Local Monte Carlo for electrostatics in anisotropic and nonperiodic geometries

We present an implementation of a local Monte Carlo algorithm for simulating charged particles in anisotropic and nonperiodic geometries. Specifically, we consider a quasi-two-dimensional periodic slab geometry with an either infinite or finite third dimension. For the infinite case, we show that the method generates accurate electrostatics equivalent to standard two-dimensional Ewald formulas. We then implement constant charge or constant potential (Dirichlet) boundary conditions, which frequently occur in experimental studies of charged complex fluids or polyelectrolytes. As a demonstration of the versatility of the approach, we compute ion density profiles in front of oppositely charged surfaces (the electric double layer) and find excellent agreement with theory in known analytic limits.     

外型-1,4-氧桥-环己基-2,3-二羧酸的晶体及分子结构

外型-1,4-氧桥-环己基-2,3-二羧酸晶体属单斜晶系,空间群为P2_1/n;晶胞参数为:α=5.594(3)A,b=11.178(7)A,c=14.675(11)A,β=91.46(5)°;Ζ=4.从直接法得到结构的初始模型,经块矩阵最小二乘修正后,最后的R值为0.072.在晶体中,分子间的O—H…O氢键将分子连接成层型氢键体系.使用自编的CNDO/2程序,计算得电子的能量、分子的总能量、偶极矩及各原子的电荷密度和净电荷.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.     

Computation of the Madelung constant for hypercubic crystal structures in any dimension

A new method of computing the Madelung constants for hypercubic crystal structures in any dimension \(n\ge 2\) is given. It is shown for \(n\ge 3\) that the Madelung constant may be obtained in a simple, efficient and unambiguous way as the Hadamard finite part of the integral representation of the potential within the crystal which is divergent at any point charge location. Such a regularization method fails in the bidimensional case due to the logarithmic nature of singularities for the potential. In that case, a specific approach is proposed taking in account the scale invariance of the Poisson equation and the existence of a finite horizon for each point charge in the plane. Since a closed-form exact solution for the 2D electrostatic potential may be derived, one shows that the Madelung constant may be defined via an appropriate limit calculation as the mean value of potential energies of charges composing the unit cell.     

Extrapolation of real-space quantum chemical calculations from finite-size supercells to the ideal infinite system. III. Application to two-dimensional systems

A previously presented extrapolation method of the density matrix of a standard finite supercell calculation to an infinite supercell is extended to two-dimensional systems. The density matrix of the finite supercell is transformed into q space where it is interpolated and extrapolated in such a way that all its fundamental properties are guaranteed by construction. The resulting modified density matrix contains information from a continuum of q points in the first Brillouin zone which allows for a more realistic calculation of properties like the total energy E_tot per atom and the band structure ϵ₁(q). It is shown that this more realistic calculation takes better care of the crystal symmetries and is essential in reproducing both important degeneracies in the band structure and rotationally symmetric results. In the special case of π electrons only, an exact analytical solution for the density matrix of the infinite supercell is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 895–911, 1997     

LiAl的电子与几何结构

应用平面波展开和第一原理赝势法研究了锂铝单晶的电子和几何结构,给出LiAl各种可能结构的能量～体积关系图以及相关的能带结构,电子态密度和电荷密度分布等各种性质变化关系.讨论了B32结构与其他结构电子键合性质的不同,指出B32结构之所以成为LiAl最稳定的结构是由于Al＿Al原子形成了类似于Si＿Si的共价键合.计算得到的能量最低的稳定结构与实验以及其它的理论计算结果一致.     

Density functional crystal vs. cluster models as applied to zeolites

In order to compare solid and cluster models of zeolites, we have studied the substitution Si⁴⁺→Al³⁺+H⁺ on the T₁ site of mordenite in the dilute limit using a self-consistent, full potential, local density functional (LDF) approach. Clusters size ranged from 9 to 105 atoms. Two crystal models with different Al concentrations were used. The first contained one substitution site per primitive cell of 72 atoms, the other one per conventional cell, containing 144 atoms. The unrelaxed substitution energies as computed with cluster and crystal models correspond well if the cluster results are extrapolated to infinite radius. Size effects are much smaller in crystal models. In addition, a structure relaxation (with fixed unit cell) was carried out for pure-silica offretite, a zeolite with 54 atoms per unit cell, and pure-silica mordenite, with 144 atoms per unit cell, starting from the low aluminum content X-ray crystallographic structure. In the offretite and mordenite optimizations full use was made of the D_3h¹–P $ \bar 6 $m2 and the nonsymmorphic D_2h¹⁷–Cmcm space group symmetry, respectively. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 135–144, 1998     

Charge state of the fast gate in chloride channels: insights from electrostatic calculations in a schematic model

Fast gating is a unique property of chloride channels, where a permeating Cl(-) ion acts as its own ligand in opening the channel. The glutamate residue implicated in fast gating normally carries a unit negative charge. Whether this charge needs to be protonated to enable permeation of a Cl(-) ion is an important question that will affect how models of chloride channels are constructed. We investigate the energetic consequences of the charge state of this glutamate residue from continuum electrostatics using a schematic cylindrical channel model. Both analytical solutions of the Poisson equation for an infinite cylinder and numerical ones for a finite cylinder are employed in the calculations.     

