The Landau free energy of hard ellipses obtained from microscopic simulations

Systems of two-dimensional hard ellipses of varying aspect ratios and packing fractions are studied by Monte Carlo simulations in the generalised canonical ensemble. From this microscopic model, we extract a coarse-grained macroscopic Landau-de Gennes free energy as a function of packing fraction and orientational order parameter. We separate the free energy into the ideal orientational entropy of non-interacting two-dimensional spins and an excess free energy associated with excluded volume interactions. We further explore the isotropic-nematic phase transition using our empirical expression for the free energy and find that the nature of the phase transition is continuous for the aspect ratios we studied.

Glycogen phosphorylase inhibitors: a free energy perturbation analysis of glucopyranose spirohydantoin analogues

GP catalyzes the phosphorylation of glycogen to Glc-1-P. Because of its fundamental role in the metabolism of glycogen, GP has been the target for a systematic structure-assisted design of inhibitory compounds, which could be of value in the therapeutic treatment of type 2 diabetes mellitus. The most potent catalytic-site inhibitor of GP identified to date is spirohydantoin of glucopyranose (hydan). In this work, we employ MD free energy simulations to calculate the relative binding affinities for GP of hydan and two spirohydantoin analogues, methyl-hydan and n-hydan, in which a hydrogen atom is replaced by a methyl- or amino group, respectively. The results are compared with the experimental relative affinities of these ligands, estimated by kinetic measurements of the ligand inhibition constants. The calculated binding affinity for methyl-hydan (relative to hydan) is 3.75 +/- 1.4 kcal/mol, in excellent agreement with the experimental value (3.6 +/- 0.2 kcal/mol). For n-hydan, the calculated value is 1.0 +/- 1.1 kcal/mol, somewhat smaller than the experimental result (2.3 +/- 0.1 kcal/mol). A free energy decomposition analysis shows that hydan makes optimum interactions with protein residues and specific water molecules in the catalytic site. In the other two ligands, structural perturbations of the active site by the additional methyl- or amino group reduce the corresponding binding affinities. The computed binding free energies are sensitive to the preference of a specific water molecule for two well-defined positions in the catalytic site. The behavior of this water is analyzed in detail, and the free energy profile for the translocation of the water between the two positions is evaluated. The results provide insights into the role of water molecules in modulating ligand binding affinities. A comparison of the interactions between a set of ligands and their surrounding groups in X-ray structures is often used in the interpretation of binding free energy differences and in guiding the design of new ligands. For the systems in this work, such an approach fails to estimate the order of relative binding strengths, in contrast to the rigorous free energy treatment.

Rovibrational energy levels of hydrogen peroxide, studied by MULTIMODE with a reaction path Hamiltonian

Recently. Carter and Handy [J. Chem. Phys. 113 (2000) 987] have introduced the theory of the reaction path Hamiltonian (RPH) [J. Chem. Phys. 72 (1980) 99] into the variational scheme MULTIMODE, for the calculation of the J = 0 vibrational levels of polyatomic molecules, which have a single large-amplitude motion. In this theory the reaction path coordinate s becomes the fourth dimension of the moment-of-inertia tensor, and must be treated separately from the remaining 3N - 7 normal coordinates in the MULTIMODE program. In the modified program, complete integration is performed over s, and the M-mode MULTIMODE coupling approximation for the evaluation of the matrix elements applies only to the 3N - 7 normal coordinates. In this paper the new algorithm is extended to the calculation of rotational-vibration energy levels (i.e. J > 0) with the RPH, following from our analogous implementation for rigid molecules [Theoret. Chem. Acc. 100 (1998) 191]. The full theory is given, and all extra terms have been included to give the exact kinetic energy operator. In order to validate the new code, we report studies on hydrogen peroxide (H2O2), where the reaction path is equivalent to torsional motion. H2O2 has previously been studied variationally using a valence coordinate Hamiltonian; complete agreement for calculated rovibrational levels is obtained between the previous results and those from the new code, using the identical potential surface. MULTIMODE is now able to calculate rovibrational levels for polyatomic molecules which have one large-amplitude motion. (C) 2003 Elsevier B.V. All rights reserved.

