Study on the behavior of energy convergence in ab initio crystal orbital calculations

Summary This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N ₀). The energy convergence behavior with respect to N ₀ depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C₂H₄ unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N ₀ a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N ₀ = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N ₀ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.     

On the Pace–Datyner theory of diffusion of small molecules through polymers

The Pace–Datyner theory for diffusion of penetrant molecules in polymers has been analyzed. It has been found that the correct solution of the problem they pose is possible only at 0 K, since then the separation of two chains at x = ∞ is equal to the minimum of the DiBenedetto potential for their interaction. Otherwise the energy of symmetrical separation is infinite. By using the linearization method to solve the differential equation, Pace and Datyner neglected the problem of unnatural boundary conditions at x = ∞ for temperatures above 0 K. The exact numerical solutions of differential equations at temperature 0 K were therefore compared with the results of the Pace–Datyner linear approximation. For temperatures different from 0 K the solution of the problem is possible only when the proper cutoff is imposed. The analytical expression for the coeffients in the DiBenedetto potential has been found, and the potential can be written as     

Diffusion of two different water models and thermal conductivity in a protein—water system

The diffusion constant of dynamics simulation data evaluated by the time-dependent displacement or the velocity autocorrelation function provides equivalent results. The diffusion constant (D) increases with the cutoff distance for electrostatic energy. An extended version of the TIP 3P water model provides a proper value of D at small cutoff distance (8.5 Å); the SPC/E water model requires a larger cutoff distance (11.0 Å). Considering Langevin dynamics with a total friction γ, the Einstein relation (D ∼ 1/γ) is valid for large enough friction (γ > 5 ps⁻¹) only. Heating of a protein-water system by stochastic dynamics at the boundary is studied in detail. The calculated thermal conductivity of water agrees with experiment. The thermal conductivity of a protein molecule is about a factor of two smaller. © 1996 John Wiley & Sons, Inc.     

Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

This article is concerned with the construction of the general algorithm for evaluating two-center, two- and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function r^k_ij derived in Part I of this series for k = ?1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two- and three-electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.     

Identifying essential pairwise interactions in elastic network model using the alpha shape theory

Elastic network models (ENM) are based on the idea that the geometry of a protein structure provides enough information for computing its fluctuations around its equilibrium conformation. This geometry is represented as an elastic network (EN) that is, a network of links between residues. A spring is associated with each of these links. The normal modes of the protein are then identified with the normal modes of the corresponding network of springs. Standard approaches for generating ENs rely on a cutoff distance. There is no consensus on how to choose this cutoff. In this work, we propose instead to filter the set of all residue pairs in a protein using the concept of alpha shapes. The main alpha shape we considered is based on the Delaunay triangulation of the Cα positions; we referred to the corresponding EN as EN(∞). We have shown that heterogeneous anisotropic network models, called αHANMs, that are based on EN(∞) reproduce experimental B‐factors very well, with correlation coefficients above 0.99 and root‐mean‐square deviations below 0.1 Ų for a large set of high resolution protein structures. The construction of EN(∞) is simple to implement and may be used automatically for generating ENs for all types of ENMs. © 2014 Wiley Periodicals, Inc.     

New optimization method for conformational energy calculations on polypeptides: Conformational space annealing

A new optimization method is presented to search for the global minimum-energy conformations of polypeptides. The method combines essential aspects of the build-up procedure and the genetic algorithm, and it introduces the important concept of “conformational space annealing.” Instead of considering a single conformation, attention is focused on a population of conformations while new conformations are obtained by modifying a “seed conformation.” The annealing is carried out by introducing a distance cutoff, D_cut, which is defined in the conformational space; D_cut effectively divides the whole conformational space of local minima into subdivisions. The value of D_cut is set to a large number at the beginning of the algorithm to cover the whole conformational space, and annealing is achieved by slowly reducing it. Many distinct local minima designed to be distributed as far apart as possible in conformational space are investigated simultaneously. Therefore, the new method finds not only the global minimum-energy conformation but also many other distinct local minima as by-products. The method is tested on Met-enkephalin, a 24-dihedral angle problem. For all 100 independent runs, the accepted global minimum-energy conformation was obtained after about 2600 minimizations on average. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1222–1232     

An overview of contemporary method development in liquid chromatography

Summary This paper provides an overview of method development in liquid chromatography. It is explained why every practicing chromatographer needs to understand the process of method development. Thus, this paper is directed towards chromatographers who develop new separation methods, as well as to those who apply published methods. The method-development process is first explained in broad terms, after which the different aspects of the process are described in more detail.First, attention is paid to the initial stages of method development, which consist of the accurate definition of the separation problem and the selection of the most suitable chromatographic method. Method-development expert systems are discussed with regards to their applicability in this area.Selectivity optimization is shown to rely on three main factors,i. e. the selection of the parameter space, the experimental design and the optimization criterion. Selectivity-optimization procedures are described very briefly.System optimization concerns those factors which do not affect the chemistry of the system (mobile and stationary phase), but are essentially determining the analysis time and the sensitivity.The method-validation stage can be divided into three main parts: qualitative method validation (i.e. peak integrity and identity), calibration and quantitative method validation. The requirements of calibration procedures are briefly reviewed and an inventory of method-validation procedures is presented.     

