Nonempirical Model Research Articles

A theoretical study of internal rearrangements and open channels for fission and mass exchanges in Xe n + clusters

In a previous work the equilibrium geometrical and electronic structures of Xe n + clusters had been established using a non-empirical model hamiltonian. The same model is used to determine the energetic barriers between the nearly degenerate isomers; the movement of the neutral atoms around the Xe 3 + or Xe 4 + ionized linear cores are quite easy (ΔE⋍0.9 kcal/mole), the changes from a Xe 3 + to a Xe 4 + core are more difficult (ΔE⋍2.0 kcal/mole). The energetically possible fissions from a vertical photoionization\(Xe_n \xrightarrow{{h v}}Xe_n^{v + } \to Xe_p^ + + Xe_{n - p} \) forn≦19,p=1–9 and 12–14 and mass exchanges Xe p + +Xe q →Xe p+m + +Xeq−m (m=1,2,3) from relaxed Xe p + clusters are given forp+m≦9 and 12–14 andq≦19. Surprisingly the reverse reactions are shown to occur for some values ofp andq. Numerous processes lead to Xe 13 + , which is especially stable.

First principles calculations of lattice dynamics and ionicity in La 2CuO 4 and YBa 2Cu 3O 7

Studies of the lattice dynamics of La 2CuO 4 and YBa 2Cu 3O 7 using both a non-empirical ionic model and the linearized augmented plane wave (LAPW) method show that ionic contributions are important in the high temperature oxide superconductors. Preliminary frozen phonon calculations with the LAPW method show large enhancements of electron phonon matrix elements over the rigid muffin tin approximations. Calculated phonon frequencies are in good agreement with Raman and infrared data.

Applications of ionic models to the high-temperature superconductor La 2CuO 4

The electronic structures of superconducting oxides such as La 2CuO 4 include significant ionic contributions. Application of ionic models to these materials complements band structure studies; ionic models provide useful reference models for studying the high- T c superconductors. In order to make this comparison useful, it is important to use a non-empirical model that does not involve fitting to experiment. We have applied the Potential Induced Breathing (PIB) Model, a non-empirical model which has shown success in predicting properties of insulating oxides, to La 2CuO 4. The PIB overlapping ion change density is compared to a self-consistent LAPW charge density. The out-of-plane oxygen and lanthanum ions are quite ionic, but the in-plane oxygen and copper show significant distortions, primarily displaying movement of charge out of the overlap region. Static minimum energy structures were calculated in tetragonal and orthorhombic symmetries using the PIB model. The ionic model predicts the observed tetragonal to orthorhombic distortion. PIB predicts a lower symmetry ground state. Phonon dispersion curves were calculated for both the tetragonal and orthorhombic structures. Unstable phonon branches are found for both structures using the ionic model. In the tetragonal structure these unstable branches are related to the X-point rotation of the in-plane oxygens, the octahedral tilting associated with the phase transition to the orthorhombic structure, and sliding of the O(Z) and La atoms in the x−y plane throughout the Brillouin zone.

Phase transitions and elasticity in zirconia

The potential induced breathing (PIB) model is used to calculate equations of state, relative phase stabilities, and elasticity of several different structures of ZrO 2. PIB is a non-empirical model for calculation of static and dynamic properties of ionic crystals. The cubic fluorite structure is found to be the stable zero-pressure phase. The monoclinic phase is more stable at low densities and the PbCl 2 phase is more stable at high pressures. The rutile structure is found to be relatively unstable, a result in agreement with experiment. Elastic constants are calculated for the monoclinic, tetragonal, and fluorite phases of ZrO 2. For the pure monoclinic phase, good agreement with experiment is found for the aggregate shear and Young's moduli. The elastic constants and pressure derivatives for cubic zirconia are discrepant with experimental data, and it is suggested that disorder greatly affects its elastic behavior. Furthermore, disorder and defects may be important in stabilizing the monoclinic and tetragonal structures.

Nonempirical cluster model study of the on-top chemisorption of fluorine and chlorine on C(111) surface

The interaction of atomic F and Cl with C 4H 9 cluster model has been studied by using non-empirical Hartree-Fock computations with basis sets of increasing flexibility. Although the inclusion of polarization functions is mandatory for a quantitative investigation even computations at the minimal basis set or semiempirical MNDO level are able to provide general trends both for chemisorption energies and equilibrium geometries of different absorbates. As in the case of silicon surfaces the charge transfer and the chemisorption energy decrease with the atomic number of the absorbate and the equilibrium bond length increases in the same sense. The local nature of the chemisorption bond is confirmed by computations employing the C 10H 15 cluster both at STO3G and MNDO levels.

