Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

Given a set of spherical balls, called atoms, in three‐dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well‐solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta‐decomposition, based on the recent theory of the beta‐complex. Given the beta‐complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta‐complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta‐complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ?³ that m = O(n) on average for biomolecules and m = O(n²) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ?² and extended to ?³. The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site. © 2012 Wiley Periodicals, Inc.     

A fast pairwise evaluation of molecular surface area

A fast and general analytical approach was developed for the calculation of the approximate van der Waals and solvent-accessible surface areas. The method is based on three basic ideas: the use of the Lorentz transformation formula, a rigid-geometry approximation, and a single fitting parameter that can be refitted on the fly during a simulation. The Lorentz transformation equation is used for the summation of the areas of an atom buried by its neighboring contacting atoms, and implies that a sum of the buried pairwise areas cannot be larger than the surface area of the isolated spherical atom itself. In a rigid-geometry approximation we numerically calculate and keep constant the surface of each atom buried by the atoms involved in 1-2 and 1-3 interactions. Only the contributions from the nonbonded atoms (1-4 and higher interactions) are considered in terms of the pairwise approximation. The accuracy and speed of the method is competitive with other pairwise algorithms. A major strength of the method is the ease of parametrization.     

Joint neighbors approximation of macromolecular solvent accessible surface area

A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.     

An accurate three-dimensional potential energy surface for the He-Na_2 complex

An accurate three-dimensional potential energy surface(PES) for the He-Na2 van der Waals comple was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connecte triple(CCSD(T)) level of theory.A mixed basis set,aug-cc-pVQZ for the He atom and cc-pCVQZ for th sodium atom,and an additional(3s3p2d1f) set of midbond functions were used.The computed inte action energies in 819 configurations were fitted to a 96-parameter analytic potential model by leas squares fitting.The PES has two shallow wells corresponding to the T-shaped structure and the linea configuration,which are located at 12.5a0 and 14 a0 with depths of 1.769 and 1.684 cm-1,respectivel The whole potential energy surface exhibits weak anisotropy.Based on the fitted PES,state-to-stat differential cross sections were calculated.     

Apparent molar heat capacities and volumes,van der Waals volumes and accessible surface areas of alkylated derivatives of cytosine and uracil in aqueous solutions at 25°C.

Densities and specific heat capacities of aqueous solutions: 1,3,5,6-tetramethyluracil, 1,6-dimethyl-3-ethyluracil, 1,6-dimethyl-3-propyluracil, 1,6-dimethyl-3-butyluracil, 1,N⁴-trimethylcytosine, 1,N⁴-dimethyl-5-ethylcytosine, 1,N⁴ dimethyl-5-propylcytosine, 1,N⁴-dimethyl-5-butylcytosine were determined using flow calorimetry and flow densimetry at 25°C. Apparent molar volumes and heat capacities, van der Waals volumes and accessible surface areas were determined. It was stated that for alkylcytosines and alkyluracils partial molar volumes and heat capacities correlate linearly with the number of substituted methylene groups-CH₂-as well as with the van der Waals volumes and accessible surface areas of the compounds studied; for cyclooligouracils the cyclization effect was discussed.     

Scale‐up synthesis of hyperbranched poly(amidoamine)‐grafted ultrafine silica using dendrimer synthesis methodology in solvent‐free dry‐system

Scale‐up synthesis of hyperbranched poly(amidoamine)‐grafted ultrafine silica was successfully achieved by using dendrimer synthesis methodology in solvent‐free dry‐system. The poly(amidoamine) was allowed to grow from silica surface by repeating two steps: (1) Michael addition of methyl acrylate (MA) to amino group on the surface and (2) amidation of terminal ester group with ethylenediamine (EDA). MA was sprayed onto silica having amino group and the silica agitated at 300 rpm at 50 °C. After the reaction, unreacted MA was removed under vacuum. Then EDA was sprayed and the reaction was conducted at 50 °C with agitation. After the reaction, unreacted EDA was also removed under vacuum at 50 °C and MA was sprayed again. The percentage of poly(amidoamine) grafting onto the surface was determined to be 141% with repeated reaction cycles of eight‐times. However, the value was considerably smaller than that of the theoretical value. This indicates that the propagation of poly(amidoamine) dendron from silica surface was not achieved theoretically and hyperbranched poly(amidoamine) was grafted onto the surface because of steric hindrance of grafted polymer. In addition, the effect of initial amino group content on the growth of poly(amidoamine) from the surface was investigated. It was concluded that the method is suitable for the scale‐up synthesis of hyperbranched poly(amidoamine)‐grafted silica. Copyright © 2002 John Wiley & Sons, Ltd.     

