The Diffusion of a Population¶Partly Driven by its Preferences

The goal of this paper is to investigate a stationary model for the diffusion of a population when the diffusion coefficient at one location depends on the population at another. This could simulate, for instance, attraction or repulsion between the species considered. Accepted May 29, 2000?Published online November 24, 2000     

Avoided level crossing μSR of organic free radicals

Several aspects of the ALC-μSR technique of muonated organic free radicals in liquids, including the effects of chemical dynamics and T₁-processes are discussed.     

Tri‐ and Tetrasubstituted N‐Phthalimidoaziridines in 1,3‐Dipolar Cycloaddition Reactions

The thermal reactions of the 2,2,3‐trisubstituted N‐phthalimidoaziridine 1a with dimethyl acetylenedicarboxylate (DMAD), thioketones 4a – 4d , and dimethyl azodicarboxylate ( 5 ) proceed even at room temperature leading to the five‐membered cycloadducts 2a, 6 – 8 , and 12 , respectively, with retention of the spatial arrangement of the aziridine substituents, in contrast to the expectation based on the conservation of orbital symmetry in concerted reactions. The analogous reactions of the tetrasubstituted phthalimidoaziridine 1b with thioketones at 40° lead to the 1,3‐thiazolidine derivatives 10 and 11 as mixtures of diastereoisomers. These unexpected results may be explained by either the isomerization of the intermediate azomethine ylides or a non‐concerted stepwise cycloaddition reaction of these ylides with the dipolarophiles. The structures of some adducts have been determined by X‐ray crystallography.     

Stable and tunable phosphorescent neutral cyclometalated Au(III) diaryl complexes

A series of novel luminescent cyclometalated Au(III) neutral complexes of the type cis-[(N(∧)C)AuL] [N(∧)C = 2-phenylpyridine (ppy), L = 1,1'-biphenyl (1)] and cis-[(N(∧)C)AuL(2)] [N(∧)C = 2-phenylpyridine (ppy), L = C(6)H(5) (2), C(6)F(5) (3), C(6)H(4)-CF(3)-p (4), 2-C(4)H(3)S (5)]; [N(∧)C = 2-(2-thienyl)pyridine (thpy), L = C(6)H(5) (6), C(6)F(5) (7)]; [N(∧)C = 2-(5-methyl-2-thienyl)pyridine (5 m-thpy), L = C(6)F(5) (8)] were successfully synthesized. The X-ray crystal structures of all compounds except 3 have been determined. These complexes were found to show long-lived emission in solution at room temperature. The emission origins of the complexes have been tentatively assigned to be derived from triplet states predominantly bearing intraligand (IL) character with some perturbation from the metal center. Density functional theory (DFT) calculations were performed to evaluate the stability associated with the complexes and TD-DFT calculations to ascertain the nature of the excited state. Variation of the cyclometalated ligands in the complexes readily leads to the tuning of the nature of the lower energy emissive states.     

Water soluble phosphine rhenium complexes

Reduction of [NMe₄]₂[ReBr₅(NO)] (1) with zinc in acetonitrile leads to the known trisacetonitrile compound [ReBr₂(CH₃CN)₃(NO)] (2). Attempts to turn 2 into a dihydrogen or a hydride complex applying direct reaction with H₂ or with H₂ and a base were unsuccessful. Complex 2 could be transformed into [ReBr(BF₄)mer-(CH₃CN)₃(NO)] (2a) with AgBF₄ in acetonitrile and was used as a starting material in a ligand exchange reaction with the water soluble phosphine 1,3,5-triaza-7-phosphadamantane (PTA) to obtain the complex [ReBr₂(NO)(PTA)₃] (3). When the reduction of 1 with zinc was carried out in the presence of PTA in acetonitrile, the disubstituted complex [ReBr₂(CH₃CN)(NO)(PTA)₂] (4) was formed. The olefin-coordinated rhenium complexes [ReBr₂(NO)(CH₂CH₂)(PTA)₂] (5a) and [ReBr₂(NO)(PhCHCH₂)(PTA)₂] (5b) were obtained from the reaction of 4 with the corresponding olefins. Complex 4 reacts further with NaHBEt₃ in THF to give the dihydride [ReH₂(THF)(NO)(PTA)₂] (6). In the presence of ethylene 6 is transformed into the ethyl hydride complex [ReH(CH₂CH₃)(η²-C₂H₄)(NO)(PTA)₂] (7). Complexes 6 showed catalytic activity in the hydrogenation of olefins.     

