Random number generators tested on quantum Monte Carlo simulations

We have tested and compared several (pseudo) random number generators (RNGs) applied to a practical application, ground state energy calculations of molecules using variational and diffusion Monte Carlo metheds. A new multiple recursive generator with 8th‐order recursion (MRG8) and the Mersenne twister generator (MT19937) are tested and compared with the RANLUX generator with five luxury levels (RANLUX‐[0–4]). Both MRG8 and MT19937 are proven to give the same total energy as that evaluated with RANLUX‐4 (highest luxury level) within the statistical error bars with less computational cost to generate the sequence. We also tested the notorious implementation of linear congruential generator (LCG), RANDU, for comparison. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Gas permeability and n‐butane solubility of poly(1‐trimethylgermyl‐1‐propyne)

The gas permeability and n‐butane solubility in glassy poly(1‐trimethylgermyl‐1‐propyne) (PTMGP) are reported. As synthesized, the PTMGP product contains two fractions: (1) one that is insoluble in toluene and soluble only in carbon disulfide (the toluene‐insoluble polymer) and (2) one that is soluble in both toluene and carbon disulfide (the toluene‐soluble polymer). In as‐cast films, the gas permeability and n‐butane solubility are higher in films prepared from the toluene‐soluble polymer (particularly in those films cast from toluene) than in films prepared from the toluene‐insoluble polymer and increase to a maximum in both fractions after methanol conditioning. For example, in as‐cast films prepared from carbon disulfide, the oxygen permeability at 35 °C is 330 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 73 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. After these films are conditioned in methanol, the oxygen permeability increases to 5200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 6200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. The rankings of the fractional free volume and nonequilibrium excess free volume in the various PTMGP films are consistent with the measured gas permeability and n‐butane solubility values. Methanol conditioning increases gas permeability and n‐butane solubility of as‐cast PTMGP films, regardless of the polymer fraction type and casting solvent used, and minimizes the permeability and solubility differences between the various films (i.e., the permeability and solubility values of all conditioned PTMGP films are similar). © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2228–2236, 2002     

Design, testing and optimization of a neutron radiography system based on a Deuterium–Deuterium (D–D) neutron generator

Simulations show that significant improvement in imaging performance can be achieved through collimator design for thermal and fast neutron radiography with a laboratory neutron generator. The radiography facility used in the measurements and simulations employs a fully high-voltage-shielded, axial D–D neutron generator with a radio frequency driven ion source. The maximum yield of such generators is about 10¹⁰ fast neutrons per seconds (E = 2.45 MeV). Both fast and thermal neutron images were acquired with the generator and a Charge Coupled Devices camera. To shorten the imaging time and decrease the noise from gamma radiation, various collimator designs were proposed and simulated using Monte Carlo N-Particle Transport Code (MCNPX 2.7.0). Design considerations included the choice of material, thickness, position and aperture for the collimator. The simulation results and optimal configurations are presented.     

Comparison of a quantum random number generator with pseudorandom number generators for their use in molecular Monte Carlo simulations

Four pseudorandom number generators were compared with a physical, quantum‐based random number generator using the NIST suite of statistical tests, which only the quantum‐based random number generator could successfully pass. We then measured the effect of the five random number generators on various calculated properties in different Markov‐chain Monte Carlo simulations. Two types of systems were tested: conformational sampling of a small molecule in aqueous solution and liquid methanol under constant temperature and pressure. The results show that poor quality pseudorandom number generators produce results that deviate significantly from those obtained with the quantum‐based random number generator, particularly in the case of the small molecule in aqueous solution setup. In contrast, the widely used Mersenne Twister pseudorandom generator and a 64‐bit Linear Congruential Generator with a scrambler produce results that are statistically indistinguishable from those obtained with the quantum‐based random number generator. © 2017 Wiley Periodicals, Inc.     

Separation of113mIn from113Sn on an isotope generator with inorganic ionite

A method of preparation of hydrated zirconium oxide suitable for^113mIn generators was elaborated. A good separation of^113mIn from¹¹³Sn was obtained in the course of routine use of generator, with a very small admixture of zirconium in the eluate.     

Hydrated titanium dioxide as an adsorbent for99Mo−99mTc generator

The adsorption behaviour of⁹⁹Mo in the form of molybdate and of^99mTc in the form of pertechnetate on hydrated titanium dioxide was investigated at different molarities of hydrochloric acid. The adsorption capacity of molybdate on hydrated TiO₂ is higher than on Al₂O₃. A^99mTc-generator is suggested. This generator is based on the adsorption of (⁹⁹Mo) molybdate on hydrated TiO₂, at acidities of 0.05–0.1M. HCl.^99mTc is eluted with 0.9% NaCl. Radionuclidic, radiochemical and chemical purities of the eluates were checked. This generator seems to have a great potential as compared to the traditional alumina generators.     