An accurate three-dimensional potential energy surface for the He-Na<Subscript>2</Subscript> complex

An accurate three-dimensional potential energy surface (PES) for the He-Na₂ van der Waals complex was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triple (CCSD(T)) level of theory. A mixed basis set, aug-cc-pVQZ for the He atom and cc-pCVQZ for the sodium atom, and an additional (3s3p2d1f) set of midbond functions were used. The computed interaction energies in 819 configurations were fitted to a 96-parameter analytic potential model by least squares fitting. The PES has two shallow wells corresponding to the T-shaped structure and the linear configuration, which are located at 12.5a ₀ and 14 a ₀ with depths of 1.769 and 1.684 cm⁻¹, respectively. The who potential energy surface exhibits weak anisotropy. Based on the fitted PES, state-to-state differential cross sections were calculated. Supported by the Natural Science Foundation of Anhui Educational Committee (Grant No. 2006kj072A) and the Natural Science Foundation of Anhui Province (Grant No. 070416236)     

Novel computer program for fast exact calculation of accessible and molecular surface areas and average surface curvature

New computer programs, SurfRace and FastSurf, perform fast calculations of the solvent accessible and molecular (solvent excluded) surface areas of macromolecules. Program SurfRace also calculates the areas of cavities inaccessible from the outside. We introduce the definition of average curvature of molecular surface and calculate average molecular surface curvatures for each atom in a structure. All surface area and curvature calculations are analytic and therefore yield exact values of these quantities. High calculation speed of this software is achieved primarily by avoiding computationally expensive mathematical procedures wherever possible and by efficient handling of surface data structures. The programs are written initially in the language C for PCs running Windows 2000/98/NT, but their code is portable to other platforms with only minor changes in input-output procedures. The algorithm is robust and does not ignore either multiplicity or degeneracy of atomic overlaps. Fast, memory-efficient and robust execution make this software attractive for applications both in computationally expensive energy minimization algorithms, such as docking or molecular dynamics simulations, and in stand-alone surface area and curvature calculations.     

Designed Single‐Step Synthesis,Structure, and Derivative Textural Properties of Well‐Ordered Layered Penta‐coordinate Silicon Alcoholate Complexes

The controllable synthesis of well‐ordered layered materials with specific nanoarchitecture poses a grand challenge in materials chemistry. Here the solvothermal synthesis of two structurally analogous 5‐coordinate organosilicate complexes through a novel transesterification mechanism is reported. Since the polycrystalline nature of the intrinsic hypervalent Si complex thwarts the endeavor in determining its structure, a novel strategy concerning the elegant addition of a small fraction of B species as an effective crystal growth mediator and a sacrificial agent is proposed to directly prepare diffraction‐quality single crystals without disrupting the intrinsic elemental type. In the determined crystal structure, two monomeric primary building units (PBUs) self‐assemble into a dimeric asymmetric secondary BU via strong Na⁺?O^2? ionic bonds. The designed one‐pot synthesis is straightforward, robust, and efficient, leading to a well‐ordered (10ī)‐parallel layered Si complex with its principal interlayers intercalated with extensive van der Waals gaps in spite of the presence of substantial Na⁺ counter‐ions as a result of unique atomic arrangement in its structure. However, upon fast pyrolysis, followed by acid leaching, both complexes are converted into two SiO₂ composites bearing BET surface areas of 163.3 and 254.7 m² g^?1 for the pyrolyzed intrinsic and B‐assisted Si complexes, respectively. The transesterification methodology merely involving alcoholysis but without any hydrolysis side reaction is designed to have generalized applicability for use in synthesizing new layered metal–organic compounds with tailored PBUs and corresponding metal oxide particles with hierarchical porosity.     

Method for Smoothing the Boundaries of the Van Der Waals Models of Molecules

A geometrical method is suggested for representing a molecule by a smoothed region. The effective volume and surface area are calculated, which results in more adequate proportionality of interactant molecules compared to the classical van der Waals models.     

van der Waals corrected density functional calculations of the adsorption of benzene on the Cu (111) surface

We investigate the performance of several van der Waals (vdW) functionals at calculating the interactions between benzene and the copper (111) surface, using the local orbital approach in the SIESTA code. We demonstrate the importance of using surface optimized basis sets to calculate properties of pure surfaces, including surface energies and the work function. We quantify the errors created using (3 × 3) supercells to study adsorbate interactions using much larger supercells, and show non‐negligible errors in the binding energies and separation distances. We examine the eight high‐symmetry orientations of benzene on the Cu (111) surface, reporting the binding energies, separation distance, and change in work function. The optimized vdW‐DF(optB88‐vdW) functional provides superior results to the vdW‐DF(revPBE) and vdW‐DF2(rPW86) functionals, and closely matches the experimental and experimentally deduced values. This work demonstrates that local orbital methods using appropriate basis sets combined with a vdW functional can model adsorption between metal surfaces and organic molecules.     