Ionic contributions to lattice instabilities and phonon dispersion in La2CuO

We have applied the potential-induced breathing model, a nonempirical ionic model, to La/sub 2/CuO/sub 4/. The ionic model predicts the observed tetragonal-to-orthorhombic distortion, predicts a lower-symmetry ground state, and predicts a stable oxygen breathing mode. We find unstable phonon branches that we relate to phase transitions. Harmonically unstable double-well modes will couple to the charge density in the copper-oxide planes and possibly contribute to high-T/sub c/ superconductivity. This ionic coupling is not included in recent calculations.

Vibrational properties of surface hydroxyls: Nonempirical model calculations including anharmonicities

Complete sets of harmonic, semidiagonal cubic as well as diagonal cubic and quartic force constants are reported for the internal coordinates of terminal, ≣SiOH, and bridging, ≣SiOH·Al≣, surface hydroxyls on silica and zeolites. They are obtained by numerical differentiation of analytically calculated gradients of the energy (SCF approximation, 6-31 G* basis set). A GF vibrational analysis is performed and after making a nonlinear transformation of the force constants into normal coordinates the anharmonicity constants are evaluated by perturbation theory. Comparison is made with the D2OH+ ion and the DOH molecule. The calculated anharmonicities of the OH bonds in the systems studied are remarkably constant and vary between -76 and -84 cm-1, only in agreement with the values observed for DOH (-83 cm-1) and surface silanols, ≣SiOH (-90 ± 15 cm-1).

Nonempirical model calculations of the indices of acidity and basicity of the surface groups SiO2, Al/SiO2 and ?-Al2O3

1. The model of the stoichiometric orbital cluster and the nonempirical PRDDO method have been employed to calculate the indices of acidity and basicity of the surface sites of SiO2, Al/SiO2, and γ-Al2O3. 2. A ranking has been constructed and discussed for the change in the acid and base properties of the surface structures of different types of the adsorbents studied.

Lattice dynamics of the potential-induced breathing model: Phonon dispersion in the alkaline-earth oxides.

We find the dynamical matrix for the potential-induced breathing (PIB) model for ionic solids, and calculate with no adjustable parameters the phonon-dispersion relations for the alkaline-earth oxides in the B1 structure. Our approach is similar to that of Gordon and Kim, in which the crystalline charge densities are estimated by overlapping atomic charge densities, which are then converted to energy by electron-gas approximations. It goes beyond the original Gordon-Kim model by allowing for spherical breathing of the atoms in response to the long-range potential, and beyond later refinements of the modified-electron-gas models by explicitly including the effects of PIB on the self-energy and the overlap interactions. This allows us to treat general deformations and lattice dynamics including the many-body PIB effects. PIB couples the long- and short-range forces in a way that is not present in any other lattice-dynamical model, since the spherical charge relaxation is coupled to the long-range electrostatic potential. PIB gives better agreement for the splitting of the longitudinal- and transverse-optic mode frequencies than is found with rigid-ion models, as well as much improved acoustic branches. PIB is a nonempirical model; no experimental data are used other than the values of fundamental constants such as Planck's constant and the atomic masses.

On the prediction of soil sorption coefficients of organic pollutants from molecular structure: application of molecular topology model

This study was undertaken to test the ability of the molecular connectivity model to predict the soil sorption coefficients of polycyclic aromatic hydrocarbons (PAHs), alkylbenzenes, chlorobenzenes, chlorinated alkanes and alkenes, heterocyclic and substituted PAHs, and halogenated phenols. Tests performed on 31 such compounds clearly demonstrate that this simple nonempirical model accurately predicts the soil sorption coefficients for the above classes of compounds. Moreover, the model out performs the traditional empirical models based on 1-octanol/water partition coefficients or water solubilities in accuracy, speed, and range of applicability. Additional tests on approximately 160 polar and ionic compounds show that the above topological model plus a single semiempirical variable is capable of accounting for the soil sorption properties of nearly 95% of all organic chemicals whose soil sorption coefficients have been measured. The results of these tests demonstrate that the molecular connectivity model is a very accurate predictive tool for the soil sorption coefficients of a wide range of organic chemicals and that it can be confidently used to rank potentially hazardous chemicals and thus to create a priority testing list. 55 references, 5 figures, 7 tables.

Lattice Dynamics and Ionicity in the High-Temperature Superconductors

Using a non-empirical ionic model, we find harmonically unstable, double well potential surfaces for both La2CuO4 and YBa2Cu3O7 which may be related to the high temperature superconductivity. We have applied the Potential Induced Breathing (PIB) Model to La2CuO4 and YBa2Cu3O7 and find that the ionic description gives semiquantitative agreement with structural and vibrational observations. Furthermore, comparison with self-consistent linearized augmented plane wave [1] (LAPW) calculations shows that ionic contributions to the bonding and lattice dynamics of oxide superconductors are large. For La2CuO4 we find that an ionic description predicts the observed tetragonal to orthorhombic distortion, predicts a lower symmetry ground state, and predicts a stable oxygen breathing mode. We find harmonically unstable phonon branches that we relate to phase transitions. Unstable (anharmonic) modes will couple via ionic forces to the charge density in the metallic planes. This ionic coupling has not been included in previous lattice dynamics calculations. For YBa2Cu3O7 we find similar unstable phonon branches that involve oxygen motions perpendicular to the Cu-O bonds. We find the crystalline charge density is best approximated by overlapping ions if Cu and O ions of charge +1.6 and -1.8, respectively, are used.