Extrapolation of real-space quantum chemical calculations from finite-size super cells to the ideal infinite system. I. Theory

A method is proposed how to calculate the correct density matrix of an infinite polymeric chain from that of a standard finite supercell calculation. The density matrix of the finite supercell is transformed into k-space for all k-values allowed by the periodic boundary conditions. The k-dependent matrices are then unitarily transformed, with each unitary matrix being represented by a set of complex rotation matrices. It is shown that the corresponding angles can be interpolated and extrapolated toward the zone boundaries in a straghtforward manner and that this extrapolation can be done from any finite supercell with reasonable accuracy. This gives rise to an infinite system density matrix for which all fundamental properties are guaranteed by construction. This infinite system density matrix may be used to construct a corrected density matrix for the finite supercell calculation. © 1994 John Wiley & Sons, Inc.     

C library for topological study of the electronic charge density

The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid‐based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton–Raphson method (to find the critical points, where the gradient is null) and the Cash–Karp Runge–Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three‐dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. © 2012 Wiley Periodicals, Inc.     

X-ray investigations of Langmuir-Blodgett multilayer films of side-chain liquid crystal copolymers

X-ray reflectivity studies on Langmuir-Blodgett multilayer films of side-chain liquid crystal polymers are reported. The films have a high degree of lamellar order. The layer periodicity is independent of the type of monolayer deposition, implying a reorientation of the side group mesogens following the deposition process. X-ray reflectivity from thin films displays subsidiary maxima permitting a quantitative measure of the change in side-chain density between multilayer and monolayer. A unit cell density profile is calculated for thick films assuming a symmetric unit cell.     

Investigation of topology of intermolecular interactions in the benzene–acetylene co-crystal by different theoretical methods

Crystal structure of benzene–acetylene co-crystal was analysed based on calculated energies of intermolecular interactions between basic molecules located in asymmetric part of unit cell and their neighbours belonging to their first coordination sphere. It is demonstrated that the basic structural motif of the crystal is represented by infinite chains formed by the hydrogen-bonded benzene and acetylene molecules. Energy of interaction of the basic pair of molecules to neighbours within the chain is 2.2 times higher than the energy of interactions with molecules of any neighbouring chain. This ratio almost does not depend on method of calculation of interaction energy. Also, results of calculations were compared with analysis of topology of electron density distribution in crystal. The possibility to find the basic structural motif of the crystal based on properties of intermolecular bond critical points is demonstrated.     

Crystal calculation using the PCILO method

The PCILO method is used for the study of molecular systems with translational symmetry in a two-dimensional lattice. The calculation for the whole crystal is reduced to the calculation of unit cell pairs. By using the translational symmetry and the first-neighbour approximation, one shows that only four unit cell pairs have to be considered. The procedure described yields the ground-state energy and the charge distribution of the unit cell.     

Application of London-type dispersion corrections to the solid-state density functional theory simulation of the terahertz spectra of crystalline pharmaceuticals

The effects of applying an empirical dispersion correction to solid-state density functional theory methods were evaluated in the simulation of the crystal structure and low-frequency (10 to 90 cm(-1)) terahertz spectrum of the non-steroidal anti-inflammatory drug, naproxen. The naproxen molecular crystal is bound largely by weak London force interactions, as well as by more prominent interactions such as hydrogen bonding, and thus serves as a good model for the assessment of the pair-wise dispersion correction term in systems influenced by intermolecular interactions of various strengths. Modifications to the dispersion parameters were tested in both fully optimized unit cell dimensions and those determined by X-ray crystallography, with subsequent simulations of the THz spectrum being performed. Use of the unmodified PBE density functional leads to an unrealistic expansion of the unit cell volume and the poor representation of the THz spectrum. Inclusion of a modified dispersion correction enabled a high-quality simulation of the THz spectrum and crystal structure of naproxen to be achieved without the need for artificially constraining the unit cell dimensions.     

Insight into the chemical bonding and electrostatic potential: A charge density study on a quinazoline derivative

2,3-Trimethylene-3,4-dihydroquinazoline shares the heterocyclic core with natural compounds and synthetic drugs. The hydrochloride of the compound forms excellent dihydrate crystals which have allowed us to collect high-resolution X-ray diffraction data and obtain the experimental charge density. The solid may be understood as built up from pairs of heterocyclic cations and chloride anions; a direct hydrogen bond links the halide to the formally cationic pyrimidine NH group. The hydrate water molecules interact with the anions, forming an infinite chain along the crystallographic a axis between the stacks of the heterocyclic cations. Based on the experimental charge density, a dipole moment of 16.1 Debye is calculated for a pair of the hydrogen-bonded quinazolinium cation and the chloride anion in the extended crystal structure.     

Significance of cell electrokinetic properties determined by soft-particle analysis in bacterial adhesion onto a solid surface

The influence of extracellular polymeric substances (EPSs) on bacterial cell electrokinetic properties and on cell adhesion onto glass beads in connection with bacterial cell electrokinetic properties was investigated using 12 heterotrophic bacterial strains. Bacterial cell surface properties such as the softness 1/lambda and charge density ZN were determined by Ohshima's soft-particle analysis using the measured electrophoretic mobility as a function of ionic strength. In 10 of 12 strains, when EPSs covering the cell surface were removed, the softness of the cell decreased, indicating that EPS adsorption enhanced the ease of liquid fluid in the ion-penetrable layer on the cell surface. On the other hand, the negative charge density of the cell surface increased for 9 of 12 strains, suggesting that EPSs covering the cell surface decreased the negative charge density of the cell surface layer. In addition, the characteristics of bacterial cell adhesion onto glass beads were evaluated by the packed-bed method and the data were interpreted to indicate cell adhesiveness. As a result, the efficiency of cell adhesion onto glass beads increased as negative cell surface potential psi0 decreased, whereas there seemed to be no correlation between zeta potential and cell adhesiveness. Cell surface potential psi0, which was derived by taking the bacterial polymer layer with EPSs into consideration, provided a more detailed understanding of the electrokinetic properties of bacterial cells.