Elements Of Green Function And Density Functional Theory
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Elements Of Green Function And Density Functional Theory
Author: Ferdi Aryasetiawan
language: en
Publisher: World Scientific
Release Date: 2025-03-17
If there were no Coulomb interaction among electrons, it would be relatively straightforward to solve the many-electron Schrödinger equation. It is, however, precisely this interaction that is at the heart of numerous fascinating phenomena in condensed matter physics such as superconductivity, Kondo physics, magnetism, etc. Due to the large number of electrons in a material being of the order of Avogadro's number, it is at present — and perhaps in the foreseeable future — not feasible or even desirable to solve the Schrödinger equation to obtain the many-electron wavefunction. Fortunately, a large number of important physical properties can be calculated without explicit knowledge of the wavefunction.Two of the most important formalisms for dealing with the many-electron problem which avoid a direct use of the many-electron wavefunction are the Green function and the density functional theory. Within the Kohn-Sham scheme the latter is used to calculate ground-state properties whereas the former for excitation spectra. The book presents the fundamentals of these two theories in detail with essential many-body tools, such as the occupation number representation and Grassmann algebra developed from scratch. Prior knowledge of many-body theory is not a prerequisite so that it is readable for final-year undergraduates and graduate students in physics and chemistry as well as researchers in the field of electronic structure and many-body theory. The book includes in the last chapter an exposition of a density-functional path for determining the Green function, a new formalism recently proposed by the author. The book should be a valuable companion for those embarking in the field of many-electron physics.
Recent Progress in Orbital-free Density Functional Theory
This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory.The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research.
Optical Absorption Spectra Calculated Using Linear-Scaling Density-Functional Theory
Author: Laura Ratcliff
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-05-13
The development of linear-scaling density functional theory (LS-DFT) has made ab initio calculations on systems containing thousands of atoms possible. These systems range from nanostructures to biomolecules. These methods rely on the use of localized basis sets, which are optimised for the representation of occupied Kohn-Sham states but do not guarantee an accurate representation of the unoccupied states. This is problematic if one wishes to combine the power of LS-DFT with that of theoretical spectroscopy, which provides a direct link between simulation and experiment. In this work a new method is presented for optimizing localized functions to accurately represent the unoccupied states, thus allowing theoretical spectroscopy of large systems. Results are presented for optical absorption spectra calculated using the ONETEP code, but the method is equally applicable to other spectroscopies and LS formulations. Other topics covered include a study of some simple one dimensional basis sets and the presentation of two methods for band structure calculation using localized basis sets, both of which have important implications for the use of localized basis sets within LS-DFT.