Two‐dimensional square‐grid frameworks formed by self‐associating copper(II) complexes with 1‐(3‐pyridyl)‐ and 1‐(4‐pyridyl)‐substituted butane‐1,3‐diones

In bis­[1‐(3‐pyridyl)butane‐1,3‐dionato]copper(II) (the Cu atom occupies a centre of inversion), [Cu(C₉H₈NO₂)₂], (I), and bis­[1‐(4‐pyridyl)butane‐1,3‐dionato]copper(II) methanol solvate, [Cu(C₉H₈NO₂)₂]·CH₃OH, (II), the O,O′‐chelating diketonate ligands support square‐planar coordination of the metal ions [Cu—O = 1.948 (1)–1.965 (1) Å]. Weaker Cu⋯N inter­actions [2.405 (2)–2.499 (2) Å], at both axial sides, occur between symmetry‐related bis­(1‐pyridylbutane‐1,3‐dion­ato)copper(II) mol­ecules. This causes their self‐organization into two‐dimensional square‐grid frameworks, with uniform [6.48 Å for (I)] or alternating [4.72 and 6.66 Å for (II)] inter­layer separations. Guest methanol mol­ecules in (II) reside between the distal layers and form weak hydrogen bonds to coordinated O atoms [O⋯O = 3.018 (4) Å].     

Density distributions in the water shell of myoglobin

Two different approaches were used to explain the distribution of water coordinates in the crystallographically invisible part of the unit cell. Monte Carlo calculations were done starting from different initial water structures. Extended Monte Carlo calculations using equal initial structures were also used to obtain two further water structures. The differences between the Monte Carlo water structures were used to calculate the mean-square displacements of the water molecules. Monte Carlo calculations starting from different structures lead to a mean-square displacement of 0.58 Ų, whereas extended Monte Carlo moves using the same initial structure only show a mean-square displacement of 0.17 Ų. The mean-square displacement of 0.58 Ų can be used to explain the experimental data. © 1996 John Wiley & Sons, Inc.     

Pore-size distributions of cationic 2-hydroxyethyl methacrylate (HEMA) hydrogels

Pore-size distributions have been measured for cationic 2-hydroxyethyl methacrylate (HEMA) hydrogels varying in cross-linker/monomer ratio and initial concentration of cationic comonomer MAPTAC, at swelling capacities ranging from 12 to 24 g swollen gel/g dry gel. Swelling capacities were measured at about 6 °C in pure water and in aqueous sodium-azide solutions ranging in concentration from 5 × 10⁻⁴ to 2 × 10⁻¹ M. The mixed-solute-exclusion method (introduced by Kuga) was used to obtain the experimental solute-exclusion curve, representing the amount of imbibed liquid inside the gel inaccessible to a solute of radius r. The pore-size distributions were obtained by using Casassa's Brownian-motion model and numerically solving the Fredholm integral equation. The pore-size distributions shift to higher mode values (57.8-60.9 Å) with decreasing initial cross-linker concentration at the same swelling capacity of about 12. Raising swelling capacities from 11.1 to 23.9 significantly increases the variance from 5.66 × 10³ to 2.67 × 10⁴ Ų. Changes in the concentration of the cationic comonomer MAPTAC do not significantly influence the pore-size distributions.     

Estimation of parameters of the scattering particles in horn keratin by low-angle X-ray scattering

Low-angle x-ray scattering methods have been applied to determine the parameters of the scattering materials in horn keratin. A low-angle camera of Kratky's latest design has been used for the experimental measurements. By treating the substance as a densely packed system, the evaluation of the parameters has been made after theories of Porod and Kratky. Pore analysis of the substance yields a specific inner surface of 4.7 × 10^?1m²/cm³, a heterogeneity distance l_c = 290.2Å and a reduced inhomogeneity length l_r = 99.4Å. The volume of the pores has also been determined approximately.     

Theoretical Study on the Hydration Structure of Divalent Radium Ion Using Fragment Molecular Orbital–Molecular Dynamics (FMO–MD) Simulation

Using fragment molecular orbital–molecular dynamics (FMO–MD) simulation at the FMO3-HF/6-31G(d,p) level, the hydration of a Ra²⁺ ion was theoretically investigated. The first peaks of the radial distribution function (RDF) for Ra–O and Ra–H lengths were predicted to be 2.85 and 3.45 Å with broad envelopes in the ranges of 2.5–3.5 and 2.8–4.3 Å, respectively. The broad peaks shows that the first hydration shell of Ra²⁺ is much more flexible than those in the other hydrated divalent alkaline earth metal ions, i.e., Ra²⁺ is a structure-breaking ion. The hydration number of Ra²⁺ was predicted to be 8.1. From the angular distribution function (ADF), it was clarified that the octa hydrated Ra²⁺ ion has a flexible square antiprism structure at room temperature.     

