exchange is presented. Nitrido anion [1a-N]- is obtained in a heterodinuclear N2 scission reaction employing the molybdenum trisamide system, Mo(N[R]Ar)3 (R = t-Bu, 2a; R = Np, 2b), as a reaction partner. Reductive scission of the heterodinuclear bridging N2 complexes, (Ar[R]N)3Mo-(mu-N2)Nb(N[Np]Ar)3 (R = t-Bu, 3b; R = Np, 3c) with sodium amalgam provides 1 equiv each of the salt Na[1a-N] and neutral N[triple bond]Mo(N[R]Ar)3 (R = t-Bu, 2a-N; R = Np, 2b-N). Separation of 2-N from Na[1a-N] is readily achieved. Treatment of salt Na[1a-N] with acid chloride substrates in tetrahydrofuran (THF) furnishes the corresponding organic nitriles concomitant with the formation of NaCl and the oxo niobium complex O[triple bond]Nb(N[Np]Ar)3 (1a-O). Utilization of 15N-labeled 15N2 gas in this chemistry affords a series of 15N-labeled organic nitriles establishing the utility of anion [1a-N]- as a reagent for the 15N-labeling of organic molecules. Synthetic and computational studies on model niobium systems provide evidence for the intermediacy of both a linear acylimido and niobacyclobutene species along the pathway to organic nitrile formation. High-yield recycling of oxo 1a-O to a niobium triflate complex appropriate for heterodinuclear N2 scission has been developed. Specifically, addition of triflic anhydride (Tf2O, where Tf = SO2CF3) to an Et2O solution of 1a-O provides the bistriflate complex, Nb(OTf)2(N[Np]Ar)3 (1a-(OTf)2), in near quantitative yield. One-electron reduction of 1a-(OTf)2 with either cobaltocene (Cp2Co) or Mg(THF)3(anthracene) provided the monotriflato complex, Nb(OTf)(N[Np]Ar)3 (1a-(OTf)), which efficiently regenerates complexes 3b and 3c when treated with the molybdenum dinitrogen anions [N2Mo(N[t-Bu]Ar)3]- ([2a-N2]-) or [N2Mo(N[Np]Ar)3]- ([2b-N2]-), respectively.     

A General Chemical Method for the Stereochemical Analysis of Nucleoside-5′ [16o,18o] Phosphorothioates

Abstract

A simple chemical method of configurational analysis is presented which will facilitate stereochemical investigation of any restriction endonuclease enzyme reaction.