On Bateman's method for second kind integral equations

Summary Under suitable conditions, we prove the convergence of the Bateman method for integral equations defined over bounded domains inR ^d ,d1. The proof makes use of Hilbert space methods, and requires the integral operator to be non-negative definite. For one-dimensional integral equations over finite intervals, estimated rates of convergence are obtained which depend on the smoothness of the kernel, but are independent of the inhomogeneous term. In particular, for aC kernel andn reasonably spaced Bateman points, the convergence is shown to be faster than any power of 1/n. Numerical calculations support this result.     

Mössbauer effect of iodine at pressures to 30 GPa

We report the first high pressure¹²⁹I Mössbauer measurements with elemental iodine at pressures to 30 GPa. A 20 mg/cm^{2 129}I₂ absorber was mounted in a diamond anvil cell with an effective diameter of 0.21 mm. The source used was Mg₃ ^129mTeO₆. Experiments were performed mainly at 4 K and the pressure was monitored by the ruby fluorescence method. With increasing pressure we observe a gradual decrease in ¦e²qQ¦ and an increase in IS and values of the low pressure, molecular phase; at 16 GPa a new phase (HP1) is detected characterized by a change in sign of e²qQ and a smaller value of ¦e²qQ¦, and a substantial increase in . At 24 GPa a new phase (HP2) is formed that is characterized by a smaller value of . In general the population of the molecular phase decreases from 1.0 near 15 GPa to a value of 0.4 at 30 GPa. The fraction of the high pressure phase (HP1 + HP2) increases at the expense of the molecular phase and that of the HP2 at the expense of the HP1 phase. These observations are discussed in relation to the onset of a metallic phase near 16 GPa and recent x-ray diffraction studies.Work performed under the auspices of the U.S. Department of Energy.     

Heteroatom transfer to alkenes by N-protected-oxaziridines: new reaction pathways and products

N-Alkoxycarbonyl- and N-carboxamido-oxaziridines are shown to react with aromatic alkenes to give epoxide, aziridine or hydro-oxidation products, in ratios depending on the oxaziridine structure. Chiral oxaziridines can effect epoxidation and hydro-oxidation with promising levels of asymmetric induction.     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.     

Probe metal binding mode of imine covalent organic frameworks: cycloiridation for (photo)catalytic hydrogen evolution from formate

Metalation of covalent organic frameworks (COFs) is a critical strategy to functionalize COFs for advanced applications yet largely relies on the pre-installed specific metal docking sites in the network, such as porphyrin, salen, 2,2′-bipyridine, etc. We show in this study that the imine linkage of simple imine-based COFs, one of the most popular COFs, readily chelate transition metal (Ir in this work) via cyclometalation, which has not been explored before. The iridacycle decorated COF exhibited more than 10-fold efficiency enhancement in (photo)catalytic hydrogen evolution from aqueous formate solution than its molecular counterpart under mild conditions. This work will inspire more functional cyclometallated COFs to be explored beyond catalysis considering the large imine COF library and the rich metallacycle chemistry.

This study describes cyclometallation as a new metal binding mode for imine-based COFs. The iridacycle decorated COF could be used for catalytic hydrogen evolution from aqueous formate solution with high stability and high efficacy.     

Molecular cluster decay viewed as escape from a potential of mean force

We show that evaporation from a quasistable molecular cluster may be treated as a kinetic problem involving the stochastically driven escape of a molecule from a potential of mean force. We derive expressions for the decay rate, and a relationship between the depth of the potential and the change in system free energy upon loss of a molecule from the cluster. This establishes a connection between kinetic and thermodynamic treatments of evaporation, but also reveals differences in the prefactor in the rate expression. We perform constant energy molecular dynamics simulations of cluster dynamics to calculate potentials of mean force, friction coefficients and effective temperatures for use in the kinetic analysis, and to compare the results with the directly observed escape rates. We also use the simulations to estimate the escape rates by a probabilistic analysis. It is much more efficient to calculate the decay rate by the methods we have developed than it is to monitor escape directly, making these approaches potentially useful for the assessment of molecular cluster stability.     

Theoretical analysis of peptidyl alpha-ketoheterocyclic inhibitors of human neutrophil elastase: Insight into the mechanism of inhibition and the application of QM/MM calculations in structure-based drug design

It has been suggested from QSAR data (P. D. Edwards, D. J. Wolanin, D.A. Andisik and M. W. Davis, J. Med. Chem., 1995, 38, 76) that the inhibition of elastase by peptidyl alpha-ketoheterocyclic inhibitors can occur in two ways, the less potent inhibitors forming a non-bonded Michaelis complex and the more potent set a covalently bonded enzyme-substrate intermediate. We report QM/MM studies of both binding and reactivity that confirm these findings, showing that the activity of the least potent set of inhibitors correlates with the calculated binding energy, and that of the more potent set correlates with the stability of the intermediate. These calculations show that QM/MM methods can be successfully employed to understand complicated structure-activity relationships and might be employed in the design and assessment of new inhibitors.