Dielectric screening method

AB-INITIO CALCULATION OF THE PHONON FREQUENCIES IN COVALENT SEMICONDUCTORS USING THE DIELECTRIC SCREENING METHOD... 

The theory of the lattice dynamics of covalent semiconductors has been developed in the late sixties and early seventies [l]. The essence of this theory is the description of the density distribution of the valence electrons between the ions at their arbitrary and instantaneous positions. Originally this part of the electron distribution due to deviations of the ions from their equilibrium positions is derived from linear response theory. Subsequently phonon dispersion curves can be obtained from this dielectric screening method. From 1972 the present authors started their efforts to calculate phonon frequencies using this method. A presentation of linear response and dielectric screening theory is given in these proceedings in the paper by J.T. 

In the dielectric screening method the electron density response due to the motion of the ions around their equilibrium positions is calculated in first order perturbation theory. The potential energy of the crystal for an arbitrary configuration of the ions is expanded to second order in the ionic displacements from equilibrium. The expansion coefficients of the second order term form a matrix. The Fourier transform of this matrix is the dynamical matrix whose eigenvalues yield the phonon frequencies. The dynamical matrix has an ionic and electronic part. The electronic part can be expressed in terms of the electron density response matrix and of the ionic potential. This method has the advantage over the total energy difference m ethod that the phonon frequencies for any arbitrary wave vector can be calculated without additional difficulties. Furthermore in this method the acoustic sum rule is automatically satisfied as a consequence of the way the dynamical matrix is derived. However the dielectric screening method is limited to harmonic phonons. 

The present authors have used the dielectric screening method for all their ab-initio computations of the macroscopic dielectric constant and phonon frequencies of Si and Ge. For the calculation of the electron energies and wave functions needed in the expression of the electron density response matrix they apply the local density approximation in the Hamiltonian. The advantage and shortcomings of this approximation are treated at length in the papers by J.T. Devreese, R. Martin, K. Kune, S. Louie, A. Baldereschi and R. Resta in these proceedings. 

In the dielectric screening method the total electronic energy is expanded in a Taylor series with respect to the ionic displacements. The relationship between the... 

The calculations of the phonon dispersion relations using the dielectric screening method presented here lead to the following conclusions ... 

Values of GENp calculated from the GB approximation compare well to values obtained from numerical solution of the Poisson equation for similar collections of point charges [83,237,238], A very promising extension of the GB methods is provided by a new scaled pairwise approximation to the dielectric screening integrals [215],... 

Moreover, each Fourier component of W can be screened independently. This forms the basis for the dielectric constant method of dealing with the problem of electron screening. 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

Solvation effects have been included using a variety of simple models [16— 23]. These models have been based on exposed surface area, dielectric continuum methods, and screened or modified Coulomb interactions. The validity... 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

Conductor-like screening model (COSMO) is one of variants of PCM method [29]. In this method, the cavity is considered to be embedded in a conductor with an infinite dielectric constant [29]. An extension to this method, called COSMO-RS... 

Our research using the CCS approach has focused on the discovery of new dielectric thin films. This example illustrates the power of this approach and key considerations in utilizing high throughput synthesis and screening approaches. A variety of other problems appear well matched to such combinatorial-style methods. A few of these are discussed briefly below, touching on both experimental challenges and research opportunities. 

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