Beyond the Rigid-Ion Approximation with Spherically Symmetric Ions

Boyer, L. L.; Mehl, Michael J.; Feldman, J. L.; Hardy, J. R.; Flocken, J. W.; Fong, C. Y.

doi:10.1103/physrevlett.54.1940

Cited by 84 publications

(13 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the LAPW method we can calculate not only bulk physical properties such as equations of state and phase transitions but the electronic structure as well. Since the potential is not restricted to a particular form, results can be compared with widely used overlapping ion models such as the modified electron gas (MEG) [Cohen and Gordon, 1976;Muhlhausen and Gordon, 1981a, b] and potential induced breathing (PIB) [Boyer et al, 1985a;Mehl et al, 1986] models to study the effects of the simple approximations to local density that these models embody compared with rigorous solution of the density functional equations for the crystal. , 1986;Feldman et al, 1987].…”

Section: Introductionmentioning

confidence: 99%

Linearized augmented plane wave electronic structure calculations for MgO and CaO

Mehl¹,

Cohen²,

Krakauer³

1988

J. Geophys. Res.

Self Cite

160

View full text Add to dashboard Cite

Figure 1 lb is not correct. The band structure calculations used to create this figure included so-called "ghost states," spurious wave functions which occasionally appear in linearized methods due to the incompleteness of the basis set. A proper choice of energy parameters will eliminate these states. The self-consistent calculations did not contain ghost states. We have eliminated the ghost states in the calculations leading to the new Figure l lb presented here. The conclusions reached in the paper are actually strengthened. We have also changed Figure 1 la by including the Mg 2p semicore states. Finally, the references to Pickett [1985] and Pickett [1986] should be to the journal Comments on Solid State Physics. We would like to thank H. Lu for doing the calculations for the new Figure 11. a V=18.1A :• b V=lO,&, 3 >'8 o• Madelung Potential,• I _ Modelung Pofenfiol •,"""" .. Watson Potential Watson Potential Fig. 11. Differences in eigenvalues at the F, L, X, and K symmetry points for PIB and LAPW charge densities for the B1 phase of MgO. The curves with solid lines are the O 2p states, the dashed curves are the Mg 2p and O 2s states, and the dotted curves are the excited states. The Madelung potentials are indicated by arrows. (a) 18.1 ,•3, 0 GPa. The best fit Watson sphere potential is very close to the Madelung potential. (b) 10 ,•3, 345 GPa. The best Watson sphere potential is somewhat larger than that given by the Madelung potential, but properly chosen spherical ions give an accurate fit.

show abstract

Section: Introductionmentioning

confidence: 99%

Linearized augmented plane wave electronic structure calculations for MgO and CaO

Mehl¹,

Cohen²,

Krakauer³

1988

J. Geophys. Res.

Self Cite

160

View full text Add to dashboard Cite

show abstract

“…To be more precise, we use the generalized GKM taking into account the monopole-type polarizability of ions as well as the dipole one. The monopole polarizability arising from the Madelung potential of the surrounding ions was considered by Boyer et al [10]. They introduced the socalled potential induced breathing (PIB) model.…”

mentioning

confidence: 99%

Microscopic calculations of phonons in polarizable-ion approach

Иванов

Maksimov

1992

Phys. Rev. Lett.

