Generic determinantal schemes and the smoothability of determinantal schemes of codimension 2

The aim of this article is to prove a criterion for projectively Cohen-Macaulay two-codimensional subschemes ofP _k ^N to be smoothable. For curves inP _k ³ this criterion is due to T. Sauer [4]. The considered schemes are determinantal, so we study related generic affine determinantal schemes. We compute their dimension, and under the condition that the dimension is minimal we calculate the codimension of the singular locus.     

Fluorescence and REMPI spectroscopy of jet-cooled isolated 2-phenylindene in the S1 state

We investigated the spectroscopy of the first excited singlet electronic state S1 of 2-phenylindene using both fluorescence excitation spectroscopy and resonantly enhanced multiphoton ionization spectroscopy. Moreover, we investigated the dynamics of the S1 state by determining state-selective fluorescence lifetimes up to an excess energy of approximately 3400 cm(-1). Ab initio calculations were performed on the torsional potential energy curve and the equilibrium and transition state geometries and normal-mode frequencies of the first excited singlet state S1 on the CIS level of theory. Numerous vibronic transitions were assigned, especially those involving the torsional normal mode. The torsional potentials of the ground and first excited electronic states were simulated by matching the observed and calculated torsional frequency spacings in a least-squares fitting procedure. The simulated S1 potential showed very good agreement with the ab initio potential calculated on the CIS/6-31G(d,p) level of theory. TDDFT energy corrections improved the match with the simulated S(1) torsional potential. The latter calculation yielded a torsional barrier of V2 = 6708 cm(-1), and the simulation a barrier of V2 = 6245 cm(-1). Ground-state normal-mode frequencies were calculated on the B3LYP/6-31G(d,p) level of theory, which were used to interpret the infrared spectrum, the FDS spectrum of the transition and hot bands of the FES spectrum. The fluorescence intensities of the nu49 overtone progression could reasonably be reproduced by considering the geometry changes upon electronic excitation predicted by the ab initio calculations. On the basis of the torsional potential calculations, it could be ruled out that the uniform excess energy dependence of the fluorescence lifetimes is linked to the torsional barrier in the excited state. The rotational band contour simulation of the transition yielded rotational constants in close agreement to the ab initio values for both electronic states. Rotational coherence signals were obtained by polarization-analyzed, time-resolved measurements of the fluorescence decay of the transition. The simulation of these signals yielded corroborating evidence as to the quality of the ab initio calculated rotational constants of both states. The origin of the anomalous intensity discrepancy between the fluorescence excitation spectrum and the REMPI spectrum is discussed.     

Speeding up IP-based algorithms for constrained quadratic 0–1 optimization

In many practical applications, the task is to optimize a non-linear objective function over the vertices of a well-studied polytope as, e.g., the matching polytope or the travelling salesman polytope (TSP). Prominent examples are the quadratic assignment problem and the quadratic knapsack problem; further applications occur in various areas such as production planning or automatic graph drawing. In order to apply branch-and-cut methods for the exact solution of such problems, the objective function has to be linearized. However, the standard linearization usually leads to very weak relaxations. On the other hand, problem-specific polyhedral studies are often time-consuming. Our goal is the design of general separation routines that can replace detailed polyhedral studies of the resulting polytope and that can be used as a black box. As unconstrained binary quadratic optimization is equivalent to the maximum-cut problem, knowledge about cut polytopes can be used in our setting. Other separation routines are inspired by the local cuts that have been developed by Applegate, Bixby, Chvátal and Cook for faster solution of large-scale traveling salesman instances. Finally, we apply quadratic reformulations of the linear constraints as proposed by Helmberg, Rendl and Weismantel for the quadratic knapsack problem. By extensive experiments, we show that a suitable combination of these methods leads to a drastic speedup in the solution of constrained quadratic 0–1 problems. We also discuss possible generalizations of these methods to arbitrary non-linear objective functions.     

Isoelectronic caesium compounds: the triphosphenide Cs[tBu3SiPPPSitBu3] and the enolate Cs[OCH=CH2

The caesium triphosphenide Cs[tBu3SiPPPSitBu3] was accessible from the reaction of CsF with the sodium triphosphenide Na[tBu3SiPPPSitBu3] in tetrahydrofuran at room temperature. In contrast to the preparation of tetrahydrofuran-solvated silanides M[SitBu3] (M = Li, Na, K), our efforts to synthesize the caesium silanide Cs[SitBu3] as a tetrahydrofuran complex failed. When tBu3SiBr was treated with an excess of caesium metal in tetrahydrofuran at room temperature, the caesium enolate Cs[OCH=CH2] and the supersilane tBu3SiH formed rather than the silanide Cs[SitBu3]. X-Ray quality crystals of the enolate Cs[OCH=CH2] (orthorhombic, Pnma) were obtained from tetrahydrofuran at ambient temperature. In contrast to the structures of its homologues M[tBu3SiPPPSitBu3] (M = Na, K), the caesium triphosphenide Cs[tBu3SiPPPSitBu3] features a polymer in the solid state (orthorhombic, Cmcm).     

Correlation between the molecular structure and photoresponse in aliphatic self-assembled monolayers with azobenzene tailgroups

We have compared the structural and photoisomerization properties of self-assembled monolayers (SAMs) comprising either the trans or cis isomers of azobenzene terminated dithiolane with in-chain amide unit, viz., 4-(phenyldiazenyl)phenyl-4-(1,2-dithiolane-3-yl)-butylcarboxamide ( 1). These films were prepared on Au(111) from solutions of both isomers. Structure and composition of the SAMs were studied by X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy. The photoresponse of the films was monitored in real time by ellipsometry. SAMs fabricated from the trans isomer were found to be densely packed and highly ordered. These films did not show any discernible photoresponse upon irradiation with UV light, which, under favorable conditions, triggers the trans- cis isomerization. In contrast, films prepared from solutions containing predominantly the cis isomer were loosely packed and mostly disordered but exhibited reversible photoreactivity. The results confirm that steric effects, i.e., available free volume, play a dominant role for the photoresponse of aliphatic SAMs bearing the photoactive azobenzene group. The crystal structure of 1 ( trans isomer) exhibits a row-like aggregation of neighboring molecules by weak hydrogen bonds and can be taken as a model for the arrangement of 1 in the monolayer films. Further, in addition to the surface coordination behavior, we have also mimicked the chemisorption of the 1,2-dithiolane moiety onto the gold substrate in molecular coordination chemistry in oxidative addition reactions with the zero-valent platinum complex [Pt(PPh 3) 4].     

Dissecting entropic coiling and poor solvent effects in protein collapse

The early events in protein collapse and folding are guided by the protein's elasticity. The contributions of entropic coiling and poor solvent effects like hydrophobic forces to the elastic response of proteins are currently unknown. Using molecular simulations of stretched ubiquitin in comparison with models of proteins as entropic chains, we find a surprisingly high stiffness of the protein backbone, reflected by a persistence length of 1.2 nm, which is significantly reduced by hydrophobic forces acting between protein side chains to an apparent persistence length of 0.3-0.6 nm frequently observed in single-molecule stretching experiments. Thus, the poor solvent conditions of a protein in water lead to a protein compaction much beyond the coiling of an entropic chain and thereby allow a protein to appear softer than when using good solvents.