Lattice Of Point Charges Research Articles

Analysis of electrostatic stability and ordering in quaternary perovskite solid solutions

There are three distinct classes of perovskite structured metal oxides, defined by the charge states of the cations: ${A}^{\text{I}}{B}^{\text{V}}{\mathrm{O}}_{3},{A}^{\text{II}}{B}^{\text{IV}}{\mathrm{O}}_{3}$, and ${A}^{\text{III}}{B}^{\text{III}}{\mathrm{O}}_{3}$. We investigated the stability of cubic quaternary solid solutions $AB{\mathrm{O}}_{3}\text{\ensuremath{-}}{A}^{\ensuremath{'}}{B}^{\ensuremath{'}}{\mathrm{O}}_{3}$ using a model of point-charge lattices. The mixing enthalpies were calculated and compared for the three possible types of combinations of the compounds, both for the random alloys and the ground-state-ordered configurations. The mixing enthalpy of the (I,V)${\mathrm{O}}_{3}$-(III,III)${\mathrm{O}}_{3}$ alloy is always larger than the other alloys. We found that, different from homovalent alloys, for these heterovalent alloys a lattice constant mismatch between the constituent compounds could contribute to stabilize the alloy. At low temperatures, the alloys present a tendency to spontaneous ordering, forming superlattices consisting of alternated layers of ${AB\text{O}}_{3}$ and ${A}^{\ensuremath{'}}{B}^{\ensuremath{'}}{\mathrm{O}}_{3}$ along the $[110]$ direction.

Discrete Charge Effects on the Potential Distribution in and around Soft Particles

The potential distribution in and around a soft particle, i.e., a porous polyelectrolyte particle, in an electrolyte solution is usually derived via a continuum model in which fixed charges inside the soft particle are distributed with a continuous charge density. In this paper, on the basis of a previous result for a plate like soft particle consisting of a cubic lattice of fixed point charges, we derive expressions for the electric potential distribution for the case of a soft sphere and a soft cylinder. These expressions are given in terms of a sum of the screened Coulomb potentials produced by the point charges within the soft particle. We show how the discrete charge model approaches the continuous charge model as the lattice spacing becomes very small.

Electroosmotic flow on an arbitrarily charged planar surface

A general expression for the electroosmotic flow on an arbitrarily (i.e., both uniformly and nonuniformly) charged planar surface under an applied static electric field is derived. We treat the case in which the applied field is weak so that the flow is slow enough to obey the Stokes approximation at low Reynolds numbers and the electric potential is low enough to obey the linearized Poisson-Boltzmann equation. As examples, the flow around a sinusoidally charged planar surface and that around a charged planar surface carrying a square lattice of point charges are considered. The latter is related to the discrete-charge effect upon the electroosmotic flow.

Special quasirandom structure in heterovalent ionic systems

The use of a special quasirandom structure (SQS) is a rational and efficient way to approximate random alloys. A wide variety of physical properties of metallic and semiconductor random alloys have been successfully estimated by a combination of an SQS and density functional theory calculation. Here, we investigate the application of an SQS to the ionic multicomponent systems with configurations of heterovalent ions, including point-charge lattices, ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{ZnSnP}}_{2}$. It is found that the physical properties do not converge with the supercell size of the SQS. This is ascribed to the fact that the correlation functions of long-range clusters larger than the period of the supercell are not optimized in the SQS. However, we demonstrate that the physical properties of the perfectly disordered structure can be estimated by linear extrapolation using the inverse of the supercell size.

Ewald-type formulas for Gaussian-basis studies of one-dimensionally periodic systems

The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation.

Linear scaling solution of the all-electron Coulomb problem in solids

We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which the Coulomb potential and energy of a continuous electronic density and singular nuclear density are required. Linear scaling is achieved by introducing smooth, strictly local neutralizing densities to render nuclear interactions strictly local, and solving the remaining neutral Poisson problem for the electrons in real space. While the formulation includes singular nuclear potentials without smearing approximations, the required Poisson solution is in Sobolev space $H^1$, as required for convergence in the energy norm. We employ enriched finite elements, with enrichments from isolated atom solutions, for an efficient solution of the resulting Poisson problem in the interacting solid. We demonstrate the accuracy and convergence of the approach by direct comparison to standard Ewald sums for a lattice of point charges, and demonstrate the accuracy in all-electron quantum mechanical calculations with an application to crystalline diamond.

