Pseudopotential Approximation Research Articles

Modelling and Monte Carlo simulation of the atomic ordering processes in Ni3Al intermetallics

The evolution of atomic ordering processes in Ni3Al has been modelled by a Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitudes of atomic ordering energies of atomic pairs in the Ni3Al system have been calculated by means of electronic theory in pseudopotential approximation up to the 4th coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg–Williams long-range order (LRO) and Cowley–Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of the MC simulation for each predefined temperature and Al concentration levels which reveal the evolution of the system from the L12 → disordered state as the temperature increases. The values of the LRO and SRO parameters at temperatures below 800 °C justify the existence of L12-type ordered Ni3Al alloys for all concentration levels whereas at temperatures above 850 °C, the values of the LRO parameter implies the presence of a disordered solid solution of Ni3Al alloys. However, a higher degree of the SRO order parameter above the predicted order–disorder transition temperature is preserved up to the melting point of Ni3Al intermetallics. The composition dependence of the LRO and SRO parameters agrees well with the experimental results.

First-principles calculations of hyperfine parameters with the Gaussian and augmented-plane-wave method: Application to radicals embedded in a crystalline environment

A method for the calculation of hyperfine parameters in extended systems under periodic boundary conditions is presented, using the Gaussian and augmented-plane-wave density functional method, and implemented in QUICKSTEP. In order to increase the efficiency in larger systems, a hybrid scheme is proposed, in which an all-electron treatment for the nuclei of interest and a pseudopotential approximation for the remaining atoms in the simulation cell are combined. The method is validated first by comparing the hyperfine parameters for a selection of atoms and small molecules (using a supercell technique) with other theoretical methods and experimental data from literature. As a typical example of a periodic system where our hybrid method can be applied, the hyperfine parameters of the well-characterized $R2$ $L\text{\ensuremath{-}}\ensuremath{\alpha}$-alanine derived radical are evaluated, yielding results in excellent agreement with the available experimental data.

On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions

A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X1(2)II(3/2) states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core-valence correlation, relativistic effects (scalar and spin-orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 A and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 A, presumably due to an underestimation of molecular spin-orbit coupling effects. Spectroscopic constants for the spin-orbit excited X2(2)III(1/2) states are also reported for each species. The predicted bond lengths and harmonic frequencies for the closed-shell anions are expected to be accurate to within about 0.001 A and 2 cm-1, respectively. The dissociation energies of the radicals have been determined by both direct calculation and through use of negative ion thermochemical cycles, which made use of a small amount of accurate experimental data. The resulting values of D0, 63.5, 55.8, and 54.2 kcal/mol for ClO, BrO, and IO, respectively, are the most accurate ab initio values to date, and those for ClO and BrO differ from their experimental values by just 0.1 kcal/mol. These dissociation energies lead to heats of formation, DeltaH(f) (298 K), of 24.2 +/- 0.3, 29.6 +/- 0.4, and 29.9 +/- 0.6 kcal/mol for ClO, BrO, and IO, respectively. Also, the final calculated electron affinities are all within 0.2 kcal/mol of their experimental values. Improved pseudopotential parameters for the iodine atom are also reported, together with revised correlation consistent basis sets for this atom.

Laser controlled quantum motion of two Paul trapped ions

We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.

Computer simulation and visualization of vacancy defects in MgSiO3 perovskite

We have performed the first-principles simulations within the local density and pseudopotential approximations to investigate the effects of pressure on the energetics and atomic and electronic structural behaviour of vacancy defects in MgSiO3 perovskite. The simulations use a supercell containing 160 atoms whose positions are fully optimized for each defective system. Schottky formation energy is shown to increase by a factor of 2.5 over the pressure regime (0 to 150 GPa) studied. The calculated three-dimensional datasets for atomic configuration and electron charge density are visualized in detail. It is shown that these point defects induce substantial distortions in the surrounding atomic and electronic structures, and these distortions remain nearly unchanged with pressure.

Electronic structure of nanocrystal quantum-dot quantum wells

The electronic states of $\mathrm{Cd}\mathrm{S}∕\mathrm{Cd}\mathrm{Se}∕\mathrm{Cd}\mathrm{S}$ colloidal nanocrystal quantum-dot quantum wells are studied by large-scale pseudopotential local density approximation (LDA) calculations. Using this approach, we determine the effects of CdS core size, CdSe well thickness, and CdS shell thickness on the band-edge wave functions, band-gap, and electron-hole Coulomb interactions. We find the conduction-band wave function to be less confined to the CdSe well layer than predicted by $\mathbf{k}∙\mathbf{p}$ effective-mass theory, which accounts for the previous underestimation of the electron $g$ factor.