Inelastic neutron scattering in spectroscopic studies of hydrogen on carbon-supported catalysts-experimental spectra and computed spectra of model systems

Inelastic neutron scattering spectroscopy has been used to observe and characterise hydrogen on the carbon component of a Pt/C catalyst. INS provides the complete vibration spectrum of coronene, regarded as a molecular model of a graphite layer. The vibrational modes are assigned with the aid of ab initio density functional theory calculations and the INS spectra by the a-CLIMAX program. A spectrum for which the H modes of coronene have been computationally suppressed, a carbon-only coronene spectrum, is a better representation of the spectrum of a graphite layer than is coronene itself. Dihydrogen dosing of a Pt/C catalyst caused amplification of the surface modes of carbon, an effect described as H riding on carbon. From the enhancement of the low energy carbon modes (100-600 cm(-1)) it is concluded that spillover hydrogen becomes attached to dangling bonds at the edges of graphitic regions of the carbon support. (C) 2003 Elsevier Science B.V. All rights reserved.

Homoleptic copper(II) and copper(I) complexes of 5,6-dihydro-5,6-epoxy-1,10-phenanthroline. Six-coordinate copper(I) in solution

Reaction of 5,6-dihydro-5,6-epoxy-1,10-phenanthroline (L) with Cu(ClO(4))(2)center dot 6H(2)O in methanol in 3:1 M ratio at room temperature yields light green [CuL(3)](ClO(4))(2)center dot H(2)O (1). The X-ray crystal structure of the hemi acetonitrile solvate [CuL(3)](ClO(4))(2)center dot 0.5CH(3)CN has been determined which shows Jahn-Teller distortion in the CuN(6) core present in the cation [CuL(3)](2+). Complex 1 gives an axial EPR spectrum in acetonitrile-toluene glass with g(parallel to) = 2.262 (A(parallel to) = 169 x 10 (4) cm (1)) and g(perpendicular to) = 2.069. The Cu(II/I) potential in 1 in CH(2)Cl(2) at a glassy carbon electrode is 0.32 V versus NHE. This potential does not change with the addition of extra L in the medium implicating generation of a six-coordinate copper(I) species [CuL(3)](+) in solution. B3LYP/LanL2DZ calculations show that the six Cu-N bond distances in [CuL(3)](+) are 2.33, 2.25, 2.32, 2.25, 2.28 and 2.25 angstrom while the ideal Cu(I)-N bond length in a symmetric Cu(I)N(6) moiety is estimated as 2.25 angstrom. Reaction of L with Cu(CH(3)CN)(4)ClO(4) in dehydrated methanol at room temperature even in 4:1 M proportion yields [CuL(2)]ClO(4) (2). Its (1)H NMR spectrum indicates that the metal in [CuL(2)](+) is tetrahedral. The Cu(II/I) potential in 2 is found to be 0.68 V versus NHE in CH(2)Cl(2) at a glassy carbon electrode. In presence of excess L, 2 yields the cyclic voltammogram of 1. From (1)H NMR titration, the free energy of binding of L to [CuL(2)](+) to produce [CuL(3)](+) in CD(2)Cl(2) at 298 K is estimated as -11.7 (+/-0.2) kJ mol (1).

Laser granulometry of Holocene estuarine silts: effects of hydrogen peroxide treatment

The Holocene estuarine silts of the Severn Estuary Levels (southwest Britain) are representative of their kind in northwest Europe. They contain two broad types of plant material: particles codeposited with mineral grains from the estuarine water body, and extraneous debris (stems of indigenous prior plants; post depositional root matter) which is difficult to remove completely by physical means. Treatment with hydrogen peroxide before laser granulometry removes all plant material regardless of kind, drastically reduces values for the mean grain size and median size relative to untreated samples, but has little effect on the mode, except for a restricted group of bimodal-platykurtic, medium-coarse silts. It is concluded that, in the case of sediments of the general kind examined, no advantages acrue from the treatment of samples with hydrogen peroxide prior to analysis. Although a discrete rather than continuous variable, values of the mode obtained from untreated sediments are suggested to be acceptable for most purposes where a measure of central tendency is required.

The fundamental vibration-rotation band of hydrogen chloride

The fundamental vibration-rotational absorption band of hydrogen chloride near 3 45,t has been remeasured using higher resolving power than previously. The wave-lengths of the absorption lines have been determined more precisely, and the isotopic splitting of lines has been completely resolved. The results have provided new and more satisfactory values for the rotational constants Bi, and the centrifugal stretching constants Di, and their relative values for the two isotopic species agree closely with what is to be expected for the difference in mass. The positions of the lines in the pure rotational absorption spectrum have been calculated from the derived data, and agree closely with those recently observed. The bond lengths re for each isotopic species H35C1 and H37C1 is found to be 1-2744A.