Quantifying Degradation Parameters of Single-Crystalline Ni-Rich Cathodes in Lithium-Ion Batteries

Single-crystal LiNi_xCo_yMn_zO₂ (SC-NCM, x+y+z=1) cathodes are renowned for their high structural stability and reduced accumulation of adverse side products during long-term cycling. While advances have been made using SC-NCM cathode materials, careful studies of cathode degradation mechanisms are scarce. Herein, we employed quasi single-crystalline LiNi_0.65Co_0.15Mn_0.20O₂ (SC-NCM65) to test the relationship between cycling performance and material degradation for different charge cutoff potentials. The Li/SC-NCM65 cells showed >77 % capacity retention below 4.6 V vs. Li⁺/Li after 400 cycles and revealed a significant decay to 56 % for 4.7 V cutoff. We demonstrate that the SC-NCM65 degradation is due to accumulation of rock-salt (NiO) species at the particle surface rather than intragranular cracking or side reactions with the electrolyte. The NiO-type layer formation is also responsible for the strongly increased impedance and transition-metal dissolution. Notably, the capacity loss is found to have a linear relationship with the thickness of the rock-salt surface layer. Density functional theory and COMSOL Multiphysics modeling analysis further indicate that the charge-transfer kinetics is decisive, as the lower lithium diffusivity of the NiO phase hinders charge transport from the surface to the bulk.     

On the accuracy of the many-points local procedures

As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M > N) can be connected in a simple way with the errors of the (^M_N) partial calculations N points/N functions. This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.     

Anionic syntheses of terminally functionalized ethylene oligomers

Synthetic procedures for preparation of terminally functionalized linear ethylene oligomers are described. The preferred synthetic method is anionic oligomerization of ethylene with n-butyllithium–tetramethylethylenediamine and electrophilic substitution of the living oligomer so-formed. Conditions and procedures for subsequent chemistry to elaborate the end groups of these oligomers are described. These procedures afford strictly linear ethylene oligomers which contain a wide variety of end groups and which range in molecular weight from 1000 to 4500 (M_n). The product oligomers were characterized spectroscopically as toluene-d₈ solutions at 110°C using multinuclear NMR, FT-IR, fluorescence, and UV-visible spectroscopies as appropriate. Alternative stepwise approaches to such oligomers are also discussed.     

New spherical-cutoff methods for long-range forces in macromolecular simulation

New atom- and group-based spherical-cutoff methods have been developed for the treatment of nonbonded interactions in molecular dynamics (MD) simulation. A new atom-based method, force switching, leaves short-range forces unaltered by adding a constant to the potential energy, switching forces smoothly to zero over a specified range. A simple improvement to group-based cutoffs is presented: Switched group-shifting shifts the group–group potential energy by a constant before being switched smoothly to zero. Also introduced are generalizations of atom-based force shifting, which adds a constant to the Coulomb force between two charges. These new approaches are compared to existing methods by evaluating the energy of a model hydrogen-bonding system consisting of two N-methyl acetamide molecules and by full MD simulation. Thirty-five 150 ps simulations of carboxymyoglobin (MbCO) hydrated by 350 water molecules indicate that the new methods and atom-based shifting are each able to approximate no-cutoff results when a cutoff at or beyond 12 Å is used. However, atom-based potential-energy switching and truncation unacceptably contaminate group–group electrostatic interactions. Group-based potential truncation should not be used in the presence of explicit water or other mobile electrostatic dipoles because energy is not a state function with this method, resulting in severe heating (about 4 K/ps in the simulations of hydrated MbCO). The distance-dependent dielectric (? ∝? r) is found to alter the temperature dependence of protein dynamics, suppressing anharmonic motion at high temperatures. Force switching and force shifting are the best atom-based spherical cutoffs, whereas switched group-shifting is the preferred group-based method. To achieve realistic simulations, increasing the cutoff distance from 7.5 to 12 Å or beyond is much more important than the differences among the three best cutoff methods. © 1994 by John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Determination of sulfur components in natural gas: A review

More stringent environmental regulations as well as higher demands presently being imposed on the sulfur content of natural gas feed-stocks for chemical processes necessitate the development of new analytical procedures for sulfur determination in natural gas. Only analytical procedures based on gas chromatography can meet the sensitivity and accuracy requirements dictated by environmental regulation institutions and modern chemical industry. The complexity of the natural gas matrix as well as the extremely low concentration levels at which the sulfur species occur make the development of these analytical methods a true challenge. In this review the three steps common for analytical methods for trace analysis in complex matrices, i.e. pretreatment, chromatographic separation, and detection, are discussed in detail. Possible methods for calibration of the system are discussed in the final section. Various techniques to determine sulfur in natural gas are described. Depending on the application, the most suitable system has to be selected. For example, for on-line application in a hazardous area a simple and rugged system is required, i.e. a simple gas chromatograph with a flame photometric detector, while for laboratory application a more complex instrument including preconcentration, column switching, and more exotic detection systems could be more suitable. Therefore it is crucial to define the requirements of the instrument at an early stage and use the information in this review article to develop/select a dedicated instrument/procedure for the problem at hand.     

