An accurate analytic representation of the water pair potential

The ab initio water dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site-site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site-site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol(-1), compared to 0.42 kcal mol(-1) of the CC-pol fit (0.010 kcal mol(-1) compared to 0.089 kcal mol(-1) for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration-rotation-tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.     

An analytical depth resolution function for the MRI model

The mixing roughness information depth model is frequently used for the quantification of sputter depth profiles. In general, the solution of the convolution integral for any kind of in‐depth distributions is achieved by numerical methods. For a thin delta layer, an analytical depth resolution function is presented, which enables a simple and user‐friendly quantification of measured delta layer profiles in AES, XPS and SIMS. Copyright © 2013 John Wiley & Sons, Ltd.     

MedusaScore: an accurate force field-based scoring function for virtual drug screening

Virtual screening is becoming an important tool for drug discovery. However, the application of virtual screening has been limited by the lack of accurate scoring functions. Here, we present a novel scoring function, MedusaScore, for evaluating protein-ligand binding. MedusaScore is based on models of physical interactions that include van der Waals, solvation, and hydrogen bonding energies. To ensure the best transferability of the scoring function, we do not use any protein-ligand experimental data for parameter training. We then test the MedusaScore for docking decoy recognition and binding affinity prediction and find superior performance compared to other widely used scoring functions. Statistical analysis indicates that one source of inaccuracy of MedusaScore may arise from the unaccounted entropic loss upon ligand binding, which suggests avenues of approach for further MedusaScore improvement.     

An accurate expression for radial distribution function of the Lennard-Jones fluid

A simple and accurate expression for radial distribution function (RDF) of the Lennard-Jones fluid is presented. The expression explicitly states the RDF as a continuous function of reduced interparticle distance, temperature, and density. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The distance dependence of this expression is expressed by an equation which contains 11 adjustable parameters. These parameters are fitted to 353 RDF data, obtained by molecular dynamics calculations, and then expressed as functions of reduced distance, temperature and density. This expression, having a total of 65 constants, reproduces the RDF data with an average root-mean-squared deviation of 0.0152 for the range of state variables of 0.5  T^*  5.1 and 0.35  ρ^*  1.1 (T^*=kT/ε and ρ^* = ρσ³ are reduced temperature and density, respectively). The expression predicts the pressure and the internal energy of the Lennard-Jones fluid with an uncertainty that is comparable to that obtained directly from the molecular dynamics simulations.     

An accurate and graphable solution for the integral of the Arrhenius function

An approximation to the integral of the Arrhenius function is found by incorporating a nearly-constant integrating factor. The solutions, which can be determined graphically, are of an accuracy comparable to that of the rational approximations.     

An accurate analytical formula for the van der Waals potentials of homonuclear rare-gas dimers with one adjustable parameter

In the present article, the Tang–Toennies–Yiu (TTY) potential model is modified by introducing one adjustable parameter. Then, the van der Waals potentials of He₂, Ne₂, Ar₂, Kr₂, and Xe₂ are calculated by this model with the adjustable parameter being determined by the well determined well depth D_e of these systems. Based on the derived potentials, the vibrational energy spacings of these systems are also calculated. It is shown that the present derived potentials and vibrational energy spacings agree well with experiment and other theoretical calculations. Finally, the normalization constant A in the asymptotic wave function of rare-gas atoms is estimated. The present derived normalization constant A is very close to the one by calculating the ratio between the Hartree–Fock function and the asymptotic wave function. The results confirm that absorbing the first-order polarization energy into the exchange energy expression is a well approximation for the present systems.     

An analytical representation of the response of the NaI(T1) detector for the gamma-ray spectrum analysis

An analytical function for describing the response function of γ-rays from the NaI(Ti) detector was constructed with the purpose of establishing the method of automatic γ-ray spectrum analysis. The response was found to be divided into six portions; the function of each portion joins smoothly to the one representing the adjacent part. Empirical equations for the parameters specifying the response function were found as functions of the γ-ray energy in relation to the detector dimension. The obtained response function was fitted to the observed spectrum by the least squares method. The calculated spectrum agreed well with the observed one.     

