The embedded atom model of liquid cesium

The embedded atom potential was calculated for cesium over the temperature range 323–1923 K at pressures up to 9.8 GPa from the diffraction data on the structure of the metal close to the temperature of fusion (T _f). The parameters of the embedded atom potential were adjusted using the data on the thermodynamic properties and structure of liquid cesium. The embedded atom potential well predicts the structural and thermodynamic characteristics of the liquid metal as the temperature increases along the liquid-vapor equilibrium line and under strong compression. The calculated potential energy and structure of liquid cesium closely agree with the experimental data at temperatures up to 1373 K. The calculated bulk compression modulus is close to its experimental values at all temperatures except 323 K. The self-diffusion coefficients increase as the temperature grows by a power law with an exponent close to 2 and satisfy the Stokes-Einstein equation. Deviations from experimental data at temperatures above 1400 K are explained by the metal-nonmetal transition that occurs as the density decreases.     

The embedded atom model for liquid metals: Liquid gallium and bismuth

A method for calculating embedded atom potentials in liquid metals is suggested. The method uses diffraction structural data, density, bulk compression modulus, and thermal expansion coefficient close to the melting point. The method was applied to liquid gallium and bismuth at temperatures from their melting to critical points. The critical temperatures of these metals were estimated at 4940 and 4225 K. The other critical parameters were also determined. The self-diffusion coefficients were found to increase almost linearly as the temperature grew. The model allows changes in the structural characteristics of the metals when the temperature increases by several hundred kelvin units to be correctly described.     

The use of the embedded atom model for liquid metals: Liquid potassium

The method for calculations the embedded atom potential for liquid metals based on the diffraction data on the structure close to the melting temperature was applied to potassium. The embedded atom potential parameters were adjusted using the data on the structure of potassium at 343, 473, and 723 K and the thermodynamic properties of potassium at temperatures up to 37240 K. The use of the molecular dynamics method and the embedded atom potential gave close agreement with the experimental data on the structure, density, and potential energy of liquid metal along the p ? 0 isobar at temperatures up to 2200 K and along the shock adiabat up to a pressure of ～85 GPa and 37240 K. The calculated bulk compression modulus at 343 K was close to its actual value, and the self-diffusion coefficients increased under isobaric heating conditions following a power law with an exponent of 1.6478. The melting temperature of body-centered potassium with the embedded atom potential was (319 ± 1) K, which was close to the actual melting temperature. The potential obtained incorrectly described crystalline potassium.     

Account for electron contributions in embedded atom model for iron and nickel in molecular dynamics simulation

Potentials of embedded atom model (EAM) are calculated in analytical form for liquid iron and nickel. A series of models of these metals is created up to the temperature of 4000–4200 K. It is shown that these potentials enable us to obtain good agreement between the density of models and real metals; upon heating, however, the energy of the models is reduced relative to the real energies. It is established that the divergence of energies at ～4000 K is 32 kJ/mol for iron and 33 kJ/mol for nickel. It is shown that most of this divergence is determined by the contribution from the heat energy of electrons; after subtracting this contribution, a divergence of energies of 8.1 kJ/mol for iron and 14.3 kJ/mol for nickel remains. It is concluded that this divergence could be due partly to the insufficient adequacy of EAM potential in describing broad temperature ranges.     

DFT study on Raman frequencies of molten lead (II) chloride

The study concerns ab inito calculations of the essential Raman frequencies of molten lead (II) chloride near the melting point. Modelling of topologically disordered lead (II) chloride was carried out within the framework of the density functional theory using the Perdew–Burke-Ernzerhof (PBE) functional and optimised basis sets. Calculations were performed for a cluster containing 24 formula units. The optimum geometry of the cluster was determined and the local structure parameters were found. Nano-size effect leads to the picture of damped oscillations on radial atomic density distributions typical of molten salts. Distorted octahedra of PbCl₆ were detected inside the cluster. Ab initio calculation of the Raman spectrum of the octahedral complexes inside the cluster structure was implemented. It was shown that the spectrum has a peak at 192 cm^?1, which agrees well with the experimental Raman spectra of lead (II) chloride melt near the melting point.     