Rate constants for hydrogen abstraction reactions of the sulfate radical,SO4−. Alcohols

Rate constants have been determined for the reactions of SO₄^? with a series of alcohols, including hydrated formaldehyde. The SO₄^? radical was produced by the laser-flash photolysis of persulfate, S₂O₈^2?. Rate constants for the reactions of SO₄^? with alcohols range from 1.0 × 10⁷ for methanol to 3.4 × 10⁸ M^?1 s^?1 for 1-octanol. Rate constants for the reactions of SO₄^? with deuterated methanol and ethanol are lower by about a factor of 2.5. For methanol, ethanol, and 2-propanol, the temperature dependence of the rate constant was determined over the range 10–45°C.     

State of water in amorphous silica samples from rice hulls: A <Superscript>1</Superscript>H NMR study

Behavior of molecules of adsorbed water in rice hulls, weevil, and amorphous samples of carbon-containing (carbonized, SiO₂ content 47%) and pure silica was studied by ¹H NMR spectroscopy in the temperature range from 200 to 298 K. The temperature dependence of the signal intensity from humid samples shows a decrease in temperature of freezing of the adsorbed water and presence of unfrozen water. This dependence was used for estimating the pore size distribution. For pure amorphous silica, the pore diameter is in the range from 50 to 150 Å with a maximum at about 85 Å.     

Revisiting the structure and dynamics of hydrated Cd2+ in aqueous solutions: Insights from the RI-SCS-MP2/MM molecular dynamics simulation

The spin component scale MP2/molecular mechanics molecular dynamics simulation investigated the hydration shell formation and hydrated Cd²⁺ dynamics in the water environment. At the first hydration shell, six water molecules with 2.27 Å for the average distance between water and Cd²⁺. Dynamical properties were analyzed by computing the water molecule's mean residence time (MRT) in its first and second hydration shells. The MRT of each shell was determined to be 31.8 and 1.92 ps, suggesting the strong influence of Cd²⁺ in the first hydration shell. The second shell was labile, with an average number of water molecules being 18. Despite the strong interaction between Cd²⁺ and water molecules in the first shell, the influence of ions in the second hydration shell remained weak.     

Selenoarsenate aus wäßriger Lösung. Die Kristallstruktur von Na3AsO3Se · 12 H2O und Na3AsSe4 · 9H2O

Selenoarsenates from Aqueous Solutions. Crystal Structures of Na₃AsO₃Se · 12 H₂O and Na₃AsSe₄ · 9 H₂O Selenoarsenates are obtained from aqueous solutions as colourless hydrated salts by reactions either of As₂O₃ with NaOH and selenium or of Na₂Se with As₂Se₃ and selenium under strictly anaerobic conditions. Besides of tetrahedral anions AsO₃Se³⁻ and AsSe₄³⁻, extensive hydrogen bridge systems with rather strong O H …︁s Se bonds determine the structures. Na₃AsO₃Se · 12 H₂O is orthorhombic (P2₁2₁2₁) with a = 9.220(3), b = 13.018(3), c = 14.048(4) Å, Z = 4. Cubic Na₃AsSe₄ ·s 9H₂O (P2₁3) with a = 12.149(3) Å is isotypic to Schlippe's salt, Na₃SbS₄ · 9 H₂O. The full X-ray structure analyses from four-circle diffractometer data show the selenium atoms of the AsO₃Se³⁻ and AsSe₄³⁻ anions to be H-acceptors in six Se …︁ H O hydrogen bridges with d(Se …︁ O) = 3.357–3.693 Å and d(Se …︁ H) = 2.47–2.89 Å. The As Se bond in AsO₃Se³⁻ (2.283 Å) is shorter than in AsSe₄³⁻ (2.319 Å).     

meso‐5,5,7,12,12,14‐Hexa­methyl‐4,11‐di­aza‐1,8‐diazo­nia­cyclo­tetra­decane (S)‐malate(2–) methanol disolvate: a chain of rings generated by two pairs of N—H⃛O hydrogen bonds

The title compound is a methanol‐solvated salt, C₁₆H₃₈N₄²⁺·C₄H₄O₅²⁻·2CH₃OH, in which the ionic components are linked into chains by two pairs of N—H⃛O hydrogen bonds [H⃛O = 1.78–2.21 Å, N⃛O = 2.702 (14)–3.094 (8) Å and N—H⃛O = 160–179°]. The methanol mol­ecules are pendent from the chain and are linked to it by O—H⃛O hydrogen bonds [H⃛O = 1.86 and 1.89 Å, O⃛O = 2.691 (9) and 2.708 (16) Å, and O—H⃛O = 168 and 165°].     

