A retrospective trust-region method for unconstrained optimization

We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to first- and second-order critical points is proved under classical assumptions and preliminary numerical experiments on CUTEr problems indicate that the new method is very competitive.     

Wave Operators on Quantum Algebras via Noncanonical Quantization

We suggest a method to quantize basic wave operators of Relativistic Quantum Mechanics (Laplace, Maxwell, Dirac ones) without using canonical coordinates. We define two-parameter deformations of the Minkowski space algebra and its 3-dimensional reduction via the so-called Reflection Equation Algebra and its modified version. Wave operators on these algebras are introduced by means of quantized partial derivatives described in two ways. In particular, they are given in so-called pseudospherical form which makes use of a q-deformation of the Lie algebra sl(2) and quantum versions of the Cayley-Hamilton identity.     

Single-crystal colloidal nanosheets of GeS and GeSe

Narrow-band-gap IV-VI semiconductors offer promising optoelectronic properties for integration as light-absorbing components in field-effect transistors, photodetectors, and photovoltaic devices. Importantly, colloidal nanostructures of these materials have the potential to substantially decrease the fabrication cost of solar cells because of their ability to be solution-processed. While colloidal nanomaterials formed from IV-VI lead chalcogenides such as PbS and PbSe have been extensively investigated, those of the layered semiconductors SnS, SnSe, GeS, and GeSe have only recently been considered. In particular, there have been very few studies of the germanium chalcogenides, which have band-gap energies that overlap well with the solar spectrum. Here we report the first synthesis of colloidal GeS and GeSe nanostructures obtained by heating GeI(4), hexamethyldisilazane, oleylamine, oleic acid, and dodecanethiol or trioctylphosphine selenide to 320 °C for 24 h. These materials, which were characterized by TEM, SAED, SEM, AFM, XRD, diffuse reflectance spectroscopy, and I-V conductivity measurements, preferentially adopt a two-dimensional single-crystal nanosheet morphology that produces fully [100]-oriented films upon drop-casting. Optical measurements indicated indirect band gaps of 1.58 and 1.14 eV for GeS and GeSe, respectively, and electrical measurements showed that drop-cast films of GeSe exhibit p-type conductivity.     

An algorithm for stochastic programs with first-order dominance constraints induced by linear recourse

We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage.     

Triazene formation via reaction of imidazol-2-ylidenes with azides

Treatment of N-heterocyclic carbenes (as their free carbenes or generated in situ) with alkyl, aryl, acyl or tosyl azides afforded the respective substituted triazenes in excellent yields.     

Challenges to computational quantum chemistry from contemporary advances in polyatomic molecular electronic spectroscopy

Molecular electronic spectroscopy featuring intramolecular proton transfer and twisted intramolecular charge transfer poses a whole new range of problems for computational quantum chemistry. The development of the four-level laser based on the intramolecular proton-transfer focuses on the subtleties of the interaction of the singlet and triplet electronic state manifolds of the two different tautomeric species. Examples are given of the sensitive variation of proton-transfer fluorescence with chemical substitution. A competing excitation channel is shown to exist when internal molecular torsion couples with sudden polarization to yield a twisted intramolecular charge transfer configuration. In such systems, three competing fluorescences can be observed. Several electronic puzzles will be presented that can provide fertile territory for quantum chemical computations. © 1993 John Wiley & Sons, Inc.     

Density functional theory calculations and exploration of a possible mechanism of N2 reduction by nitrogenase

