AsS2Cl - An arsenic(V) compound? Formation, stability and structure of gaseous AsSCl and AsS2Cl - A combined experimental and theoretical study

By reaction of solid As4S4 with gaseous Cl2 at a temperature of 410 K gaseous AsSCl and AsS2Cl are formed. Unexpectedly in AsS2Cl the arsenic is not of formal oxidation state +V but +III: the molecular structure of AsS2Cl is arranged as a 1-chloro-dithia-arsirane and comprises an hitherto unknown AsS2 three-membered ring. Thermodynamic data on AsSCl and AsS2Cl are obtained by mass spectrometry (MS). The experimental data are extended and confirmed by ab initio quantum chemical calculations (QC). The following values are given: ΔfH0298(AsSCl) = −5.2 kJ mol−1 (MS), ΔfH0298(AsSCl) = 1.7 kJ mol−1 (QC), S0298(AsSCl) = 296.9 J K−1 mol−1 (QC) and cp0T(AsSCl) = 55.77 + 3.97 × 10−3T − 4.38 × 105T−2 − 1.83 × 10−6T2 and ΔfH0298(AsS2Cl) = −39.0 kJ mol−1 (MS), ΔfH0298(AsS2Cl) = −20.2 kJ mol−1 (QC), S0298(AsS2Cl) = 321.3 J K−1 mol−1 (QC) and cp0T(AsS2Cl) = 80.05 + 5.09 × 10−3T − 7.61 × 105T−2 − 2.35 × 10−6T2 (298.15 K < T < 1000 K) (QC). The ionization energies are determined (IP(AsSCl) = 10.5, IP(AsS2Cl) = 10.2 eV). The IR spectrum of AsSCl is detected by means of matrix isolation spectroscopy. The estimated force constant f(As[double bond, length as m-dash]S) = 4.47 mdyn·Å−1 gives rise to an As[double bond, length as m-dash]S double bond

Large Scales - Long Times: Adding High Energy Resolution to SANS

The Neutron Spin Echo (NSE) variant MIEZE (Modulation of IntEnsity by Zero Effort), where all beam manipulations are performed before the sample position, offers the possibility to perform low background SANS measurements in strong magnetic fields and depolarising samples. However, MIEZE is sensitive to differences \DeltaL in the length of neutron flight paths through the instrument and the sample. In this article, we discuss the major influence of \DeltaL on contrast reduction of MIEZE measurements and its minimisation. Finally we present a design case for enhancing a small-angle neutron scattering (SANS) instrument at the planned European Spallation Source (ESS) in Lund, Sweden, using a combination of MIEZE and other TOF options, such as TISANE offering time windows from ns to minutes. The proposed instrument allows studying fluctuations in depolarizing samples, samples exposed to strong magnetic fields, and spin-incoherently scattering samples in a straightforward way up to time scales of \mus at momentum transfers up to 0.01 {\AA}-1, while keeping the instrumental effort and costs low.Comment: 5 pages, 8 figure

A cyclopentadienyl functionalized silylene-a flexible ligand for Si- And C-coordination

The synthesis of a 1,2,3,4-tetramethylcyclopentadienyl (Cp$^{4}$) substituted four-membered N-heterocyclic silylene [{PhC(NtBu) $_{2}$}Si(C$_{5}$Me$_{4}$H)] is reported first. Then, selected reactions with transition metal and a calcium precursor are shown. The proton of the Cp$_{4}$-unit is labile. This results in two different reaction pathways: (1) deprotonation and (2) rearrangement reactions. Deprotonation was achieved by the reaction of [{PhC(NtBu) $_{2}$}Si(C$_{5}$Me$_{4}$H)] with suitable zinc precursors. Rearrangement to [{PhC(NtBu) $_{2}$}(C$_{5}$Me$_{4}$)SiH], featuring a formally tetravalent silicon R$_{2}$CSi(R′)-H unit, was observed when the proton of the Cp$^{4}$ ring was shifted from the Cp$^{4}$-ring to the silylene in the presence of a Lewis acid. This allows for the coordination of the Cp$^{4}$-ring to a calcium compound. Furthermore, upon reaction with transition metal dimers [MCl(cod)] $_{2}$ (M = Rh, Ir; cod = 1,5-cyclooctadiene) the proton stays at the Cp$^{4}$-ring and the silylene reacts as a sigma donor, which breaks the dimeric structure of the precursors

Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.Comment: In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytop

Integer polyhedra for program analysis

Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron

A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274