Finite reservoir replica exchange to enhance canonical sampling in rugged energy surfaces

A "finite reservoir" replica exchange method is presented to further enhance sampling upon the regular replica exchange method (REM) in a rugged energy surface. The present method can facilitate important sampling more efficiently by exchanging structures with configurations randomly selected from a finite-sized reservoir; this finite reservoir is pregenerated and updated by a mechanism of replica exchange with neighboring "temperature" simulations. In practice, this proposal revises exchange schedule in REM simulations in order to make productive exchange for conformational "tunneling" more frequent.     

The algebraic degree of semidefinite programming

Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes.     

Dynamic Wave Propagation in Porous Media Semi-Infinite Domains

The problem of dynamic wave propagation in semi-infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half-space and soil-structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary-value problems (IBVP). Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid-fluid aggregates. Based on the continuum-mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi-static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time-integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two-dimensional IBVP. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distortion Varieties

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distortion varieties comes from multi-view geometry in computer vision. Our theory furnishes a new framework for formulating and solving minimal problems for camera models with image distortion.     

An ab initio quantum mechanical charge field molecular dynamics simulation of a dilute aqueous HCl solution

An ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation has been performed to study the structural and dynamical properties of a dilute aqueous HCl solution. The solute molecule HCl and its surrounding water molecules were treated at Hartree‐Fock level in conjunction with Dunning double‐ζ plus polarization function basis sets. The simulation predicts an average H? Cl bond distance of 1.28 Å, which is in good agreement with the experimental value. The H_HCl···O_w and Cl_HCl···H_w distances of 1.84 and 3.51 Å were found for the first hydration shell. At the hydrogen site of HCl, a single water molecule is the most preferred coordination, whereas an average coordination number of 12 water molecules of the full first shell was observed for the chloride site. The hydrogen bonding at the hydrogen site of HCl is weakened by proton transfer reactions and an associated lability of ligand binding. Two proton transfer processes were observed in the QMCF MD simulation, demonstrating acid dissociation of HCl. A weak structure‐making/breaking effect of HCl in water is recognized from the mean residence times of 2.1 and 0.8 ps for ligands in the neighborhood of Cl and H sites of HCl, respectively. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Unusual photochemical dynamics of a bridged azobenzene derivative

In a large-scale simulation study of ultrafast photochemical dynamics for an azobenzene compound with an additional ethylenic bridge we have found unexpected features: while the dynamics starting from the Z isomer follow a barrierless path with steep gradients, the dynamics starting from the E isomer proceed through a different conical intersection surrounded by a rather flat potential energy landscape and then encounter a sizeable barrier in the electronic ground state that markedly influences the reaction behavior. Direct comparisons with experimental static UV spectra, quantum yields, and transient absorption spectra show good agreement and reveal signatures of this unusual behavior.     

A Facile Route for the Synthesis of Polycationic Tellurium Cluster Compounds: Synthesis in Ionic Liquid Media and Characterization by Single‐Crystal X‐ray Crystallography and Magnetic Susceptibility

An innovative soft chemical approach was applied, using ionic liquids as an alternative reaction medium for the synthesis of tellurium polycationic cluster compounds at room temperature. [Mo₂Te₁₂]I₆, Te₆[WOCl₄]₂, and Te₄[AlCl₄]₂ were isolated from the ionic liquid [BMIM]Cl/AlCl₃ ([BMIM]⁺: 1‐n‐butyl‐3‐methylimidazolium) and characterized. Black, cube‐shaped crystals of [Mo₂Te₁₂]I₆, which is not accessible by conventional chemical transport reaction, were obtained by reaction of the elements at room temperature in [BMIM]Cl/AlCl₃. The monoclinic structure (P2₁/n, a = 1138.92(2) pm, b = 1628.13(2) pm, c = 1611.05(2) pm, β = 105.88(1) °) is homeotypic to the triclinic bromide [Mo₂Te₁₂]Br₆. In the binulear complex [Mo₂Te₁₂]⁶⁺, the molybdenum(III) atoms are η⁴‐coordinated by terminal Te₄²⁺ rings and two bridging η²‐Te₂^2– dumbbells. Despite the short Mo···Mo distance of 297.16(5) pm, coupling of the magnetic moments is not observed. The paramagnetic moment of 3.53 μ_B per molybdenum(III) atom corresponds to an electron count of seventeen. Black crystals of monoclinic Te₆[WOCl₄]₂ are obtained by the oxidation of tellurium with WOCl₄ in [BMIM]Cl/AlCl₃. Tellurium and tellurium(IV) synproportionate in the ionic liquid at room temperature yielding violet crystals of orthorhombic Te₄[AlCl₄]₂.     

High resolution 1H-detected solid-state NMR spectroscopy of protein aliphatic resonances: access to tertiary structure information

Biological magic angle spinning (MAS) solid-state nuclear magnetic resonance spectroscopy has developed rapidly over the past two decades. For the structure determination of a protein by solid-state NMR, routinely (13)C,(13)C distance restraints as well as dihedral restraints are employed. In protonated samples, this is achieved by growing the bacterium on a medium which contains [1,3]-(13)C glycerol or [2]-(13)C glycerol to dilute the (13)C spin system. Labeling schemes, which rely on heteronuclei, are insensitive both for detection and in terms of quantification of distances, since they are relying on low-γ nuclei. Proton detection can in principle provide a gain in sensitivity by a factor of 8 and 31, compared to the (13)C or (15)N detected version of the experiment. We report here a new labeling scheme, which enables (1)H-detection of aliphatic resonances with high resolution in MAS solid-state NMR spectroscopy. We prepared microcrystals of the SH3 domain of chicken α-spectrin with 5% protonation at nonexchangeable sites and obtained line widths on the order of 25 Hz for aliphatic (1)H resonances. We show further that (13)C resolved 3D-(1)H,(1)H correlation experiments yield access to long-range proton-proton distances in the protein.     

Synthesis of musafluorone: a naphthoxanthenone isolated from Musa acuminata

5-Methoxy-3H-naphtho[2,1,8-mna]xanthen-3-one (musafluorone, 1), the only naphthoxanthenone reported so far from Musaceae, was synthesized starting from 2-naphthol in nine steps and resulted in an overall yield of 3%. Grignard addition of phenylmagnesium bromide to 4-methoxyperinaphthenone afforded the corresponding 4-methoxy-9-phenylphenalenone which, after epoxidation and methyl transposition, was subjected to a photochemical cyclization procedure to furnish 1.