Errors in the Ewald summation method with electrostatic layer correction for Coulomb interactions in slab geometry

New theoretical expressions for cut-off errors in 2D reciprocal-space summation of the electrostatic layer correction (ELC) term in energy and forces are derived, and a procedure to determine optimal parameters of the method is proposed. The procedure is tested in numerical calculations for charges distributed uniformly in a cubic box and charges located in two layers near the box basis. The summation errors for conventional Ewald method can be used to find out optimal values of the convergence parameter, and real- and reciprocal-space cut-off radii, whereas the ELC errors give possibility to choose an optimal value of an empty space gap in the simulation box.     

The sum rule for dipolar absorptions and rotational kinetic energy of wate and some dipolar molecules in condensed phases

Another form of the sum rule for dipolar absorptions has been derived by means of quantum statistics. The difference between this and usually used form results from a quantum effect on the molecular rotational motion. By the joint use of the two forms, average rotational kinetic energies of water molec in the liquid and solid phases and some dipolar molecules in solutions have been estimated. It has been shown that the average rotational kinetic energ larger than the value expected from the classical equipartition rule, with an increase in the hindering potential for the rotational motion of the mole The dipole moments of water molecules in liquid and solid water have been estimated. These are considerably smaller than the gas-phase value.     

Ewald summation versus direct summation of shifted-force potentials for the calculation of electrostatic interactions in solids: A quantitative study

The calculated Madelung energies and Madelung forces of the electrostatic interaction for nine crystal structures are reported. The method of direct summation with two different shifted-force potentials is compared to the Ewald summation. There is a considerable difference in the convergence of the energy and the force for the two shifted-force potentials regarding the cutoff radius. The convergence depends not only on the potential itself, but also on the crystal structure. One of the shifted-force potentials used is implemented in the CHARMM force field. The energy calculated with this potential shows a good convergence for small cutoff radii. With the other shifted-force potential, the force shows a better convergence for small cutoff radii. The number of pair interactions for obtaining the Madelung limit using the Ewald summation and the direct summation of a shifted-force potential is also reported. For complex structures like zeolites, the number of relevant pair interactions is smaller using the direct summation of a shifted-force potential. For simple structures such as cesium chloride, the number of significant pair interactions is smaller using the Ewald summation. © 1997 by John Wiley & Sons, Inc.     

DNA cholesteric phases: the role of DNA molecular chirality and DNA-DNA electrostatic interactions

DNA molecules form dense liquid-crystalline twisted phases both in vivo and in vitro. How the microscopic DNA chirality is transferred into intermolecular twist in these mesophases and what is the role of chiral DNA-DNA electrostatic interactions is still not completely clear. In this paper, we first give an extended overview of experimental observations on DNA cholesteric phases and discuss the factors affecting their stability. Then, we consider the effects of steric and electrostatic interactions of grooved helical molecules on the sign of cholesteric twist. We present some theoretical results on the strength of DNA-DNA chiral electrostatic interactions, on DNA-DNA azimuthal correlations in cholesteric phases, on the value of DNA cholesteric pitch, and on the regions of existence of DNA chiral phases stabilized by electrostatic interactions. We suggest for instance that 146 bp long DNA fragments with stronger affinities for the nucleosome formation can form less chiral cholesteric phases, with a larger left-handed cholesteric pitch. Also, the value of left-handed pitch formed in assemblies of homologous DNA fragments is predicted to be smaller than that of randomly sequenced DNAs. We expect also the cholesteric assemblies of several-kbp-long DNAs to require higher external osmotic pressures for their stability than twisted phases of short nucleosomal DNA fragments at the same DNA lattice density.     

Single-center method of calculation for clusters and molecules other than hydrides

A new single-center method is proposed for solving the one-particle Schrödinger equation for molecules other than hydrides and for clusters, based on the method of associated differential and integral equations. The higher terms of the expansion of the wave function of the electron are replaced by linear combinations of analytical functions. This reduces the system of integro-differential equations to a system of differential and algebraic equations, for which stable numerical solutions have been worked out. Calculations are given of the energy and functions of the 2s state of an oxygen atom with a displaced center.Translated from Teoreticheskaya i Éksperimental'naya Khimiya,Vol. 25, No. 1, pp. 12–20, January–February, 1989.The authors are grateful to A. G. Kochur for making available the program for the SC expansion of atomic functions, and also to V. L. Sukhorukov for discussing the results.     

Accounting for fluctuations in cluster parameters upon the description of nucleation in supersaturated vapor

A theory is proposed for stationary homogeneous nucleation in supersaturated vapor in which a modified expression for the rate of cluster evaporation was used to calculate the equilibrium distribution over the nucleus sizes and the rates of their formation. This rate was determined by the extrapolation to the region of small sizes of the corresponding expression for the macroscopic droplet derived according to thermodynamic notions that take fluctuations into account. Modified dependences of the size of critical nucleus and the rate of nucleation on the supersaturation and the temperature are determined and compared with the data of the classical theory of nucleation and experimental results.     