Synthesis of (2-hydroxo-5-chlorophenylaminoisonitrosoacetyl)phenyl ligands and their complexes: Spectral,thermal and solvent-extraction studies

Four different types of new ligands Ar[COC(NOH)R] _n (Ar=biphenyl, n = 1 H₂L¹; Ar=biphenyl, n = 2 H₄L²; Ar=diphenylmethane, n = 1 H₂L³; Ar=diphenylmethane, n = 2 H₄L⁴; R=2-amino-4-chlorophenol in all ligands) have been obtained from 1 equivalent of chloroketooximes Ar[COC(NOH)Cl] _n (HL¹-H₂L⁴) and 1 equivalent of 2-amino-4-chlorophenol (for H₂L¹ and H₂L³) or 2 equivalent of 2-amino-4-chlorophenol (for H₄L² and H₄L⁴). (Mononuclear or binuclear cobalt(II), nickel(II), copper(II) and zinc(II) complexes were synthesized with these ligands.) These compounds have been characterized by elemental analyses, AAS, infra-red spectra and magnetic susceptibility measurements. The ligands have been further characterized by ¹H NMR. The results suggest that the dinuclear complexes of H₂L¹ and H₂L³ have a metal:ligand ratio of 1:2; the mononuclear complexes of H₄L² and H₄L⁴ have a metal:ligand ratio of 1:1 and dinuclear complexes H₄L² and H₄L⁴ have a metal:ligand ratio of 2:1. The binding properties of the ligands towards selected transition metal ions (Mn^II, Co^II, Ni^II, Cu^II, Zn^II, Pb^II, Cd^II, Hg^II) have been established by extraction experiments. The ligands show strong binding ability towards mercury(II) ion. In addition, the thermal decomposition of some complexes is studied in nitrogen atmosphere.     

Rhenium hydride/boron Lewis acid cocatalysis of alkene hydrogenations: activities comparable to those of precious metal systems

Dibromonitrosyl(dihydrogen)rhenium(I) complexes [ReBr(2)(NO)(PR(3))(2)(η(2)-H(2))] (1; R = iPr, a; Cy, b) and Me(2)NH·BH(3) (DMAB) catalyze at either 90 °C or ambient temperature under 10 bar of H(2) the hydrogenation of various terminal and cyclic alkenes (1-hexene, 1-octene, cyclooctene, styrene, 1,5-cyclooctadiene, 1,7-octadiene, α-methylstyrene). Maximum turnover frequency (TOF) values of 3.6 × 10(4) h(-1) at 90 °C and 1.7 × 10(4) h(-1) at 23 °C were achieved in the hydrogenation of 1-hexene. The extraordinary catalytic performance of the 1/DMAB system is attributed to the formation of five-coordinate rhenium(I) hydride complexes [Re(Br)(H)(NO)(PR(3))(2)] (2; R = iPr, a; Cy, b) and the action of the Lewis acid BH(3) originating from DMAB. The related 2/BH(3)·THF catalytic system also exhibits under the same conditions high activity in the hydrogenation of various alkenes with a maximum turnover number (TON) of 1.2 × 10(4) and a maximum TOF of 4.0 × 10(4) h(-1). For the hydrogenations of 1-hexene with 2a and 2b, the effect of the strength of the boron Lewis acid was studied, the acidity being in the following order: BCl(3) > BH(3) > BEt(3) ≈ BF(3) > B(C(6)F(5))(3) > BPh(3) ? B(OMe)(3). The order in catalytic activity was found to be B(C(6)F(5))(3) > BEt(3) ≈ BH(3)·THF > BPh(3) ? BF(3)·OEt(2) > B(OMe)(3) ? BCl(3). The stability of the catalytic systems was checked via TON vs time plots, which revealed the boron Lewis acids to cause an approximate inverse order with the Lewis acid strength: BPh(3) > BEt(3) ≈ BH(3)·THF > B(C(6)F(5))(3). For the 2a/BPh(3) system a maximum TON of 3.1 × 10(4) and for the 2a/B(C(6)F(5))(3) system a maximum TOF of 5.6 × 10(4) h(-1) were obtained in the hydrogenation of 1-hexene. On the basis of kinetic isotope effect determinations, H(2)/D(2) scrambling, halide exchange experiments, Lewis acid variations, and isomerization of terminal alkenes, an Osborn-type catalytic cycle is proposed with olefin before H(2) addition. The active rhenium(I) monohydride species is assumed to be formed via reversible bromide abstraction with the "cocatalytic" Lewis acid. Homogeneity of the hydrogenations was tested with filtration and mercury poisoning experiments. These "rhenium(I) hydride/boron Lewis acid" systems demonstrate catalytic activities comparable to those of Wilkinson- or Schrock-Osborn-type hydrogenations accomplished with precious metal catalysts.     

