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1994 | Buch

Planewaves, Pseudopotentials and the LAPW Method

verfasst von: David J. Singh

Verlag: Springer US

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Über dieses Buch

Over the past decade the world's technological and industrial base has become increasingly dependent on advanced materials. There is every indication that this trend will accelerate and that progress in many areas will increasingly depend on the development of new materials and processing techniques. A second and equally significant trend is the continuing ascent of the information technologies, which now touch almost every aspect of life in some way. In this environment it is natural that there is a strong interest in using numerical modeling in materials science.
With its extreme accuracy and reasonable computational efficiency, the linearized augmented plane wave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. Planewaves, Pseudopotentials and the LAPW Method presents a thorough and self-contained exposition of the LAPW method, making this powerful technique more accessible to researchers and students who have some familiarity with local density approximation calculations. Theory is discussed, but the emphasis is on how practical implementation proceeds. In addition, the author suggests future directions for adapting the LAPW method to simulations of complex materials requiring large unit cells. He does this by elucidating the connections between the LAPW method and planewave pseudopotential approaches and by showing how Car--Parrinello type algorithms can be adapted to the LAPW method.
Planewaves, Pseudopotentials and the LAPW Method is a valuable resource for researchers already involved in electronic structure calculations, as well as for newcomers seeking quick mastery of the LAPW technique.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
Over the past decade, our technological and industrial base has become increasingly dependant on advanced materials. There is every indication that this trend will accelerate, and that progress in many areas will depend increasingly on the development of new materials and processing techniques.
David J. Singh
2. Overview of Density Functional Theory and Methods
Abstract
Condensed matter physics and materials science are concerned fundamentally with understanding and exploiting the properties of systems of interacting electrons and atomic nuclei. This has been well known since the development of quantum mechanics. With this comes the recognition that, at least in principal, almost all properties of materials can be addressed given suitable computational tools for solving this particular problem in quantum mechanics. Unfortunately, the electrons and nuclei that compose materials comprise a strongly interacting many body system, and this makes the direct solution of Schrodinger’s equation an extremely impractical proposition. Rather, as was stated concisely by Dirac (1929), progress depends on the development of sufficiently accurate, but tractable, approximate techniques.
David J. Singh
3. Planewave Pseudopotential Methods
Abstract
A perusal of the electronic structure literature during the late 1970’s and early 1980’s when density functional calculations and particularly ab initio total energy methods were first showing their muscle, reveals that the field was largely dominated by planewave based pseudopotential methods. There is an interesting parallel today. The advent of ab initio molecular dynamics using the Car-Parrinello (CP) method has resulted in a quantum leap in the capability of planewave based density functional methods, and application of these approaches has permitted the solution of numerous previously intractable problems. But even now, fully eight years after the publication of Car and Parrinello’s 1985 paper, no substantial application to non-planewave based methods has occurred. Why?
David J. Singh
4. Introduction to the LAPW Method
Abstract
The LAPW method is fundamentally a modification to the augmented planewave method of Slater (1937, 1964). Thus, before embarking on an exposition of the LAPW method, we review the relevant aspects of the APW method and the motivation for its modification to the LAPW method. Further details about the APW method may be found in the book by Loucks (1967), which also reprints several early papers that develop and use this method.
David J. Singh
5. Nitty-Gritties
Abstract
The efficiency of the LAPW basis derives from its use of carefully chosen representations of the wavefunctions in different regions. In particular, a spherical harmonics expansion on a radial mesh is used inside the spheres and a planewave expansion outside. With this choice, rapid variations of the wavefunctions inside the spheres pose no particular problems, and accordingly the method is well suited to all-electron calculations (i.e. no pseudopotential) as well as d- and f-electron materials. However, rapidly varying wavefunctions imply rapidly varying charge densities and potentials, and this requires that the representations of the charge density and potential be equally flexible.
David J. Singh
6. Car-Parrinello, the LAPW Method and Large Systems
Abstract
The development of the Car-Parrinello (CP) technique and its application to planewave based calculations resulted in a quantum increase in the size and complexity of the problems that can be treated within a fully ab initio LDA framework. This and related techniques combined with ultrasoft pseudopotentials make detailed structural investigations for unit cells of several hundred atoms quite feasible (Stich et al., 1992, Brommer et al., 1992). However, besides the general observations of Car and Parrinello, there are several special features of planewaves that are exploited, and these are crucial in making the CP method as efficient as it is (see Chapter 3). These are difficult to generalize to non-planewave basis sets, and because of this CP-like algorithms have yet to have a large impact with non-planewave basis methods.
David J. Singh
Backmatter
Metadaten
Titel
Planewaves, Pseudopotentials and the LAPW Method
verfasst von
David J. Singh
Copyright-Jahr
1994
Verlag
Springer US
Electronic ISBN
978-1-4757-2312-0
Print ISBN
978-1-4757-2314-4
DOI
https://doi.org/10.1007/978-1-4757-2312-0