Density functional theory (DFT) calculations have been performed on the nitrogenase cofactor, FeMoco. Issues that have been addressed concern the nature of M-M interactions and the identity and origin of the central light atom, revealed in a recent crystallographic study of the FeMo protein of nitrogenase (Einsle, O.; et al. Science 2002, 297, 871). Introduction of Se in place of the S atoms in the cofactor and energy minimization results in an optimized structure very similar to that in the native enzyme. The nearly identical, short, lengths of the Fe-Fe distances in the Se and S analogues are interpreted in terms of M-M weak bonding interactions. DFT calculations with O or N as the central atoms in the FeMoco marginally support the assignment of the central atom as N rather than O. The assumption was made that the central atom is the N atom, and steps of a catalytic cycle were calculated starting with either of two possible states for the cofactor and maintaining the same charge throughout (by addition of equal numbers of H(+) and e(-)) between steps. The states were [(Cl)Fe(II)(6)Fe(III)Mo(IV)S(9)(H(+))(3)N(3-)(Gl)(Im)](2-), [I-N-3H](2-), and [(Cl)Fe(II)(4)Fe(III)(3)Mo(IV)S(9)(H(+))(3)N(3-)(Gl)(Im)], [I-N-3H](0) (Gl = deprotonated glycol; Im = imidazole). These are the triply protonated ENDOR/ESEEM [I-N](5-) and M?ssbauer [I-N](3-) models, respectively. The proposed mechanism explores the possibilities that (a) redox-induced distortions facilitate insertion of N(2) and derivative substrates into the Fe(6) central unit of the cofactor, (b) the central atom in the cofactor is an exchangeable nitrogen, and (c) the individual steps are related by H(+)/e(-) additions (and reduction of substrate) or aquation/dehydration (and distortion of the Fe(6) center). The Delta E's associated with the individual steps of the proposed mechanism are small and either positive or negative. The largest positive Delta E is +121 kJ/mol. The largest negative Delta E of -333 kJ/mol is for the FeMoco with a N(3-) in the center (the isolated form) and an intermediate in the proposed mechanism.     

Synthesis and characterization of sulfur-voided cubanes. Structural analogues for the MoFe(3)S(3) subunit in the nitrogenase cofactor.

A new class of Mo/Fe/S clusters with the MoFe(3)S(3) core has been synthesized in attempts to model the FeMo-cofactor in nitrogenase. These clusters are obtained in reactions of the (Cl(4)-cat)(2)Mo(2)Fe(6)S(8)(PR(3))(6) [R = Et (I), (n)Pr (II)] clusters with CO. The new clusters include those preliminarily reported: (Cl(4)-cat)MoFe(3)S(3)(PEt(3))(2)(CO)(6) (III), (Cl(4)-cat)(O)MoFe(3)S(3)(PEt(3))(3)(CO)(5) (IV), (Cl(4)-cat)(Pyr)MoFe(3)S(3)(PEt(3))(2)(CO)(6) (VI), and (Cl(4)-cat)(Pyr)MoFe(3)S(3)(P(n)Pr(3))(3)(CO)(4) (VIII). In addition the new (Cl(4)-cat)(O)MoFe(3)S(3)(P(n)Pr(3))(3)(CO)(5) cluster (IVa), the (Cl(4)-cat)(O)MoFe(3)S(3)(PEt(3))(2)(CO)(6)cluster (V), the (Cl(4)-cat)(O)MoFe(3)S(3)(P(n)Pr(3))(2)(CO)(6) cluster (Va), the (Cl(4)-cat)(Pyr)MoFe(3)S(3)(P(n)Pr(3))(2)(CO)(6) cluster (VIa), and the (Cl(4)-cat)(P(n)Pr(3))MoFe(3)S(3)(P(n)Pr(3))(2)(CO)(6) cluster (VII) also are reported. Clusters III-VIII have been structurally and spectroscopically characterized. EPR, zero-field (57)Fe-M?ssbauer spectroscopic characterizations, and magnetic susceptibility measurements have been used for a tentative assignment of the electronic and oxidation states of the MoFe(3)S(3) sulfur-voided cuboidal clusters. A structural comparison of the clusters with the MoFe(3)S(3) subunit of the FeMo-cofactor has led to the suggestion that the storage of reducing equivalents into M-M bonds, and their use in the reduction of substrates, may occur with the FeMo-cofactor, which also appears to have M-M bonding. On the basis of this argument, a possible N(2)-binding and reduction mechanism on the FeMoco-cofactor is proposed.