An accurate and simple universal curve for the energy‐dependent electron inelastic mean free path

The values of inelastic mean free paths (IMFPs) calculated from optical data for the three material categories of elements, inorganic compounds and organic compounds are re‐assessed to provide a simple equation giving an estimate of the IMFP, knowing only the identities of the elements in an analysed layer and the atomic density of that layer. This simple equation is required for quantification of the thicknesses for layers of mixed elements in which the required parameters for use of the popular equation, TPP‐2M, are insufficiently known. It describes the published values, calculated from optical data for energies above 100 eV, to a similar root mean square (RMS) deviation as that for TPP‐2M in the three material categories. The RMS deviation for all three categories averages 8.4%, provided the inorganic data are ‘corrected’ for the published sum rule errors. If, in an analysed layer, only elements are identified and the atomic density is unknown, i.e. only the average Z value of the layer is known, a simpler relation is provided for the IMFP in monolayers with only one unknown parameter Z that exhibits an RMS deviation from the IMFPs calculated from optical data of 11.5%. Copyright © 2011 Crown copyright.     

A numerical basis for the accurate representation of the continuum spectrum of atomic Hamiltonians

We present a method for the accurate calculation of the complete spectrum of the Schrödinger equation in terms of B-splines polynomial basis. The method is capable to represent numerically the bound and continuum spectrum of complex atomic systems. The theoretical method is discussed, and an application to hydrogenic Hamiltonian is given.AMS subject classification: 65705, 34L40     

Super-fermion representation of quantum kinetic equations for the electron transport problem

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space. We transform the liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.     

Conditions for accurate description of the electron density of atoms and molecules

Based on the Kato's cusp condition of the electron density and our recent relations for local strongly decaying properties in an electronic system, necessary conditions for trial electron densities of atomic and molecular systems are derived. These conditions take the form of integral‐differential equations, and their validity is verified numerically. The relevance of these conditions to the Thomas–Fermi problem in the orbital‐less density functional approach is discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Rigorous integral screening for electron correlation methods

We derive rigorous multipole-based integral estimates (MBIE) in order to account for the distance dependence occurring in atomic-orbital (AO) formulations of electron correlation theory, where our focus is on AO-MP2 theory within a Laplace scheme. We find for the exact transformed integral products an extremely early onset of a linear-scaling behavior and a very small number of significant products. To preselect the significant integral products we adapt our MBIE method as rigorous upper bound. In this way it is possible to exploit the favorable scaling behavior observed and to reduce the scaling of estimated products asymptotically to linear, without sacrificing accuracy or reliability. By separating Coulomb- and exchange-type contractions only half-transformed integrals need to be computed. Furthermore, our scheme of rigorously preselecting transformed integral products via MBIE seems to offer particularly interesting perspectives for a direct formation of half- or fully transformed integrals by using multipole expansions and auxiliary basis sets.     

Radial‐template approach for accurate density representation in computational quantum theory

A method for improved representation of electronic charge and spin densities for molecular and solid state systems is presented, based upon extensions of least squares fits to quantum mechanical “true” densities using basis functions of limited support. Attention is given to optimization of radial degrees of fit freedom, and the design of fit functions permitting rapid analytic manipulation and calculation of properties, such as Coulomb potentials. The method is demonstrated for covalent CO and for a large metal‐organic crystalline structure. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Silicate particles engulfed in human alveolar macrophages: An analytical electron microscopy study

The chemical composition and crystalline structure of silicate particles engulfed in human alveolar macrophages were investigated by transmission analytical electron microscopy. A crystalline ZrSiO₄ and an amorphous Si₂AlO₄ particle were identified. Small crystalline Fe microparticles (2–4 nm), which are likely ferritin molecules, were found concentrated mainly at the amorphous particle-tissue interface.     