View full text Add to dashboard Cite

The Gordon-Kim electron gas model is generalized to include a dipole polarization of the ions. The expression for the total energy of ionic crystals is derived including its polarization part. The frequencies of LO and TO phonons at the T point are calculated. Good agreement with experimental data for a number of alkali halides is obtained.PACS numbers: 71.45.Gm, 71.45.Jp, 77.20.+y The theory of lattice dynamics of ionic crystals is very old but still popular. There are many semiempirical models for treating lattice dynamics. Two of them are well known as the shell model [l] and the deformational dipole model [2], The relations between these models are discussed in detail by Hardy and Karo [3]. Several attempts have been made to justify these models by quantum mechanical calculations of the energy of crystals, starting from the classical works of Lowdin [4] and Tolpygo [5]. A more recent one was given by Zeyher [6]. All of them are based on considerations of the energy in terms of electron wave functions of ions and different types of overlap integrals.In recent years some ab initio approaches to lattice dynamics were proposed [7], using the density functional theory (DFT). These approaches are powerful but extremely complicated and lose the attractive and clear physical picture of ionic crystals as consisting of individual ions. It is not surprising therefore that there continue to be new attempts to formulate a first-principles theory of ionic crystals involving the consideration of individual ions in the framework of DFT, including a new book [8] where the so-called spherical model of ionic crystals has been presented.Here we give a theory of the lattice dynamics using the Gordon-Kim electron gas model (GKM) [9]. To be more precise, we use the generalized GKM taking into account the monopole-type polarizability of ions as well as the dipole one. The monopole polarizability arising from the Madelung potential of the surrounding ions was considered by Boyer et al [10]. They introduced the socalled potential induced breathing (PIB) model. The dipole polarizability was included in the generalized GKM in our preceding work [11], where the electronic dielectric constant was obtained. The method developed in Ref. [11] can be easily adopted to the lattice dynamics. In this case the role of an external electric field is played by the Madelung field due to ionic displacements.The main idea of the GKM is that the electronic density of an ionic crystal can be approximated by the superposition of individual ion densities. Then the total energy can be calculated using the formulas of DFT in the local density approximation (LDA). The inherent idea of superposition seems to be not too far from reality, as experimental investigations show [12]. For the present calculations we use ionic charge densities calculated in the DFT approach. The Schrodinger-like equation for a single ion in the presence of the neutralizing Watson sphere, simulating the Madelung potential, and an external electric field is solved by the modified St...

show abstract

“…30 Among the many methods proposed to date to model interactions in ionic materials, 31 we mention, e.g., the fully ionic model of This model generates in-crystal anion wave functions able to provide accurate cohesive energies. The potential-induced breathing model 35 assumes that the breathing motion of the ion is directly coupled to the Madelung potential. Another example, the modified electron gas, 36,37 is based on the assumption that the crystal density is the sum of the densities of individual ions, which are calculated from first principles.…”

mentioning

confidence: 99%

Classical polarizable force fields parametrized from ab initio calculations

Tabacchi

Mundy

Hutter

et al. 2002

The Journal of Chemical Physics

View full text Add to dashboard Cite

A computationally efficient molecular dynamics implementation of a polarizable force field parametrized from ab initio data is presented. Our formulation, based on a second-order expansion of the energy density, models the density response using Gaussian basis functions derived from density functional linear response theory. Polarization effects are described by the time evolution of the basis function coefficients propagated via an extended Lagrangian formalism. We have devised a general protocol for the parametrization of the force field. We will show that a single parametrization of the model can describe the polarization effects of LiI in the condensed phase. A computationally efficient molecular dynamics implementation of a polarizable force field parametrized from ab initio data is presented. Our formulation, based on a second-order expansion of the energy density, models the density response using Gaussian basis functions derived from density functional linear response theory. Polarization effects are described by the time evolution of the basis function coefficients propagated via an extended Lagrangian formalism. We have devised a general protocol for the parametrization of the force field. We will show that a single parametrization of the model can describe the polarization effects of LiI in the condensed phase. Classical polarizable force fields parametrized from ab initio calculations

show abstract

Beyond the Rigid-Ion Approximation with Spherically Symmetric Ions

Cited by 84 publications

References 12 publications

Linearized augmented plane wave electronic structure calculations for MgO and CaO

Linearized augmented plane wave electronic structure calculations for MgO and CaO

Microscopic calculations of phonons in polarizable-ion approach

Classical polarizable force fields parametrized from ab initio calculations

Contact Info

Product

Resources

About