Quark and Nuclear Matter in the Linear Chiral Meson Model

We present an analytical description of the phase transitions from a nucleon gas to nuclear matter and from nuclear matter to quark matter within the same model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential $\mu$ associated to conserved baryon number. An approximate solution for vanishing temperature is used to discuss possible phase transitions as the baryon density increases. For a nucleon gas and nuclear matter we find a substantial density enhancement as compared to quark models which neglect the confinement to baryons. The results point out that the latter models are not suitable to discuss the phase diagram at low temperature.Comment: 27 pages, Int.J.Mod.Phys.A versio

Theoretical study of M+ RG2: (M+= Ca, Sr, Ba and Ra; RG= He–Rn)

Ab initio calculations were employed to investigate M+ RG2 species, where M+ = Ca, Sr, Ba and Ra and RG= He–Rn. Geometries have been optimized, and cuts through the potential energy surfaces containing each global minimum have been calculated at the MP2 level of theory, employing triple-ζ quality basis sets. The interaction energies for these complexes were calculated employing the RCCSD(T) level of theory with quadruple-ζ quality basis sets. Trends in binding energies, De, equilibrium bond lengths, Re, and bond angles are discussed and rationalized by analyzing the electronic density. Mulliken, natural population, and atoms-in-molecules (AIM) population analyses are presented. It is found that some of these complexes involving the heavier Group 2 metals are bent whereas others are linear, deviating from observations for the corresponding Be and Mg metal-containing complexes, which have all previously been found to be bent. The results are discussed in terms of orbital hybridization and the different types of interaction present in these species

Sodium ion interactions with aqueous glucose: Insights from quantum mechanics, molecular dynamics, and experiment

In the last several decades, significant efforts have been conducted to understand the fundamental reactivity of glucose derived from plant biomass in various chemical environments for conversion to renewable fuels and chemicals. For reactions of glucose in water, it is known that inorganic salts naturally present in biomass alter the product distribution in various deconstruction processes. However, the molecular-level interactions of alkali metal ions and glucose are unknown. These interactions are of physiological interest as well, for example, as they relate to cation-glucose cotransport. Here, we employ quantum mechanics (QM) to understand the interaction of a prevalent alkali metal, sodium, with glucose from a structural and thermodynamic perspective. The effect on B-glucose is subtle: a sodium ion perturbs bond lengths and atomic partial charges less than rotating a hydroxymethyl group. In contrast, the presence of a sodium ion significantly perturbs the partial charges of α-glucose anomeric and ring oxygens. Molecular dynamics (MD) simulations provide dynamic sampling in explicit water, and both the QM and the MD results show that sodium ions associate at many positions with respect to glucose with reasonably equivalent propensity. This promiscuous binding nature of Na + suggests that computational studies of glucose reactions in the presence of inorganic salts need to ensure thorough sampling of the cation positions, in addition to sampling glucose rotamers. The effect of NaCl on the relative populations of the anomers is experimentally quantified with light polarimetry. These results support the computational findings that Na + interacts similarly with a- and B-glucose

Nature of the bonding in metal-silane σ-complexes

The nature of metal silane σ-bond interaction has been investigated in several key systems by a range of experimental and computational techniques. The structure of [Cp′Mn(CO)2(η2-HSiHPh2)] 1 has been determined by single crystal neutron diffraction, and the geometry at the Si atom is shown to approximate a trigonal bipyramid; salient bond distances and angles are Mn−H(1) 1.575(14), Si−H(1) 1.806(14), Si−H(2) 1.501(13) Å, and H(1)−Si−H(2) 148.5(8)°. This complex is similar to [Cp′Mn(CO)2(η2-HSiFPh2)] 2, whose structure and bonding characteristics have recently been determined by charge density studies based on high-resolution X-ray and neutron diffraction data. The geometry at the Si atom in these σ-bond complexes is compared with that in other systems containing hypercoordinate silicon. The Mn−H distances for 1 and 2 in solution have been estimated using NMR T1 relaxation measurements, giving a value of 1.56(3) Å in each case, in excellent agreement with the distances deduced from neutron diffraction. Density functional theory calculations have been employed to explore the bonding in the Mn−H−Si unit in 1 and 2 and in the related system [Cp′Mn(CO)2(η2-HSiCl3)] 3. These studies support the idea that the oxidative addition of a silane ligand to a transition metal center may be described as an asymmetric process in which the Mn−H bond is formed at an early stage, while both the establishment of the Mn−Si bond and also the activation of the η2-coordinated Si−H moiety are controlled by the extent of Mn → σ*(X−Si−H) back-donation, which increases with increasing electron-withdrawing character of the X substituent trans to the metal-coordinated Si−H bond. This delocalized molecular orbital (MO) approach is complemented and supported by combined experimental and theoretical charge density studies: the source function S(r,Ω), which provides a measure of the relative importance of each atom’s contribution to the density at a specific reference point r, clearly shows that all three atoms of the Mn(η2-SiH) moiety contribute to a very similar extent to the density at the Mn−Si bond critical point, in pleasing agreement with the MO model. Hence, we advance a consistent and unifying concept which accounts for the degree of Si−H activation in these silane σ-bond complexes

Numerical hydrodynamics in general relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.Comment: 105 pages, 12 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.or

Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells

Structure and bonding in WCn (n = 2–5) clusters

Stochastic explorations of the configurational spaces for WC n (n = 2–5) clusters lead to densely populated spin states at each molecularity. We found 8, 16, 42, and 68 well-defined minima for n = 2, 3, 4, 5, respectively, in spin states ranging from singlets to quintuplets. The lowest energy isomers are triplets in all cases, except for n = 2 where there is competition between a quintuplet and a triplet state for the global minimum. The transition from planar to 3D structural preferences occurs between n = 4 and n = 5. For the global minima, the structures may be considered as the result of the interaction between two fragments: a tungsten cation and a covalently bonded anionic carbon chain. We found that spin–orbit (SO) effects reduce energy differences among isomers. Likewise, SO effects diminish as a function of the carbon content in the clusters to the point that for n = 5 they become negligible