Simulation of Water Adsorption on Kaolinite under Atmospheric Conditions

Grand canonical Monte Carlo calculations are employed to investigate water adsorption on kaolinite at 298 and 235 K. Both basal planes (the Al and Si surfaces) as well as two edge-like surfaces are considered. The general force field CLAYFF is used together with the SPC/E and TIP5P-E models for water. Problems that occur in single slab simulations due to arbitrary truncation of the point charge lattice are identified, and a working remedy is discussed. The edges and the Al surface adsorb water at subsaturation in the atmospherically relevant pressure range. The Si surface remains dry up to saturation. Both edges have a very strong affinity for water and adsorb continuously up to monolayer coverage. The Al surface has a weaker affinity for water but forms a subsaturation monolayer. On the Al surface, the monolayer is formed in an essentially sharp transition, and strong hysteresis is observed upon desorption. This indicates collective behavior among the water molecules which is not present for the edges. Binding energies of singly adsorbed water molecules at 10 K were determined to understand the differences in water uptake by the four kaolinite surfaces. Binding energies (SPC/E) of -21.6, -46.4, -73.5, and -94.1 kJ/mol, were determined for the Si surface, Al surface, unprotonated edge, and protonated edge, respectively. The water monolayer on the Al surface, particularly at 235 K, exhibits hexagonal patterns. However, the associated lattice parameters are not compatible with ice Ih. Water density and hydrogen bonding in the monolayers at both 298 and 235 K were also determined to better understand the structure of the adsorbed water.

Vanishing gap in LiF for electronic excitations by slow antiprotons

We study the influence of antiprotons and protons traveling through LiF on the band structure of the insulator using the embedded-cluster method. The crystal is represented by ${\text{F}}_{m}^{\ensuremath{-}}{\text{Li}}_{n}^{+}$ clusters with up to 19 fluorine ions embedded in a lattice of point charges representing the remainder of the crystal. The minimum excitation energy of LiF perturbed by the (anti)proton impurity is calculated employing the multiconfiguration self-consistent field method. The repulsive potential of the antiproton causes a dramatic local perturbation of the LiF band structure. We find a strong suppression of the excitation energy by more than an order of magnitude compared to that of the unperturbed crystal. The present results provide a simple explanation of recent stopping-power experiments for antiprotons in LiF which, surprisingly, found a ``metal-like'' behavior of the wide-band-gap insulator LiF. Our results also agree with recent experimental data indicating a deviation from metallic behavior of the stopping power of proton projectiles.

Simulating CH4 physisorption on ionic crystals

We use quantum chemical techniques to evaluate the electrostatic and polarization components of the interaction between a rigid CH4 molecule and a lattice of point charges representing the MgO(100) surface. We find that CH4 positioned above Mg adopts an edge-down configuration in which two H atoms are oriented downward towards the MgO(100) surface and point at O ions in the surface layer. The CH4–MgO(100) electrostatic interaction is substantially less favorable (but is still attractive) for the face-down configuration in which three H atoms point downward. Neither configuration is energetically favorable for CH4 molecules positioned above O ions. We show that for edge-down CH4 molecules above Mg, the electrostatic component of the CH4-substrate interaction varies considerably as the CH4 molecule rotates about the surface normal; the polarization component of the interaction, by contrast, is nearly constant during this rotation. We show that a point-charge model for the CH4 charge distribution, in which the C and H atoms carry effective partial charges, predicts that the CH4-surface electrostatic interaction should be more favorable for face-down CH4 molecules than for edge-down CH4 molecules, in disagreement with the quantum chemical results. We show that this is because the point-charge model poorly represents the high-order electric multipoles of CH4.

Distribution of electric and magnetic hyperfine fields in Fe-rich gallo-germanates

The crystal field disorder in some tetragonal and trigonal Ca-gallo-germanates, i.e., A2Fe2Z07 and A2LnFe3Ge3014 with A=Ba or Sr, Ln=La or Nd and Z=Ge or Si, has been studied by 57Fe Mossbauer spectroscopy. The observed distribution of the hyperfine fields is analysed from a theoretical model based on the additive perturbation approximation of crystal fields, a rigid lattice of ionic point charges and the random substitution of Fe3+/Z4+ and A2+/Ln3+.

