The finite state projection algorithm for the solution of the chemical master equation

This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods.     

An efficient local coupled cluster method for accurate thermochemistry of large systems

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo?ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.     

Introduction

Silicon is taken as a test system for assessing present-day feasibility of calculations for crystalline solids of near-Hartree–Fock quality. The calculations have been performed using CRYSTAL, an ab initio Hartree–Fock crystalline-orbital LCAO program for periodic systems. The influence of the computational parameters that control the truncation of infinite sums on the results has been investigated; it is shown that a reasonable accuracy (numerical errors on total energy per atom below 10^?3 a.u.) can be obtained while keeping the computational burden within manageable limits. The effect on the results of basis-set size and quality is discussed. A number of basis sets have been tested, from minimal to relatively extended sets (28 atomic orbitals per atom). The quality of the wave function has been checked using variational criteria and also through a comparison with experimental data, such as equilibrium geometry, bulk modulus, electron charge density, and electron momentum distribution. For the latter quantities, which are a measure of the accuracy of the one-electron density matrix, the best basis sets provide agreement with experiment that is almost within the experimental error. The correlation energy has been estimated using nonlocal density functionals, based on the one-electron density matrix: After this correction, the atomization energy agrees with experiment to within 2%. The generalization of the above analysis to other crystals is briefly discussed.     

Molecular dynamics study of a new metastable allotropic crystalline form of gallium—supertetrahedral gallium

A new metastable crystalline form of gallium has been computationally designed using density functional calculations with imposing periodic boundary conditions. The geometric and electronic structures of the predicted new allotrope were calculated on the basis of a diamond lattice in which all carbon atoms are replaced by gallium Ga₄ tetrahedra. This form does not have any imaginary phonons, thus it is a metastable crystalline form of gallium. The new form of gallium is a metal and shows high plasticity and low-melting temperature. Molecular dynamics simulations show that this form of gallium will melt at about 273 K with a sharp increase in temperature in the system during the melting process from 273 to 1800 K. This melting process is very different from conventional melting, where temperature stays the same until complete melting. That unusual melting can be explained by the fact that supertetrahedral gallium is a metastable structure that has an excess of strain energy released during melting. If made this new material may find many useful applications as a new low density metal with stored internal energy. © 2019 Wiley Periodicals, Inc.     

Ab initio quality properties for macromolecules using the ADMA approach

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.     

Carbon-13 NMR distinction between categories of molecular order and disorder in cellulose

Differences between values of proton rotating-frame spin relaxation time constants can be exploited to separate a solid-state¹³C NMR spectrum of cellulose into subspectra of crystalline and noncrystalline regions. Variations in chemical shifts and¹³C spin-lattice relaxation time constants can then be used to study variations in molecular order and disorder within each of the two broader categories. Mechanical damage during Wiley milling increases the content of noncrystalline cellulose and changes the nature of molecular disorder within that category. Resolution enhancement of the subspectrum assigned to crystalline cellulose reveals pairs of signals at 83.9 and 84.9 ppm (cellulose I) or 86.8 and 88.3 ppm (cellulose II) assigned to C-4 on well-ordered crystal surfaces. A broader peak in the subspectrum of crystalline cellulose I is assigned to poorly-ordered surfaces. Relative proportions in Avicel microcrystalline cellulose were estimated as: 54% in crystal interiors, 22% on well-ordered surfaces, 8% on poorly-ordered surfaces, 16% in domains of disorder extending more than a few nanometres.     

论络合物中心过渡金属离子的径向波函数

考虑中心对称配体场影响,提出一种不同基混合的束缚态过渡金属离子的3d径向波函数。利用这种波函数,计算了一些Cu⁺⁺络离子的晶场谱。假设适当的边界条件,用一个拟合参数,就能得到和实验一致的结果。这种方法的实质在于,在晶体场静止点荷模型基础上,考虑了诸配体等效中心对称场的部份分子轨道效应。这种混合基单电子3d径向波函数也能用于完全的分子轨道理论计算。     

Effect of oscillatory shear on the mechanical properties and crystalline morphology of linear low density polyethylene

In this study,effects of oscillatory shear with different frequencies(0-2.5 Hz) and amplitudes(0-20 mm) on the mechanical properties and crystalline morphology of linear low density polyethylene(LLDPE) were investigated.It was found that the mechanical properties of LLDPE are improved because of the more perfect crystalline structure when LLDPE crystallizes under low-frequency and small-amplitude(0.2 Hz/4 mm) oscillatory shear.The mechanical properties can be further improved by increasing either the frequency or the amplitude of oscillatory shear.The Young's modulus and tensile strength of LLDPE are improved by 27% and 20%,respectively,when the frequency is increased to 2.5 Hz and the amplitude is maintained at 4 mm; while the Young's modulus and tensile strength are improved by 49% and 47%,respectively,when the amplitude is increased to 20 mm and the frequency is remained as 0.2 Hz.The crystallinity and microstructure of LLDPE under different oscillatory shear conditions were investigated by using differential scanning calorimetry,wide angle X-ray diffraction and scanning electron microscopy to shed light on the mechanism for the improvement of mechanical properties.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.     