Improved embedded molecular cluster model

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one-electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On fitting a gold embedded atom method potential using the force matching method

We fit a new gold embedded atom method (EAM) potential using an improved force matching methodology which included fitting to high-temperature solid lattice constants and liquid densities. The new potential shows a good overall improvement in agreement to the experimental lattice constants, elastic constants, stacking fault energy, radial distribution function, and fcc/hcp/bcc lattice energy differences over previous potentials by Foiles, Baskes, and Daw (FBD) [Phys. Rev. B 33, 7983 (1986)] Johnson [Phys. Rev. B 37, 3924 (1988)], and the glue model potential by Ercolessi et al. [Philos. Mag. A 50, 213 (1988)]. Surface energy was improved slightly as compared to potentials by FBD and Johnson but as a result vacancy formation energy is slightly inferior as compared to the same potentials. The results obtained here for gold suggest for other metal species that further overall improvements in potentials may still be possible within the EAM framework with an improved fitting methodology. On the other hand, we also explore the limitations of the EAM framework by attempting a brute force fit to all properties exactly which was found to be unsuccessful. The main conflict in such a brute force fit was between the surface energy and the liquid lattice constant where both could not be fitted identically. By intentionally using a very large number of spline sections for the pair potential, electron-density function, and embedding energy function, we eliminated a lack of functional freedom as a possible cause of this conflict and hence can conclude that it must result from a fundamental limitation in the EAM framework.     

An embedded atom method study of the equilibrium shapes of small platinum and palladium clusters

The embedded atom method (EAM) was used to determine the equilibrium shapes of small platinum and palladium clusters (N=5–60 atoms). The stability of various polyhedral symmetries was performed at 0K. A search for the presence of any other lower energy structures was also carried out. Pt clusters reconstructed to lower energy clusters even at the magic numbers. Pd also reconstructed to lower energy structures except at the magic number sizes where the icosahedron was found to be the most stable.     

The experimental library multipolar atom model refinement of l‐aspartic acid

The crystal structure of l ‐aspartic acid, C₄H₇NO₄, has been determined using two types of refinement, viz. the standard independent atom model (IAM) and the experimental library multipolar atom model (ELMAM). The ELMAM refinement shows a good improvement of the statistical indices compared with the IAM model, notably in terms of thermal displacement parameters and bond distances involving H atoms.     

The compressibility of molten salts

Values of the adiabatic and isothermal compressibility, κ_S and κ_T, of some 80 molten salts at the corresponding temperature of T = 1.1T_m (T_m is the melting point) are obtained from literature data either directly or re-calculated here. For some of the series of salts: alkali metal halides and nitrates, divalent metal halides, and alkali metal sulfates and carbonates the κ_T values are inversely proportional to the corresponding cohesive energy densities ced (internal energies per unit volume, separately for each class of compounds). The ced values for 1:2 and 2:1 salts not previously evaluated are presented here too.     

A scaled united atom model for diatomic hydrides

An eigenfunction for a diatomic hydride is approximated by a scaled eigenfunction (or linear combination of scaled eigenfunctions) for the corresponding united atom or separated ion (e.g., LiH, Be and Li^–, respectively). All atomic contributions to the resulting energy expressions are obtained exactly from experiment. The sum of one-electron two-center coulomb interactions between the scaled united atom or separated ion charge density and proton are approximated by integrals over orthogonalized Slater atomic orbitals. Configuration interaction is invoked in three cases. Force constants, equilibrium internuclear distances and electronic excitation energies are computed and compared with available experimental data.