Point-charge calculation of quadrupolar parameters for bridging oxygen sites in vitreous silica: Structural implications

The quadrupolar coupling constant Cq and the asymmetry parameter $\ensuremath{\eta}$ for the bridging oxygen sites in vitreous silica structures derived via classical molecular dynamics simulation have been calculated using the point-charge lattice summation method. The results of these calculations indicate that while Cq is a function of both the Si-O-Si angle and the associated Si-O distances, $\ensuremath{\eta}$ depends only on the Si-O-Si angle. The analytical forms of these functional dependences are found to be similar to those reported in previous studies based on ab initio calculations on small clusters. However, the magnitude of Cq is found to decrease with increasing Si-O distance in contrast with a reverse trend obtained in previous ab initio calculations on small clusters. The present results, when combined with the previously reported $^{17}\mathrm{O}$ nuclear magnetic resonance spectroscopic results for bridging oxygen sites in vitreous silica, imply a strong negative correlation between Si-O bond lengths and Si-O-Si bond angles in the glass structure. Such a negative correlation is consistent with the anomalous density variation in silica as well as with energetic considerations.

Electronic structure of lithium tetraborate Li2B4O7 crystals. Cluster calculations and x-ray photoelectron spectroscopy

The results of an investigation of the electronic structure of lithium tetraborate crystals using experimental (x-ray photoelectron spectroscopy) and theoretical (quantum-chemical modeling) methods are reported. The experimental spectrum of the valence-band states of the crystal lies 2–15 eV below the Fermi level and is due primarily to boron-oxygen groups (B4O9). The quantum-chemical calculations were performed self-consistently, using the standard variant of the scattered-wave method in the model of a cluster embedded in a lattice of point charges. The data obtained on the partial contribution of the model densities to the one-electron spectrum of the [B4O9]6 cluster make it possible to interpret the fine structure of the experimental spectrum of the valence-band states.

A fast and simple method for calculating electrostatic potentials

A fast and simple method for calculating the electrostatic potential of an electrically neutral lattice of point charges has been developed. It is applicable to orthogonal and non-orthogonal unit cells with the rate of convergence independent of the degree of non-orthogonality. Results from the method has been compared to values obtained from the Ewald method with good agreement obtained for a number of structures including ZnS, CsCl, NaCl, CaF 2, Rutile and a general triclinic lattice.

Subpicosecond vibronic dynamics in KBrFcenters

Based on a symmetry analysis of recent results of femtosecond pump-probe optical-absorption experiments on KBr $F$ centers, we present a twofold theoretical analysis. The first part is concerned with a density-matrix calculation of the experimentally observed beating pattern of two modes of ${A}_{1g}$ symmetry in the sample transmission. This allows us to assign the observed frequencies to the breathing modes of the surrounding octahedron of cations in the electronic ground and excited state. The stiffening of the ${A}_{1g}$ mode in the unrelaxed excited state is consistent with simple arguments based on a lattice of point charges. In the second part, the observed ultrafast loss of initial orientation of the excited $p$ state is analyzed using a real-time integration of the wave function in the Hilbert space spanned by the vibrations of lower symmetries ${(E}_{1g}$ and ${T}_{2g})$ and the three degenerate $p$ states. The resulting reorientation of the $p$ state can be regarded as the transient analogue of the Jahn-Teller effect, and it turns out that the total wave function loses its initial orientation on a very fast time scale. This phenomenon is interpreted as a loss of coherence, so that the breathing mode oscillation becomes observable only if the pulse length is of the order of the so-defined coherence time of ${\ensuremath{\tau}}_{c}=12$ fs.