First-principles calculations of the structural, dynamical, and electronic properties of liquid MgO

The structural, dynamical, and electronic properties of liquid MgO have been investigated over a wide range of pressure 0t o 240 GPa and temperature 3000– 10 000 K using first-principles molecular dynamics FPMD within the framework of density-functional theory and the pseudopotential approximation. Our results show that the liquid structure is highly sensitive to compression: the Mg-O coordination number increases from 5 at zero pressure to 7 at high pressure. The Gruneisen parameter and heat capacity are found to increase upon twofold compression by 40% and 20%, respectively. The dynamical behavior of the liquid phase is characterized by the diffusion coefficient, which is found to decrease with increasing pressure and to increase with increasing temperature in a way that can be accurately characterized by an Arrhenius relationship with activation energy and volume of 0.85 eV and 1.3 A 3 , respectively. The calculated electronic density of states show that the electronic structure of the liquid phase differs substantially from that of the crystalline phase: the liquid has no band gap and a density of states at the Fermi level increases with increasing volume and temperature.

Vacancy defects in MgO at high pressure

First-principles calculations within the local density and pseudopotential approximations were performed to investigate the effects of pressure on the energetics and structural behavior of charged vacancy defects in MgO. The simulations were performed for a supercell containing 216 atoms with their positions being fully optimized. In particular, the formation and migration energies of cation and anion vacancies were shown to substantially increase over the pressure regime of the Earth’s mantle. Our results thus suggest that pressure should suppress intrinsic diffusion mediated by ionic vacancies in MgO over the mantle pressure regime. The calculated three-dimensional data sets for atomic displacements and electron charge density were explored in detail using an interactive visualization system. Although the atomic and electronic structures are highly distorted in the close vicinity of the defects (i.e., in the region covering up to the nearest and next-nearest atoms), the effects are not negligible at farther distances.

First-principles calculation of the EPRgtensor in extended periodic systems

A method for the ab initio prediction of the EPR $g$ tensor for paramagnetic defects in systems under periodic boundary conditions is presented. It is based on density functional theory and the pseudopotential approximation. The formalism is applicable to crystalline and amorphous insulators, as well as to isolated molecules using a supercell technique. The method is validated by comparison with a well-established theoretical approach and experimental data for a series of small isolated molecules. Finally the EPR parameters of an $\mathrm{O}_{3}{}^{\ensuremath{-}}$ defect in a KCl lattice are evaluated following the new procedure, yielding results in good agreement with experiment and at an attractive computational cost.

Two-component relativistic density-functional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and all-electron methods

A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.

Comparison of the full-potential and frozen-core approximation approaches to density-functional calculations of surfaces

We scrutinize the accuracy of the pseudopotential approximation in density-functional theory (DFT) calculations of surfaces by systematically comparing to results obtained within a full-potential setup. As model system we choose the CO oxidation at a RuO2(110) surface and focus in particular on the adsorbate binding energies and reaction barriers as target quantities for the comparison. Rather surprisingly, the major reason for discrepancy does not result from the neglected semi-core state relaxation in the frozen-core approximation, but from an inadequate description of the local part of the Ru pseudopotential, responsible for the scattering of f like waves. Tiny, seemingly irrelevant, imprecisions appearing in these properties can have a noticeable influence on the surface energetics. At least for the present example, we obtain excellent agreement between both approaches, if the pseudopotential describes these scattering properties accurately.

Scalar relativistic correction to nucleus-independent chemical shifts of coinage-metal compounds: How does the pseudopotential approximation perform?

The performance of commonly used pseudopotentials for calculations of nucleus-independent chemical shifts (NICS) at the center of coinage-metal rings (M 4Li 2 (D 4h), M = Cu, Ag, Au) is investigated. The scalar relativity, which has a non-negligible effect on NICS, is found to be accurately described by the pseudopotential approximation. Overall, good agreement is obtained with all-electron relativistic methods, however, careful comparisons with these calculations and consideration for large triple- ζ basis sets are recommended when aiming to accurately define the relative degree of diatropicity among a series of compounds.

Two atoms in an anisotropic harmonic trap

We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows to extend the validity of our results to the case of tight traps and large scattering lengths.

Ab Initio Calculations of Intrinsic Defects in Rutile TiO2

This paper presents the results of density functional theory calculations of the defect formation enthalpies of Frenkel and Schottky defects in rutile TiO2. The calculations are performed within the generalized gradient, supercell, and pseudopotential approximations and predict that Frenkel defects are more energetically favorable in TiO2 than Schottky defects. The calculations also indicate that both Frenkel and Schottky defects prefer to cluster together rather than spread out across the unit cell. Possible diffusion routes for interstitial Ti atoms are investigated and strong anisotropy in interstitial diffusion in TiO2 is supported by the results.

Theoretical prediction of the structure and properties of Sn3N4

First-principles calculations based on plane-wave pseudopotential and local-density approximation (LDA) were carried out to study the structure and properties of Sn3N4. In agreement with experimentally determined crystal structure, γ-Sn3N4, which has a high density, was found to be most energetically favored among the structures considered. We also searched for other possible polymorphs of Sn3N4, which may be stable at higher pressure, by studying the properties of six additional high-pressure structures. Phase transition from the spinel structure to the CaFe2O4 and CaTi2O4-type structures can be expected at pressures of 60GPa and 40GPa, respectively. Sn3N4 is predicted to be a semiconductor with a band gap of 1.15eV within the LDA.