A Crystallographic Charge Density Study of the Partial Covalent Nature of Strong N⋅⋅⋅Br Halogen Bonds

The covalent nature of strong N?Br???N halogen bonds in a cocrystal ( 2 ) of N‐bromosuccinimide ( NBS ) with 3,5‐dimethylpyridine ( lut ) was determined from X‐ray charge density studies and compared to a weak N?Br???O halogen bond in pure crystalline NBS ( 1 ) and a covalent bond in bis(3‐methylpyridine)bromonium cation (in its perchlorate salt ( 3 ). In 2 , the donor N?Br bond is elongated by 0.0954 Å, while the Br???acceptor distance of 2.3194(4) is 1.08 Å shorter than the sum of the van der Waals radii. A maximum electron density of 0.38 e Å^?3 along the Br???N halogen bond indicates a considerable covalent contribution to the total interaction. This value is intermediate to 0.067 e Å^?3 for the Br???O contact in 1 , and approximately 0.7 e Å^?3 in both N?Br bonds of the bromonium cation in 3 . A calculation of the natural bond order charges of the contact atoms, and the σ*(N1?Br) population of NBS as a function of distance between NBS and lut , have shown that charge transfer becomes significant at a Br???N distance below about 3 Å.     

Investigations on Tetragonally Distorted Sodium Thallide NaTl-tI8

In-depth investigations of the long-time known Zintl phase NaTl revealed a phase transition of tetragonal NaTl-tI8 [I4₁/amd; a = 5.2268(9) Å, c = 7.539(1) Å, V = 205.97(9) ų] to Zintl's cubic NaTl-cF16 [Fd3 m; a = 7.4697(6) Å, V = 416.79(5) ų] between 351 and 355 K. This phase transformation was observed for NaTl prepared by two different synthetic routes including Zintl's original procedure. An excess of sodium applied during the synthesis in liquid ammonia also resulted in the formation of NaTl-tI8. DSC measurements suggest a first order phase transition. In addition to in-situ temperature dependent powder X-ray diffraction experiments, DSC measurements and solid-state NMR investigations, we also performed theoretical DOS and band structure calculations for the cubic and tetragonal phase, respectively. The results suggest Na-Tl interactions in the second coordination sphere being responsible for the observed tetragonal distortion of Zintl's cubic NaTl.     

Low‐dimensional compounds containing cyano groups. VI.

The title compound, [Cu₂(C₄H₁₂N₂)₂{Ag(CN)₂}₄(NH₃)]·2H₂O or [Ag₄Cu₂(CN)₈(C₄H₁₂N₂)₂(NH₃)]·2H₂O, contains two crystallographically different Cu^II atoms lying on twofold axes. The first Cu atom is hexacoordinated in the form of an elongated tetragonal bipyramid and is part of a plane in which Cu atoms are connected by two bridging di­amino­butane mol­ecules [Cu—N = 2.033 (4) Å] and two di­cyano­argentate anions [Cu—N = 2.622 (6) Å]. The ammine ligand stands perpendicular to this plane [Cu—N = 2.011 (6) Å] in a trans position to it. Another [Ag(CN)₂]⁻ anion connects the hexacoordinated Cu atom [Cu—N = 1.997 (8) Å] with the second Cu atom [Cu—N = 2.026 (7) Å], which is pentacoordinated in the form of a slightly distorted trigonal bipyramid by two monodentate di­cyano­argetate anions [Cu—N = 2.040 (5) Å]. The axial positions are occupied by two bridging di­amino­butane mol­ecules [Cu—N = 2.011 (4) Å] that connect the Cu atoms into chains parallel to the above plane. The water mol­ecules remain uncoordinated and thus a unique combination of two‐ and one‐dimensional structures is formed.     

Study of the structure of molecular complexes. Coordination numbers for Li+, Na+, K+, F− and Cl− in water

A cluster of 200 water molecules containing a single ion (either Li⁺ or Na⁺ or K⁺ or F^? or Cl^?) has been studied at T = 298 K using Monte Carlo techniques. The waterwater interaction is obtained from a quantum-mechanical study of CI type; the ionwater potentials have been obtained from HartreeFock type computations. The computed coordination numbers in the first shell for Li⁺, Na⁺, K⁺, F^? and Cl^? are 4.0, 4.3, 5.1, 3.85 and 4.3, respectively; the corresponding first hydration shell radii are 2.28 Å, 2.59 Å, 3.27 Å, 1.99 Å and 2.85 Å, respectively. A discussion of the second and third hydration shell radii and coordination numbers is given.