Erosion of efficiency in non-uniform linear chromatography

In linear chromatography (i.e. chromatography performed in the absence of sample overloading), when the plate height of a column is roughly uniform along its length, variations in the velocities of solutes are the only possible causes of erosion of efficiency. The sources of these variations (variations in capacity ratio and in the density of the mobile phase, etc.) play no direct role in the erosion of efficiency except through their effect on solute velocities. In other words, what eventually causes the erosion of efficiency is merely variation in the time required for solutes to traverse equally small segments of a column. Significant erosion can only arise from abrupt and deep deceleration of solutes in one or several relatively small segments of a column. If erosion of efficiency caused by pressure gradients in linear SFC is to be large, the depth and the sharpness of the deceleration of a solute must go beyond that hitherto confirmed experimentally. Many relevant examples are analyzed graphically.     

Effects of the chain microstructure on the properties of polyketones terpolymers characterized by scanning force microscopy

A new approach is described to tailor properties of polyketones based on the controlled modification of the block structure by varying the polymerization process. Ethylene-propylene-CO (ECOPCO) terblock copolymers with similar composition but different chain microstructures have been synthesized using either preset polymerization (PSP) or pulsed-feed polymerization (PFP), respectively. Whereas by PSP an ABC-triblock structure is obtained, the PFP results in [AB]_n-multiblock structure. In this paper we investigate the influence of the chain microstructure on the mechanical behavior and the surface properties.SFM phase images display a phase-separated bulk morphology where triblock polymers due to the larger block lengths form coarser structures than the multiblock samples. If the ECO content is above 50%, partially crystalline lamellar structures can be found, which in case of the multiblock sample form a continuous network of lamellar-like ECO rich domains. All ECOPCO terpolymers reveal elastomeric behavior with an elastic recovery of at least 82% but tensile strength and elongation vary with the block length of the chain microstructures. Differences in elasticity are explained by the formation of different amounts of cross-links consisting of blocks of parallel-aligned ECO chain segments or crystalline lamellae. It can be shown that the surface morphology differs from bulk morphology, mainly by the point that no distinct phase separation appears but ECO rich domains can be detected. Surface tension measurements enable to correlate the surface energy with surface composition and surface morphology.     

Magnetic exchange coupling in bis-nitroxides: a theoretical analysis of the solvent effects

Magnetic properties of nitroxide radicals can be greatly affected by solvent effects. In this study, the change of the magnetic exchange interaction J, coupling the two unpaired electrons of a model solvated antiferromagnetic bis-iminyl-nitroxide molecule (2IN), is rationalized thanks to different geometric and electronic criteria provided by density functional theory calculations. It is shown that for a given geometry, simple tools can be used to analyze with good accuracy the dependence of J with the solvent polarity. Estimates of two important magnetic parameters are given: the magnetic orbitals exchange and the in-site energy gap between ionic and neutral configurations. 2IN can be engaged in different hydrogen-bonds with first shell water molecules, modifying both the 2IN geometry and the electrostatic potential felt by the molecule. In all, the additivity of electrostatic and hydrogen-bond solvent effects is found to be responsible for J variations as large as 50%.     

Development of a Unified X-ray Fluorescence Procedure for Determining Heavy Metals in Biological Materials

A unified procedure for the X-ray fluorescence determination of Pb, Mo, Rb, As, Zn, Ni, Fe, and Mn in biological materials was developed using the internal standard technique (gallium was the reference element). The samples were prepared for analysis by ashing the materials. The effects of variations in the chemical composition and of the surface density of unsaturated radiators on the accuracy of the analytical results were studied with the use of theoretical intensities; this effect varied from 2.5 to 22%. Based on this information, an optimum calibration function was chosen. Ashes of plant and animal tissues can be analyzed with the use of this function. The errors due to sample preparation for analysis and the reproducibility and accuracy of the results of X-ray fluorescence analysis were evaluated.     

RigFit: A new approach to superimposing ligand molecules

If structural knowledge of a receptor under consideration is lacking, drug design approaches focus on similarity or dissimilarity analysis of putative ligands. In this context the mutual ligand superposition is of utmost importance. Methods that are rapid enough to facilitate interactive usage, that allow to process sets of conformers and that enable database screening are of special interest here. The ability to superpose molecular fragments instead of entire molecules has proven to be helpful too. The RigFit approach meets these requirements and has several additional advantages. In three distinct test applications, we evaluated how closely we can approximate the observed relative orientation for a set of known crystal structures, we employed RigFit as a fragment placement procedure, and we performed a fragment-based database screening. The run time of RigFit can be traded off against its accuracy. To be competitive in accuracy with another state-of-the-art alignment tool, with which we compare our method explicitly, computing times of about 6s per superposition on a common day workstation are required. If longer run times can be afforded the accuracy increases significantly. RigFit is part of the flexible superposition software FlexS which can be accessed on the WWW [http://cartan.gmd.de/FlexS].     