Two-step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.     

A protophilic solvent‐assisted solvothermal approach to Cu‐BTC for enhanced CO2 capture

Cu‐BTC–ethylenediamine (EDA)/polyethyleneimine (PEI) adsorbents were synthesized using a protophilic solvent‐assisted solvothermal method. EDA was introduced to enhance the degree of activation due to its lower boiling point allowing it to be removed easily compared with dimethylformamide. A contrast experiment was done by introducing PEI to the solvothermal solution considering its higher boiling point. Powder X‐ray diffraction, scanning electron microscopy and Raman spectroscopic characterizations were performed to investigate the effect of EDA/PEI on crystallinity and morphology of the adsorbents. ¹H NMR characterization and elemental analysis were performed to study the removal rate of organic guest molecules and the degree of activation. Nitrogen physical adsorption and CO₂ adsorption isotherms were used to measure the surface area and CO₂ adsorption capacities. The CO₂ adsorption mechanism of the synthesized adsorbents is mainly dependent on physisorption determined by surface area. Furthermore, open metal sites generated by the enhancement of degree of activation also promote the CO₂ adsorption performance. Therefore, adsorbents synthesized using the protophilic solvent‐assisted solvothermal method exhibit excellent CO₂ adsorption performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Van der Waals Heterostructures Comprised of Ultrathin Polymer Nanosheets for Efficient Z‐Scheme Overall Water Splitting

Inspired by natural photosynthesis, Z‐scheme photocatalytic systems are very appealing for achieving efficient overall water splitting. Developing metal‐free Z‐scheme photocatalysts for overall water splitting, however, still remains challenging. The construction of polymer‐based van der Waals heterostructures as metal‐free Z‐scheme photocatalytic systems for overall water splitting is described using aza‐fused microporous polymers (CMP) and C₂N ultrathin nanosheets as O₂‐ and H₂‐evolving catalysts, respectively. Although neither polymer is able to split pure water using visible light, a 2:1 stoichiometric ratio of H₂ and O₂ was observed when aza‐CMP/C₂N heterostructures were used. A solar‐to‐hydrogen conversion efficiency of 0.23 % was determined, which could be further enhanced to 0.40 % by using graphene as the solid electron mediator to promote the interfacial charge‐transfer process. This study highlights the potential of polymer photocatalysts for overall water splitting.     

Design and characterization of Dendrimer of MNPs as a novel,heterogeneous and reusable nanomagnetic organometallic catalyst for one‐pot synthesis of hydroxyl naphthalene‐1,4‐dione derivatives under solvent‐free conditions

A novel super acidic magnetic nanoparticle as catalyst was successfully synthesized. The preparation of this dendrimer sulfonic acid functionalized γ‐Fe₂O₃ magnetic core‐shell silica nanoparticles as a new recoverable and heterogeneous nanocatalyst was described. The new catalyst was characterized using various techniques such as scanning electron microscopy (SEM), energy dispersive spectrum (EDS), and thermo gravimetric synthesis (TGA). Moreover, we have examined the catalytic activity of the catalyst for one‐pot, efficient and facile synthesis of 2‐hydroxy‐1,4‐naphthoquinone derivatives via a three‐component condensation reaction of 2‐hydroxynaphthalene‐1,4‐dione, aromatic aldehydes and aniline derivatives. High yields of products, short reaction times, waste‐free, mild, ambient and solvent‐free reaction conditions are advantages of this protocol. Also, the catalyst can be easily recovered by an external magnetic and reused several times without significant loss of its catalytic activity.     

Cooling,Spectroscopy and Non‐Sticking of trans‐Stilbene and Nile Red

We create and study trans‐Stilbene and Nile Red in a cryogenic (7 K) cell with a low density helium buffer gas. No molecule–helium cluster formation is observed, indicating limited atom–molecule sticking in this system. We place an upper limit of 5 % on the population of clustered He–trans‐Stilbene, consistent with a measured He–molecule collisional residence time of less than 1 μs. With its very low energy torsional modes, trans‐Stilbene is less rigid than any molecule previously buffer‐gas‐cooled into the Kelvin regime. We also report cooling and gas phase visible spectroscopy of Nile Red, a much larger molecule. Our data suggest that buffer gas cooling will be feasible for a variety of small biological molecules.