The polarizabilities of halide ions in crystals

The polarizabilities of the , and ions in their solid lithium and sodium salts in the four-coordinated B3 and eight-coordinated B2 phases are predicted from ab initio electronic structure computations. These results plus those for the experimentally observed B1 structures yield insights into the mechanisms by which the in-crystal environment modifies halide polarizabilities. The anion polarizability in each B2 phase having the cation - anion separation of the B1 structure is reduced compared with that in the B1 phase by the overlap with eight cation neighbours rather than six, these polarizabilities being essentially identical in the corresponding point charge lattices. The greater equilibrium cation - anion separation in the B2 compared with the B1 phase causes each halide polarizability at its to be greater in the B2 phase than in the B1 material. These B2 phase polarizabilities can be accurately predicted from the same function, which describes the dependence of the polarizability on for different salts having the B1 structure. This supplements previous evidence from the caesium halides that these anion polarizabilities are determined solely by , being insensitive to the precise disposition of the cation neighbours. The halide polarizabilities in the B3 phase are larger than those predicted by the above function describing the dependence of polarizability on . This phase thus differs from B1 or B2 materials, fluorite structured alkaline earth fluorides or in that the halide polarizabilities in the four latter are all essentially determined by through the same function. The halide polarizabilities in the B3 phase differ by exhibiting a specific structural dependence in addition to their variation. A new function describes the dependence of halide polarizabilities in the B3 phase.

The coupling between ripplons and the motion of ion pools trapped beneath the surface of4 He

It is well known that the motion of positive or negative ions close to the surface of superfluid4 He can excite ripplons in the helium surface. We consider a simple toy model in which a lattice of point charges couples to the4 He surface via electrostatic forces. We calculate the coupled mode spectrum of this system and present detailed information on the mode splitting which occurs when the ripplons and the normal modes of the ion pool are degenerate. Such energy gaps should, we believe, be experimentally observable.

Surface stress of point charge lattices

An expression for the Coulomb component of the stress tensor of a point charge lattice cast in the Parry-Ewald formulation is given. Also, an expansion is presented of the surface potential for charges separated by a small out-of-plane distance compared with the periodicity length parallel to the surface. This latter formula is suitable for incorporation in molecular dynamics or Monte Carlo computer simulations of thin ionic films, such as Langmuir or Langmuir-Blodgett films.

Surface stress of point charge lattices

An expression for the Coulomb component of the stress tensor of a point charge lattice cast in the Parry-Ewald formulation is given. Also, an expansion is presented of the surface potential for charges separated by a small out-of-plane distance compared with the periodicity length parallel to the surface. This latter formula is suitable for incorporation in molecular dynamics or Monte Carlo computer simulations of thin ionic films, such as Langmuir or Langmuir-Blodgett films.

Ab initio calculations for the adsorption of small molecules on metal oxide surfaces. I. Cluster calculations for carbon monoxide CO on nickel oxide NiO(100)

Quantum chemical ab initio calculations for the adsorption of CO on the NiO(100) surface have been performed at different levels of accuracy: self-consistent field (SCF), complete active space self-consistent field, and coupled electron pair approximation. Basis sets of double zeta and triple zeta + polarization (TZP) quality have been used. The NiO(100) surface is represented by a cluster containing one Ni2+ ion and the five adjacent O2− ions. The charge neutrality of the cluster and the saturation of the dangling bonds is achieved by adding eight protons, which gives the total composition Ni(H2O)3(OH)2. Alternatively, the Ni2+(O2−)5 unit is embedded in a lattice of point charges which correctly represent the half-infinite ionic crystal. In the most favorable configuration, CO is adsorbed linearly in the on-top position on the Ni2+ ion, with the C atom pointing toward the surface. The binding energies at the SCF level are rather small, only 0.08 eV and 0.03 eV for CO and OC bound to the cluster (TZP basis set, counterpoise correction for the basis set superposition error included). For the two configurations the equilibrium Ni–C and Ni–O distances are 5.40 and 5.50 a0, respectively. Electron correlation does not change these values markedly. Estimating the errors in our calculation we arrive at binding energies of 0.10±0.05 and 0.05±0.05 eV, respectively, for CO and OC on NiO(100). This is in agreement with the experimental estimates. The bonding is attributed predominantly to electrostatic and inductive forces. No genuine ‘‘chemical’’ bond (overlap, charge transfer) exists between CO and the NiO(100) surface, i.e., CO is only physisorbed to this ionic surface. The harmonic vibration frequencies for the Ni–C stretching and the Ni–C–O bending vibrations are estimated to 52 and 139 cm−1, respectively.

Incorporation of a cluster into a lattice of point charges in the SCF-CI formalism (ideal crystal)

Incorporation of a cluster into a lattice of point charges in the SCF-CI formalism (ideal crystal)