Reproducibility and transferability of topological data: experimental charge density study of two modifications of L-alanyl-L-tyrosyl-L-alanine

Two crystalline modifications of the tripeptide L-Ala-L-Tyr-L-Ala, which have different solvent molecules in the crystal structure (water and ethanol for modifications 1 and 2), were the subject of experimental charge density studies based on high resolution X-ray data collected at ultra-low temperatures of 9 K (1) and 20 K (2), respectively. The molecular structures and the intermolecular interactions were found to be rather similar in the two crystal lattices, so that this study allowed the reproducibility of the charge density of a given molecule in different (but widely comparable) crystalline environments to be examined. With respect to bond topological and atomic properties, the agreement between the two modifications of the title tripeptide was in the same range as found from the comparison with the previously reported results of tri-L-alanine. It follows that the reproducibility and transferability of quantitative topological data are comparable and that within the accuracy of experimental charge density work the replacement of the central amino acid residue L-Ala by L-Tyr has no significant influence, neither on bond nor on the atomic properties of the oligopeptide main chain. Intermolecular interactions in the form of hydrogen bonds were characterized quantitatively and qualitatively by topological criteria and by mapping the charge density distribution on the Hirshfeld surface.     

Issues in the synthesis of crystalline molecular sieves: towards the crystallization of low framework-density structures.

Fundamental and practical interest in crystalline, microporous, molecular sieves is largely a direct consequence of the fact that their bulk properties can be manipulated through variations in atomic structure. This correspondence between the macroscale and the atomic scale is due to the uniformity of these crystalline materials. Control of the atomic structure therefore is of extreme importance, and is the thesis of this Review. Synthesis mechanisms and the parameters that can direct the crystal assembly pathway and the ultimate product formed are discussed and rationalized.     

Paramagnetic DOSY: An Accurate Tool for the Analysis of the Supramolecular Interactions between Lanthanide Complexes and Proteins

Diffusion ordered NMR is implemented to determine accurately the mobility of paramagnetic tris‐dipicolinate lanthanide complexes that are versatile probes of protein structure. It is shown that diffusion coefficient ratios can be measured with an accuracy of 1 % using a standard BPPLED pulse sequence, which allows for observing significant, though weak, variations when different species are interacting with the paramagnetic compound. We demonstrate that this approach is complementary to classical chemical shift titration experiments, and that it can be applied successfully to probe the supramolecular dynamic interactions between lanthanide complexes and small molecules on the one hand, or to determine rapidly their affinity for a targeted protein.     

Side chain liquid crystalline elastomers II. Thermal properties and orientational behaviour of the LCE based on unsaturated copolyesters

The effect of crosslinking density on the phase behaviour of smectic liquid crystalline networks was studied; the results showed that crosslinking in their smectic phases can greatly enhance the stability of the liquid crystalline phase. The higher the crosslinking density, the higher the smectic-isotropic transition temperature. The mechanically-induced orientation was studied by polarized FTIR spectroscopy. The smectic liquid crystalline network could be oriented parallel to the mechanical field at higher draw ratio λ, while at lower λ the mesogenic groups are oriented perpendicular to the field for the networks with higher crosslinking density. The observed mechanically-induced orientation is interpreted by a proposed mechanism.     

Tri-alpha-naphthylbenzene as a crystalline or glassy matrix for matrix-assisted laser desorption/ionization: a model system for the study of effects of dispersion of polymer samples at a molecular level

Tri-alpha-naphthylbenzene (TalphaNB) can exist as either a crystalline or glassy solid at ambient temperatures, making it a unique matrix in matrix-assisted laser desorption/ionization (MALDI) spectroscopy. Electrosprayed TalphaNB is crystalline and has a melting point of 180 +/- 2 degrees C, as measured by differential scanning calorimetry (DSC). A glass of TalphaNB is obtained upon heating above the crystalline melting point with a glass transition temperature of 68 +/- 2 degrees C having no remaining crystallinity. MALDI samples containing mass fraction 1% polystyrene (PS) are run in both the crystalline and amorphous states. In the crystalline state, there is a strong spectrum typical of PS, but upon melting and quenching to the glassy state, the MALDI signal disappears. If the transparent, amorphous sample is treated with 1-butanol, it becomes white, and the MALDI signal returns. DSC shows that the 1-butanol treatment leads to the return of some of the crystallinity. Small angle neutron scattering (SANS) shows that the crystalline state has large aggregations of PS while the amorphous state has molecularly dispersed PS molecules. MALDI gives strong signals only when there are large aggregations of polymer molecules, with individually dispersed molecules producing no signal.     

Pressure amorphized ices--an atomistic perspective

We offer our viewpoint on the nature of amorphous ices produced by pressurization of crystalline ice Ih and the inter-relationship between them from an atomistic perspective. We argue that the transformation of high density amorphous (HDA) ice from crystalline ice is due to a mechanical process arising from the instability of the ice Ih structure. The densification of HDA upon thermal annealing under pressure is a relaxation process. The conversion of the densified amorphous ice to a lower density form (LDA) upon the release of pressure can be attributed to a similar process. It is speculated that amorphous ices are metastable frustrated structures due to the large activation barriers associated with proton reorientation in the formation of the underlying stable crystalline ice polymorphs.