Communication: Shifted forces in molecular dynamics

Simulations involving the Lennard-Jones potential usually employ a cutoff at r = 2.5σ. This communication investigates the possibility of reducing the cutoff. Two different cutoff implementations are compared, the standard shifted potential cutoff and the less commonly used shifted forces cutoff. The first has correct forces below the cutoff, whereas the shifted forces cutoff modifies Newton's equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted forces cutoff at r = 1.5σ, even though the pair force is here 30 times larger than at r = 2.5σ.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Bioanalytical procedures for determination of drugs of abuse in blood

Determination of drugs of abuse in blood is of great importance in clinical and forensic toxicology. This review describes procedures for detection of the following drugs of abuse and their metabolites in whole blood, plasma or serum: Δ9-tetrahydrocannabinol, 11-hydroxy-Δ9-tetrahydrocannabinol, 11-nor-9-carboxy-Δ9-tetrahydrocannabinol, 11-nor-9-carboxy-Δ9-tetrahydrocannabinol glucuronide, heroin, 6-monoacetylmorphine, morphine, morphine-6-glucuronide, morphine-3-glucuronide, codeine, amphetamine, methamphetamine, 3,4-methylenedioxymethamphetamine, N-ethyl-3,4-methylenedioxyamphetamine, 3,4-methylenedioxyamphetamine, cocaine, benzoylecgonine, ecgonine methyl ester, cocaethylene, other cocaine metabolites or pyrolysis products (norcocaine, norcocaethylene, norbenzoylecgonine, m-hydroxycocaine, p-hydroxycocaine, m-hydroxybenzoylecgonine, p-hydroxybenzoylecgonine, ethyl ecgonine, ecgonine, anhydroecgonine methyl ester, anhydroecgonine ethyl ester, anhydroecgonine, noranhydroecgonine, N-hydroxynorcocaine, cocaine N-oxide, anhydroecgonine methyl ester N-oxide). Metabolites and degradation products which are recommended to be monitored for assessment in clinical or forensic toxicology are mentioned. Papers written in English between 2002 and the beginning of 2007 are reviewed. Analytical methods are assessed for their suitability in forensic toxicology, where special requirements have to be met. For many of the analytes sensitive immunological methods for screening are available. Screening and confirmation is mostly done by gas chromatography (GC)–mass spectrometry (MS) or liquid chromatography (LC)–MS(/MS) procedures. Basic information about the biosample assayed, internal standard, workup, GC or LC column and mobile phase, detection mode, and validation data for each procedure is summarized in two tables to facilitate the selection of a method suitable for a specific analytic problem.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Summary. Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Iso-energy cutoff for the calculation of interionic potential of mean force in water

An iso-energy cutoff scheme is introduced for the calculation of the potential of mean force between two ions in water. The cutoff criterion is based on the optimal interaction of the water dipole with the ion pair, for which analytical expressions are derived. Formulas are also derived to characterize the solvent reorganization contribution to the potential of mean force. Treatment of the contributions from waters outside the cutoff is also discussed. © 1994 John Wiley & Sons, Inc.     

Potential energy surface determinations for nonrigid molecules: Application to acetone

In the present work, the problem of the determination of the potential energy surface for nonrigid molecules is examined in the case of the double rotation of the methyl groups in acetone. From the symmetry adapted functional form for the potential, the minimum number of configurations to be calculated is deduced in order to have a reliable surface. With this consideration in mind, the potential energy surface of acetone is determined in some Hartree–Fock semiempirical (CNDO /2) and ab initio procedures with different standard basis sets. In addition, ab initio calculations are performed using different sets of floating Gaussian functions in order to introduce some polarization effects in the wave function. Finally, the influence of the electronic correlation effects in the barrier height, and the role of the possible relaxation of the structure during the rotation is discussed.     

Overcoming the limitations of cutoffs for defining atomic coordination in multicomponent systems

A common way to understand structure in multimolecular systems is the coordination shell which comprises all the neighbors of an atom. Coordination, however, is nontrivial to determine because there is no obvious way to determine when atoms are neighbors. A common solution is to take all atoms within a cutoff at the first minimum of the radial distribution function, g(r). We show that such an approach cannot be consistently applied to model multicomponent systems, namely mixtures of atoms differing in size or charge. Coordination shells using the total g(r) are found to be too restrictive for atoms of different size while those using pairwise g(r)s are excessive for charged mixtures. The recently introduced relative angular distance algorithm, however, which defines coordination instantaneously from atomic positions, is consistently able to define coordination shells containing the expected neighboring atoms for all these systems. This more robust way to determine coordination should in turn make coordination a more robust way to understand structure. © 2017 Wiley Periodicals, Inc.