Isothermal compressibility maxima of hydrogen fluoride in the supercritical and superheated vapor regions

The highly nonideal behavior of hydrogen fluoride (HF) vapor has been considered to be the origin of its numerous vapor phase anomalies. In this work, we report one such potential vapor phase anomaly for HF. For a nonassociating substance like propane, the response functions go through a maximum only once in the supercritical region. However, for HF, when an association model is used to predict the isothermal compressibility (KT), it exhibits a maximum in the supercritical region more than once, and this peak extends well in to the superheated vapor region upon decompression. This theoretical prediction is also supported by two other models recently developed for HF. Note that experimental values of KT for HF have not been reported in the literature so far. Preliminary investigations on this KT maximum for HF have suggested no reentrant spinodal, singularity-free scenario, or any additional first-order phase transition, unlike water, and, also, no lambda (or higher-order phase) transitions, unlike liquid helium. However, this KT peak is similar to the experimentally supported heat capacity (CP) peak of HF which extends into the supercritical and superheated vapor regions. Similar to the CP peak, which is understood based on vapor-phase clustering in HF, we relate KT to the derivatives of enthalpy and entropy of the system. Also, we analyze some of the P-v-T experimental data that are available to provide an overview of the KT behavior in the region of interest, and compare them with the model results. Finally, to explore the effect of including a distribution pattern for the oligomers, we report the results on a model that only includes association. Using this approach, we report KT results with and without a Poisson-type oligomer distribution and show that the KT appears once this distribution scheme is specified.     

The viscosity of triethylamine vapor at low densities and in the saturated vapor phase

For the first time, results of high-precision measurements of the viscosity coefficient of triethylamine vapor at low densities are reported. The relative measurements with an all-quartz oscillating-disk viscometer were carried out along seven isochores at densities from 0.002 to 0.009 mol m⁻³ in the temperature range between 298 and 498 K. The uncertainty is estimated to be ±$\pm$0.2% at ambient temperature, increasing up to ±$\pm$0.3% at higher temperatures. First isothermal values were recalculated from the original experimental data and then evaluated with a first-order expansion for the viscosity, in terms of density. In addition, viscosity values of the saturated vapor were determined at low temperatures. The results are utilized to model the viscosity coefficient of triethylamine vapor at moderately low densities. A so-called individual correlation on the basis of the extended theorem of corresponding states was employed to describe the zero-density viscosity coefficient, whereas the Rainwater–Friend theory was used to represent the initial density dependence expressed as second viscosity virial coefficient.     

A fast and Space-efficient boundary element method for computing electrostatic and hydration effects in large molecules

At present, there are two widely used approaches for computing molecular hydration and electrostatic effects within the continuum approximation: the finite difference method, in which the electric potential is directly computed on a cubic grid, and the induced polarization charge or boundary element method, in which an induced charge distribution is first computed on the molecular surface and in which solvation effects are then calculated by reference to the reaction field arising from this induced surface charge. While the induced surface charge approach has a number of advantages over finite differences, especially in the computation of hydration forces and solvent stabilization, the applications of this technique have been largely restricted to small molecules. This is primarily due to the very large system of equations that results when the surface of a macromolecule is discretized into elements small enough to ensure an acceptable level of numerical accuracy within the continuum model. This article describes a new algorithm for implementing boundary element calculations within the continuum model. The essence of our approach is only to compute explicitly those interactions between surface elements that are relatively close together and to approximate long-range interactions by grid-based multipole expansion. The resulting system of equations has a relatively sparse coefficient matrix and requires disk storage that increases linearly with molecular surface area. The technique has numerous applications in the analysis of solvation effects in large molecules, especially in the area of conformational analysis, where it is critical to accurately estimate the global hydration energy for the entire structure. © 1996 by John Wiley & Sons, Inc.     

Thermogravimetric method used to determine the saturated vapor pressure in a wide range of values

Thermogravimetric method was used to study the evaporation of a number of solvents. The evaporation coefficients in the Langmuir equation were calculated in relation to the conditions of a thermogravimetric experiment (atmospheric pressure, carrier-gas) and nature of a substance under study.     

Novel structural motifs in clusters of dipolar spheres: knots, links, and coils

We present the structures of putative global potential energy minima for clusters bound by the Stockmayer (Lennard-Jones plus point dipole) potential. A rich variety of structures is revealed as the cluster size and dipole strength are varied. Most remarkable are groups of closed-loop structures with the topology of knots and links. Despite the large number of possibilities, energetically optimal structures exhibit only a few such topologies.     

Long-range Lennard-Jones and electrostatic interactions in interfaces: application of the isotropic periodic sum method

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.     

Use of electrostatic method for calculating the bond energy of H 2 + , H2, and Li2 molecules and the force constant of H2 and Li2 molecules

Journal of Structural Chemistry -     

Sampling device for a simple,fast calibration technique in gas chromatographic trace analysis of gas phases and vapor phases

In order to accommodate continually changing tasks in the [μl/l]–[nl/m³] ranges of gas chromatographic trace analysis of gas phases and vapor phases, a simple and time-saving calibration technique is presented which renders unnecessary conventional test mixtures of the abovementioned concentration ranges. This new method is based on the simulation of such mixtures at the inlet of the GC unit with the aid of commercially available multiway sampling valves of various volumes by means of partial pressure sampling.