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Zusammenfassung Eigenfunktionen für zweiatomige Hydride werden durch Eigenfunktionen mit Skalenfaktor (oder Linearkombinationen von diesen) des entsprechenden vereinigten Atoms oder getrennten Ions (z. B. LiH, Be bzw. Li^–) approximiert. Alle atomaren BeitrÄge zu den resultierenden Energieausdrücken erhÄlt man exakt vom Experiment. Die Summe der Wechselwirkungen zwischen Elektronen (beschrieben durch Funktionen des vereinigten Atoms bzw. getrennten Ions) und Proton wird durch Integrale über orthogonale Slaterfunktionen approximiert. Konfigurationswechselwirkung wird in drei FÄllen zugezogen. Kraftkonstanten, GleichgewichtsabstÄnde der Kerne und Elektronenanregungsenergien werden berechnet und mit den verfügbaren experimentellen Daten verglichen.

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Résumé La fonction propre d'un hydrure diatomique est approximée par une fonction scalée (ou une combinaison lináire de telles fontcions) pour l'atome unifié ou l'ion séparé (p. ex.: LiH, Be et Li^–, respectivement). Toutes les contributions «atomiques» aux eneries résultantes s'obtiennent exactement de l'expérience. Les interaction de Coulomb monoélectroniques dicentriques entre l'atome unifié scalé ou l'ion séparé et le proton sont approximées par d'intégrales sur des orbitales orthogonalisées de Slater. L'interaction de configurations est appelée en trois cas. On calcule les constantes de force, les distances internucléaires d'équilibre et les compare aux données expérimentales.

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This work was supported in part by a grant from the National Science Foundation.     

Path integral Monte Carlo simulation of the absorption spectra of an Al atom embedded in helium

We use a multilevel path integral Monte-Carlo (PIMC) method to simulate the arrangement of He atoms around a single Al atom doped in a He cluster. High-level ab initio Al-He pair potentials and a Balling and Wright pairwise Hamiltonian model are used to describe the full potential and the electronic asymmetry arising from the open-shell character of the Al atom in its ground and excited electronic states. Our calculations show that the doping of the Al 3p electron strongly influences the He packing. The results of the PIMC simulation are used to predict the electronic excitation spectrum of an Al atom embedded in He clusters. With inclusion of tail corrections for the ground and excited states potentials, the calculated 3d<--3p spectrum agrees reasonably well with the experimental spectrum. The blueshift of the calculated spectrum associated with the 4s<--3p transition of solvated Al is about 25 nm (2000 cm-1) larger than seen in experiments on Al embedded in bulk liquid He. We predict that the spectrum associated with the 4p<--3p transition will be blueshifted by approximately 7000 cm-1 (nearly 1 eV).     

Stereochemistry of lead(II) complexes containing sulfur and selenium donor atom ligands

The stereochemistry of lead(II) complexes with S- and Se-donor atom ligands, including mixed ligand complexes is reviewed with respect to the geometry of the first coordination sphere of the Pb(II) atom in these compounds and rationalized in terms of the valence shell electron-pair repulsion (VSEPR) model. The most comprehensively structurally characterized classes of lead(II) thio and seleno complexes are discussed, including monothio-, dithio(seleno)-, trithio- and tetrathio-complexes, as well as Pb(II) dialkyldithio(seleno)carbamates, alkylxanthates and dialkyl(aryl) phosphorodithio(seleno)lates. Data about the polyhedral shape of the primary coordination sphere, coordination number (CN), bond lengths (primary and secondary) and bond angles of the Pb(II) atom in the compounds under investigation are systematized in comprehensive tables. The particularities of the stereochemistry of Pb(II) complexes with S(Se)-donor atom ligands are comparatively discussed with the stereochemistry of lead(II) complexes with oxygen donor ligands.     