Energy distribution curves of ultrafast laser-induced field emission and their implications for electron dynamics

Energy distribution curves of laser-induced electron pulses from a tungsten tip have been measured as a function of tip voltage and laser power. Electron emission via tunneling through and/or excitation over the surface barrier from photoexcited nonequilibrium electron distributions are clearly observed. The spectral shapes largely vary with the emission processes and are strongly affected by electron dynamics. Simulations successfully reproduce the spectra, thus allowing direct insight into the involved electron dynamics and revealing the temporal tunability of electron emission via the two experimental parameters. These results should be useful to optimize the pulse characteristics for many applications based on ultrafast laser-induced electron emission.     

On the mod-Gaussian convergence of a sum over primes

We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates ${\mathrm{Im }}\log \zeta (1/2+it)$ . This Dirichlet polynomial is sufficiently long to deduce Selberg’s central limit theorem with an explicit error term. Moreover, assuming the Riemann hypothesis, we apply the theory of the Riemann zeta-function to extend this mod-Gaussian convergence to the complex plane. From this we obtain that ${\mathrm{Im }}\log \zeta (1/2+it)$ satisfies a large deviation principle on the critical line. Results about the moments of the Riemann zeta-function follow.     

The Cut-off Phenomenon for Brownian Motions on Compact Symmetric Spaces

In this paper, we prove the cut-off phenomenon in total variation distance for the Brownian motions traced on the classical symmetric spaces of compact type, that is to say:

1. the classical simple compact Lie groups: special orthogonal groups SO(n), special unitary groups SU(n) and compact symplectic groups USp(n);
2. the real, complex and quaternionic Grassmannian varieties (including the real spheres, and the complex or quaternionic projective spaces when q?=?1): SO(p?+?q)/(SO(p)×SO(q)), SU(p?+?q)/S(U(p)×U(q)) and USp(p?+?q)/(USp(p)×USp(q));
3. the spaces of real, complex and quaternionic structures: SU(n)/SO(n), SO(2n)/ U(n), SU(2n)/USp(n) and USp(n)/UU(n).

Denoting μ _t the law of the Brownian motion at time t, we give explicit lower bounds for d _TV(μ _t ,Haar) if $t < t_{\text{cut-of\/f}}=\alpha \log n$ , and explicit upper bounds if $t > t_{\text{cut-of\/f}}$ . This provides in particular an answer to some questions raised in recent papers by Chen and Saloff-Coste. Our proofs are inspired by those given by Rosenthal and Porod for products of random rotations in SO(n), and by Diaconis and Shahshahani for products of random transpositions in $\mathfrak{S}_{n}$ .