Nanostructure investigations with the analytical transmission electron microscope

Concerning the conventional TEM-imaging as well as the analytical procedures the capabilities are pointed out: electron diffraction, energy dispersive X-ray spectroscopy (EDXS) and electron energy loss spectroscopy (EELS). The possibilities of investigation of both nanocrystalline materials and multilayers are discussed, accompanied by examples of current investigations: At alloys, produced by intense milling, at single nanocrystals the imaging by diffraction contrast was successful, the analysis has failed because of the sample thickness. By means of energy spectroscopic imaging multilayers from Fe-SiB/NbCu and Fe/Cr as well as Al₂O₃/TiN have been characterized. Received: 15 July 1997 / Revised: 16 February 1998 / Accepted: 21 February 1998     

Sample screening systems in analytical chemistry

The state of the art and the potential of sample screening systems (SSS) for the expeditious, reliable selection of samples to meet the requirements of customers and legislation is presented and discussed. The underlying procedures use simple equipment and operations and provide a yes/no binary response that occasionally requires confirmation. After a brief discussion of the distinction between ‘screening' and ‘analysis' and the principal features of analytical screening systems, the main aims and features of SSS are presented. Several classifications of these allow one to offer a general view of the topic. Representative examples are classified according to the complexity of the sample pretreatment required, and are used to demonstrate the impact SSS may have on analytical chemistry in the next century.     

An accurate analytic potential function for ground-state N2 from a direct-potential-fit analysis of spectroscopic data

Two types of combined-isotopologue analysis have been performed on an extensive spectroscopic data set for ground-state N2 involving levels up to v=19, which is bound by half the well depth. Both a conventional Dunham-type analysis and a direct-potential-fit (DPF) analysis represent the data within (on average) the estimated experimental uncertainties. However, the Dunham-type parameters do not yield realistic predictions outside the range of the data used in the analysis, while the potential function obtained from the DPF treatment yields quantum mechanical accuracy over the data region and realistic predictions of the energies and properties of unobserved higher vibrational levels. Our DPF analysis also introduces a compact new analytic potential function form which incorporates the two leading inverse-power terms in the long-range potential.     

An open library of relativistic core electron density function for the QTAIM analysis with pseudopotentials

Based on two‐component relativistic atomic calculations, a free electron density function (EDF) library has been developed for nearly all the known ECPs of the elements Li (Z = 3) up to Ubn (Z = 120), which can be interfaced into modern quantum chemistry programs to save the .wfx wavefunction file. The applicability of this EDF library is demonstrated by the analyses of the quantum theory of atoms in molecules (QTAIM) and other real space functions on HeCuF, , OgF₄, and TlCl₃(DMSO)₂. When a large‐core ECP is used, it shows that the corrections by EDF may significantly improve the properties of some density‐derived real space functions, but they are invalid for the wavefunction‐depending real space functions. To classify different chemical bonds and especially some nonclassical interactions, a list of universal criteria has also been proposed. © 2018 Wiley Periodicals, Inc.     

Dansyl and dabsyl analytical constructs as tools for the accurate estimation of compounds in solid-phase synthesis

The presence of dansyl or dabsyl chromogenic moieties in a solid-phase analytical construct, an assembly of linkers/spacers/sensitizers for improving analytical characterization, allows the accurate estimation of products from solid-phase synthesis by UV detection during liquid chromatography-mass spectrometry analysis in the cleavage solution. The spectroscopic properties of dansylated molecules have been evaluated to verify the "compound-independent UV absorption" necessary for using the chromophore in the accurate estimation. First, measurements on commercial dansylated compounds were made, then a series of construct-like molecules were prepared by solution-phase synthetic procedures and their UV properties were determined. Compound calibration curves were determined, and UV absorption was shown to be both proportional to the compound concentration and compound-independent. An example of a dansyl construct derivative was then prepared on a polymeric matrix, and an accurate estimation using the calibration curves was carried out in the cleavage solution. Good agreement was found between the calculated amount of released compound using the UV calibration curves and the calculated amount using both (1)H NMR and LC/chemiluminescent nitrogen detection quantitative techniques. Preliminary studies using the dabsyl moiety as an improved chromophore with higher wavelength and extinction coefficient are also reported.