Basis set effects on frontier molecular orbital energies and energy gaps: a comparative study between plane waves and localized basis functions in molecular systems.

In order to study the Kohn-Sham frontier molecular orbital energies in the complete basis limit, a comparative study between localized functions and plane waves, obtained with the local density approximation exchange-correlation functional is made. The analyzed systems are ethylene and butadiene, since they are theoretical and experimentally well characterized. The localized basis sets used are those developed by Dunning. For the plane-waves method, the pseudopotential approximation is employed. The results obtained by the localized basis sets suggest that it is possible to get an estimation of the orbital energies in the limit of the complete basis set, when the basis set size is large. It is shown that the frontier molecular orbital energies and the energy gaps obtained with plane waves are similar to those obtained with a large localized basis set, when the size of the supercell and the plane-wave expansion have been appropriately calibrated.

The genesis of energy bands formed by sublattice states in alkaline-earth metal oxides and sulfides

The self-consistent electron energy band spectra of crystals and charged sublattices of alkaline-earth metal oxides and sulfides are calculated in the framework of the density functional theory within the pseudopotential approximation in the basis set of localized orbitals. The charge states of sublattices (such as neutral sublattices, empty metal sublattices, and doubly charged anion sublattices) are analyzed with due regard for the electrical neutrality of the crystal. It is demonstrated that the valence bands of the studied crystals are very similar to the valence bands of the doubly charged anion sublattices. The distributions of the valence electron densities of the crystals are virtually identical to those of the anion sublattices. The lower conduction bands of the crystals and doubly charged anion sublattices also almost coincide with each other for MgO and MgS but differ substantially for CaO and CaS. This is associated with the difference between the contributions from the anions and cations to the conduction band of the crystals. It is found that these contributions depend on the relative energy positions of p and d unoccupied states.

Breakdown of the pseudopotential approximation for magnetic systems: Predicting magnetic quenching at the V(001) surface with spin-dependent pseudopotentials

Both experimentally [R.L. Fink et al., Phys. Rev. B 41, 10 175 (1990)] and using all-electron density-functional theory (DFT) methods, the V(001) surface exhibits little or no magnetization. Very recently, independent pseudopotential DFT calculations demonstrated the breakdown of the pseudopotential approximation, showing large magnetic moments at the surface of a V(001) slab. Here we demonstrate that use of spin-dependent pseudopotentials systematically corrects the inaccuracies of conventional spin-neutral pseudopotentials, producing results consistent with all-electron ones. We also show how the use of the spin-dependent pseudopotentials allows one to achieve a high level of accuracy without the numerical difficulties and cost associated with accurate spin-neutral pseudopotentials.

Nonlocal pseudopotentials and magnetic fields.

We show how to describe the coupling of electrons to nonuniform magnetic fields in the framework of the widely used norm-conserving pseudopotential approximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules within density functional theory (DFT) in the local density approximation. Our results are compared with high-quality all-electron DFT results obtained using Gaussian basis sets and another recently proposed pseudopotential formalism.

Density functional study of XH4 (XSi and Ge) reactivity upon dissociative adsorption onto the Si(100) surface

AbstractTotal energy calculations based on density functional theory (DFT) with generalized gradient approximation (GGA) and ultrasoft pseudopotential approximation and an analysis tool of atom‐resolved density of states (ADOS) have been used to investigate (1) the energetic profiles for the possible initial dissociative adsorption of XH4 (XSi and Ge) onto the Si(100)(2 × 2) surface to evaluate their reactivity and (2) the effect of surface electronic states of Si(100)(2 × 2) on gaseous molecular precursors XH4 (XSi and Ge) during initial dissociative adsorption to understand the factors governing their reactivity. Our calculated lower‐energy barrier for initial dissociative adsorption of GeH4 is due to the forming of stronger bond of SiH between H within GeH4 and buckled‐down Si atom on the Si(100)(2 × 2) surface accompanying the larger extent of unbuckling of the buckled SiSi dimer on the Si(100)(2 × 2) surface at the transition state. Our evaluated better reactivity for GeH4 than SiH4 (a factor of around 14.6) is slightly larger than observed higher reactivity for GeH4 than SiH4 (a factor of between 2 and 5 depending on the incident kinetic energy) employed supersonic molecular bean techniques. Finally, our calculated ADOS indicate that the surface electronic states of buckled SiSi dimer on the Si(100)(2 × 2) surface energetically favorably participate in the transition state during GeH4 initial dissociative adsorption to reduce the energy barrier, i.e., enhance its reactivity, in comparison with SiH4 initial dissociative adsorption onto the Si(100)(2 × 2) surface under the same reaction conditions. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004