Eigenfunctions of the Inverse Dielectric Functions and Response Functions of Silicon and Argon

Abstract

The inverse dielectric function and response function are key quantities in the dielectric response of materials. The Hermitian, inverse dielectric function can be diagonalised to yield the dielectric band structure (DBS) and a set of eigenpotentials for a crystalline solid. The response function can also be diagonalised to yield a set of eigenfunctions which are similar in character to the eigenpotentials for the solid. The DBS and response functions of argon and silicon are calculated and analysed. The most important eigenpotentials of solid argon and silicon are atom-centred monopolar and dipolar functions for argon and atom-centred monopolar and dipolar functions and bond-centred dipolar functions for silicon. These ab initio calculations provide insight into the success of discrete dipole models for optical properties of semiconductor surfaces.

Band structures of rare-gas solids within theGWapproximation

“…Eigenvalues of the inverted dielectric matrix determine the pole strengths, and a plot of their dispersion with wave vector is known as the dielectric band structure; 29 the dielectric band structure for fcc Ar was reported previously. 30 Plasmon pole frequencies are calculated using the Johnson sum rule. 31 This leads to two contributions to the self-energy: an energy independent, Hartree-Fock exchange term,…”

“…(11) z ql are pole strengths, ω ql are plasmon frequencies and 0 + is a positive infinitesimal. Eigenvalues of the inverted dielectric matrix determine the pole strengths and a plot of their dispersion with wave vector is known as the dielectric band structure 27 ; the dielectric band structure for fcc Ar was reported previously 28 . Plasmon pole frequencies are calculated either using the Johnson sum rule 29 or by fitting the dielectric matrix at zero frequency and a finite, imaginary frequency, ıω f .…”

“…In another paper 12 we will present results of calculations of optical spectra of these solids using a Bethe-Salpeter formalism 9 . Calculations were performed in a Gaussian orbital basis using the EXCITON code 13 , which is interfaced to the CRYSTAL code 14 . Single particle wave functions, energy eigenvalues and matrix elements of the exchange correlation potential from CRYSTAL are used by EX-CITON to perform GW and exciton calculations.…”

Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

“…For the component Sb the action of H n would be equivalent to a nonpositive definite matrix if there are negative eigenvalues. It is established (e.g., discussion in ref ) that the Jacobian and its inverse are related to the dielectric band structure − which has positive definite eigenvalues at its solution. Hence condition b enforces a minimization structure for the components beyond the secant condition, similar to what is used for optimization problems (e.g., ref ).…”

Ab initiomany-body calculation of excitons in solid Ne and Ar

“…The CRYSTAL code 38 was used to generate single-particle wave functions for Ne and Ar in an all-electron Gaussian orbital basis and the Coulomb potential was expanded in plane waves. GW and BSE calculations were carried out using the EXCITON 39 code. The spin-orbit interaction was omitted from the calculations and experimental lattice constants were used 19 .…”