Mechanistic insights into a gas–solid reaction in molecular crystals: the role of hydrogen bonding

Reactions in (molecular) organic crystalline solids have been shown to be important for exerting control that is unattainable over chemical transformations in solution. Such control has also been achieved for reactions within metal– organic cages. In these examples, the reactants are already in place within the crystals following the original crystal growth. The post-synthetic modification of metal–organic frameworks (MOFs and indeed reactions and catalysis within MOFs have been recently demonstrated; in these cases the reactants enter the crystals through permanent channels. Another growing area of interest within molecular solid-state chemistry is synthesis by mechanical co-grinding of solid reactants—often referred to as mechanochemistry. Finally, in a small number of reported examples, molecules also have been shown to enter nonporous crystals directly from the gas or vapor phase, but in only a few of these examples does a change in covalent bonding result, which indicates that a reaction occurs within the nonporous crystals. It is this latter type of highly uncommon reaction that is the focus of the present study.

Influence of hydrogen bonding in the structure of mixed-ligand copper(II) chelates. Spectra and structure of [aquo((2,2'-dipyridylamine)-(3-chloro-2,4-pentanedionato)copper(II)] nitrate

The IR, the ligand field spectra and the crystal structure of the mixed-ligand compound [(aquo)2,2P1 , a = 8.718(5), b = 9.407(5), c = 13.484 (7) Å, = 94.17(4)°, = 105.12(5)°, = 119.75(5)°, Z = 2, R = 0.0332, R W = 0.0869).

In search of the aim of the free movement of persons provisions: has the Court of Justice missed the point?

The Court of Justice has, over the years, often been vilified for exceeding the limits of its jurisdiction by interpreting the provisions of Community legislation in a way not seem originally envisaged by its drafters. A recent example of this approach was a cluster of cases in the context of the free movement of workers and the freedom of establishment (Ritter-Coulais and its progeny), where the Court included within the scope of those provisions situations which, arguably, did not present a sufficient link with their (economic) aim. In particular, in that case law the Court accepted that the mere exercise of free movement for the purpose of taking up residence in the territory of another Member State whilst continuing to exercise an economic activity in the State of origin, suffices for bringing a Member State national within the scope of Articles 39 and 43 EC. It is argued that the most plausible explanation for this approach is that the Court now wishes to re-read the economic fundamental freedoms in such a way as to include within their scope all economically active Union citizens, irrespective of whether their situation presents a sufficient link with the exercise of an economic activity in a cross-border context. It is suggested that this approach is problematic for a number of reasons. It is, therefore, concluded that the Court should revert to its orthodox approach, according to which only situations that involve Union citizens who have moved between Member States for the purpose of taking up an economic activity should be included within the scope of the market freedoms.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

'Between slavery and freedom': the expulsion and enslavement of free women of colour in the US South before the Civil War

For free black women in the pre-Civil War American South, the status offered by ‘freedom’ was uncertain and malleable. The conceptualization of bondage and freedom as two diametrically opposed conditions therefore fails to make sense of the complexities of life for these women. Instead, notions of enslavement and freedom are better framed as a spectrum. This article develops this idea by exploring two of the ways in which some black women negotiated their status before the law—namely though petitioning for residency or for enslavement. While these petitions are atypical numerically, and often offer tantalizingly scant evidence, when used in conjunction with evidence from the US census, it becomes clear that these women were highly pragmatic. Prioritizing their spousal and broader familial affective relationships above their legal status, they rejected the often theoretical distinction between slavery and liberation. As such, the petitions can be used to reach broader conclusions about the attitudes of women who have left little written testimony.

On the available energy of an axisymmetric vortex

A theory of available energy for axisymmetric circulations is presented. The theory is a generalization of the classical theory of available potential energy, in that it accounts for both thermal and angular momentum constraints on the circulation. The generalization relies on the Hamiltonian structure of the (conservative) dynamics, is exact at finite amplitude, and has a local form. Application of the theory is presented for the case of an axisymmetric vortex on an f -plane in the context of the Boussinesq equations.