A nonempirical model of the gas-cell atomic frequency standard

In this paper a signal model of the rubidium (Rb) atomic frequency standard is developed. The model combines an analysis of the atomic physics required to describe processes occurring within the Rb absorption cell with a feedback analysis of the clock’s servocontrol circuitry, and thus allows clock performance in terms of Allan variance to be predicted from a number of electronic and physical parameters. All previous models of the Rb clock have been limited to an analysis of the clock’s short-term performance, Allan variance averaging times less than 10 000 s. However, by explicitly including the effects of discharge lamp intensity fluctuations, which are transformed into output frequency variations via the light shift effect, clock performance can be predicted for averaging times greater than 10 000 s. Furthermore, the present model is the first which incorporates the influence of an optically thick Rb vapor, along with the diffusion of optically pumped atoms to the walls of the absorption cell, into the calculation of clock performance. As part of the model’s validation, the calculations are compared with the results from a recent Rb clock long-term performance experiment. Agreement between measured and predicted Allan variances for both short and long averaging time periods is excellent.

Fluid Displacement Efficiency in Layered Porous Media. Mobility Ratio Influence

Important effects of petroleum reservoir stratification upon chemical enhanced oil recovery processes have been modelled using systems containing layers of two different permeabilities. Experimentally, visual models composed of glass bead packings have been exploited and miscible matched-density displacements performed. The results show a strong sensitivity to fluid mobility ratio. Flow pattern observation and mathematical analysis have shown that complex viscous crossflow processes are very influential. We present a non-empirical mathematical model for dual layer systems. Our calculation of crossflow effects using this analytical method compares favourably with experimental results from varions sources. Finally, we show how to apply this model to multilayer cross-sectional and three-dimensional problems.

Non-empirical model for the imaginary part of the optical potential for electron scattering

The authors propose a new kind of model for absorption of flux from the elastic scattering channel in electron-atom or electron-molecule collisions. It is a non-empirical model so it predicts the absorption cross section as well as the elastic scattering wavefunction and elastic differential cross sections. They have tested the model for electron scattering by He, Ne and Ar at impact energies 30-400 eV. Agreement with experiment is very good for both the absorption cross sections and elastic differential cross sections.

Electronic structure of the {Pd Cl4}2-ion

The structure of the {Pd Cl4}2- anion was calculated within a non-empirical pseudopotential model, using the PSHONDO program. The molecular orbital ordering is compared with previous calculations using CNDO, INDO, X α and other semiempirical schemes. A comparison with the photoelectron spectra is carried out. It is argued that the simplified molecular orbital identification proposed in semiempirical studies to reproduce such spectra is not unique and the application of Koopmans' theorem to this complex is questioned; consequently a new identification is here proposed that correlates well with the experimental data. Several other ab initio studies on different square planar complexes are reviewed, showing the same trends and conclusions reached in the present work.

Electronegativities of the elements from a nonempirical electrostatic model

An electrostatic model, according to which the electronegativity of an atom is identified with the electrostatic force between the effective nuclear charge and an electron at a distance equal to the relative radius of the atom, is used to calculate a nonempirical electronegativity scale for the first 54 elements. The relative radius is calculated from the free-atom wave function by use of the density contour approach, while intergration of the radial density from the nucleus to the relative radius yields the effective nuclear charge. In contrast to the empirical methods, the nonempirical electrostatic method is not only applicable to all elements, but treats all elements equally. In addition to correlating well with empirical scales, the proposed model is consistent with the major conclusions of the density functional approach of Parr and his co-workers. In particular, the model is easily extended to yield valence state electronegativities.

Pseudopotential SCF study of the palladium atom-ethylene system

A SCF molecular orbital study using the non-empirical pseudopotential model is reported for the palladium-ethylene interaction. This organometallic system is found to be weakly bound, while the molecular orbital energy levels of the olefin and Pd atom are only slightly perturbed. The ethylene's C-C distance is relaxed and its planar structure is almost undistorted. A comparison with experimental results for the Pd-C2H4 system, as well as with other theoretical studies on similar systems, is presented.

Nonadditive effects in metal clusters and chemisorption. Pseudopotential study of palladium clusters

AbstractThe analysis of nonadditive effects in small palladium clusters via LCAO‐MO‐SCF calculations using the nonempirical pseudopotential model is presented. The results are tentatively correlated with previous studies on various metal clusters (Li, Be, Mg, etc.) for which a good knowledge of multibody terms has provided a valuable guide for understanding the cluster stabilities and their chemisorption capacity.