Three real‐space discretization techniques in electronic structure calculations

Abstract

Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

Increased p-type conductivity in GaNxSb1−x, experimental and theoretical aspects

“…The positron was treated using the MIKA/ Doppler package. 43 All electronic structure calculations were performed using a 216-atom GaSb zincblende supercell. The defect structures were relaxed with a convergence criteria for forces of 0.01 eV/Å also taking into account the forces exerted on the ions by the localized positron.…”

Characterization of point defects in CdTe by positron annihilation spectroscopy

“…The calculations were performed with the MIKA/ Doppler package using 1000 atom supercells. 7,10,32 The electron-positron enhancement factor obtained from the data of Arponen and Pajanne, 33 both the original by parameterization by Boronski and Nieminen (BN), 34 described within the local density approximation (LDA), and with an expression obtained by Barbiellini and co-workers 35,36 (referred to as AP), described within the generalized gradient approximation (GGA) were used. The LDA calculations with BN enhancement assumed a value of 7.1 for the CdTe high frequency dielectric constant.…”

Doping Nanocrystals and the Role of Quantum Confinement

“…We solve the Kohn-Sham equation without resort to an explicit basis [8,9,10,11,12]. We solve for the wave functions on the grid with a fixed domain, which encompasses the physical system of interest.…”

“…Within a "real space" approach, one can solve the eigenvalue problem using a finite element or finite difference approach [9,12]. We use a higher order finite difference approach owing to its simplicity in implementation.…”