Semiclassic approach within the He atom sphere model

The helium atom doubly excited‐states energy levels are calculated for the ¹S‐state. The He atom is considered as the three‐atomic molecule. The electrons are supposed to move on the sphere of the equal radius. The rotation is described by the Euler angles, which can be divided in a standard way. Then, the hyperspherical coordinates are introduced. The adiabatic approach allows us to solve the equation on interelectron angle θ. We used the contour integral method for this equation. The equation on the hyperradius R was solved according to the semiclassic approach. The obtained results are in good agreement with those of some other works. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Electrical conductance,density, and viscosity of the molten system lead(II) dodecanoate/lead(II) oxide

Data are presented for densities, electrical conductances, and viscosities of the molten system lead(II) dodecanoate/lead(II) oxide concentrations up to 0.22 mole fraction of the oxide. Values of ?₀ obtained from extrapolation of graphs of density againts temperature are seen to decrease on adding small quantities of PbO, but to increase on adding further PbO. Results from thermal analysis suggest that this may be due to a change in structure of the liquid phase from small. spherical to long, cylindrical micelles. Over the concentration range studied, molar volumes are linear functions of concentration at any particular temperature. The molar volumes of the system lead(II) carboxylate/lead(II) oxide for the even chain acids C₁₀ to C₁₈ are linear functions of chain length. Arrhenius plots for the electrical conductance of the mixtures show curvature, as in other lead(II) dodecanoate systems. The activation energies for conductance in the low temperature region show a steady decrease with increasing PbO concentration and it is proposed that this arises from increased mobility of the charge carrier. The specific conductance at any temperature decreases with increasing mole fraction of oxide, indicating the oxide to be essentially undissociated in the melt. The activation energy for viscosity shows a dramatic increase on adding small amounts of PbO. This is suggested to arise from a change in the structure of the melt. Studies of the viscosities of the system lead(II) carboxylate/lead oxide as a function of chain length for the even chain acids C₁₀ to C₁₈ suggest a slight decrease in the size of the unit of viscous flow when oxide is present.     

A polarizable ion model for the structure of molten CuI

The results are reported of the molecular dynamics simulations of the coherent static structure factor of molten CuI at 938 K using a polarizable ion model. This model is based on a rigid ion potential to which the many body interactions due to the anions induced polarization are added. The calculated structure factor reproduces the clear sharp prepeak observed in neutron diffraction data. The corresponding partial structure factors and the related radial distribution functions calculated by molecular dynamics are compared with those found in the literature derived from a combination of neutron and x-ray diffraction data with the aid of the reverse Monte Carlo simulation technique, as well as those calculated by ab initio MD simulations.     

A polarizable ion model for the structure of molten AgI

The results are reported of the molecular dynamics simulations of the coherent static structure factor of molten AgI at 923 K using a polarizable ion model. This model is based on a rigid ion potential, to which the many body interactions due to the anions induced polarization are added. The calculated structure factor is in better agreement with recent neutron diffraction data than that obtained by using simple rigid ion pair potentials. The Voronoi-Delaunay method has been applied to study the relationship between voids in the spatial distribution of cations and the prepeak of the structure factor.     

Anisotropy analysis of the surface stress in Ag stepped surfaces with the modified embedded atom method

The surface stresses in Ag stepped surfaces (910), (710), (510), (410), (310), (210), (320), (430) and (540) have been calculated by using the modified embedded atom method (MEAM). The surface stresses in the surface plane τ_xx (along the step edge) and τ_yy (normal to the step edge) have similar orders of magnitude as the surface energy. For surfaces having the (100) and (110) terraces, the change of τ_xx and τ_yy is very small and the variation of the surface energy is smooth. The stress τ_zz (normal to the surface plane) is always tensile in the unrelaxed state. The linear variation of the change in surface energy per unit change in elastic strain , and (i.e. τ_xx ? γ, τ_yy ? γ and τ_zz) with the angle α between the (hk0) and (100) planes has a turning point corresponding to the (210) surface. The anisotropic ratio in the stepped surface having the (110) terrace is larger than that having the (100) terrace, and the wider the (110) terrace or the narrower the (100) terrace, the larger the ratio τ_yy/τ_xx. Copyright © 2006 John Wiley & Sons, Ltd.