Density Functional Theory: An Advanced Course
Density Functional Theory: An Advanced Course
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DOI：
10.1007/978-3-642-14090-7
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发表时间：
2011-01-01
期刊：
影响因子：
--
通讯作者：
Dreizler, Reiner M.
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文献类型：
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作者：
Engel, Eberhard;Dreizler, Reiner M.
本书源自密度泛函理论 (DFT) 课程，该课程于十多年前首次在慕尼黑大学教授。该课程以 Dreizler 和 Gross（Springer，1990）以及 Parr 和 Yang（牛津大学出版社，1989）的经典著作为基础。当时更新的主题，例如时间相关的 DFT 或轨道相关的泛函，被添加到这两本书涵盖的材料中。然而，当时就需要限制 DFT 特定方面最相关和/或最具说明性的陈述，以便控制课程的长度。当该课程后来在法兰克福大学再次开设时，很快就发现不可能将涉及形式主义和重要应用的大量新结果整合到课程中：因此，即使选择课程中涵盖的 DFT 分支也是不可避免的。本文反映了这种无可否认的主观主题选择：它集中于最广泛使用的 DFT 变体的基础知识。这意味着对相应的存在定理和有效的单粒子方程以及实现中使用的关键近似进行彻底的讨论。基态 DFT（在非相对论层面）在第 2 章中讨论。 2-6。第 2 章介绍了基本的 Hohenberg-Kohn 定理及其对自旋、电流和电流自旋密度泛函理论的扩展，以及一些基本概念，例如 v 表示性。由此产生的 Kohn-Sham 方程收集在第 1 章中。 3. 本章还讨论了 Kohn-Sham 波函数和特征值与真实多体波函数和能量之间的关系。第 4 章基于该量的两种精确表示，详细阐述了交换相关函数当前可用的近似值。第 1 章总结了对密度泛函有效的最重要的维里关系。 5. 然后在第 1 章中继续讨论交换相关函数。 6，其中引入了轨道相关泛函的概念。本章还演示了 DFT 的第一原理特征，因为它表明可以通过使用轨道相关泛函来系统地接近真实的交换相关能量和势。另一方面，存在性定理的讨论，基本的
This book emerged from a course on density functional theory (DFT), first given at the University of Munich more than a decade ago. The course was based on the classic texts by Dreizler and Gross (Springer, 1990) and by Parr and Yang (Oxford University Press, 1989). More recent topics of that time, such as time-dependent DFT or orbital-dependent functionals, were added to the material covered by the two books. However, already at that time restriction to the most relevant and/or most illustrative statements on a particular aspect of DFT was necessary, in order to keep the length of the course under control. When the course was later given again at the University of Frankfurt it soon turned out to be impossible to integrate the exploding number of new results, concerning both the formalism as well as important applications, into the course: So, even a selection of the branches of DFT covered in the course was unavoidable.The present text reflects this, admittedly subjective, choice of topics: it concentrates on the basics of the most widely used variants of DFT. This implies a thorough discussion of the corresponding existence theorems and effective singleparticle equations as well as of the key approximations utilized in implementations. Ground state DFT (on the nonrelativistic level) is addressed in Chaps. 2–6. Chapter 2 introduces the fundamental Hohenberg-Kohn theorem and its extensions to spin-, current-and current-spin-density functional theory, together with some basic notions such as v-representability. The resulting Kohn-Sham equations are collected in Chap. 3. This chapter also includes a discussion of the relation between the Kohn-Sham wavefunctions and eigenvalues and the true many-body wavefunctions and energies. Chapter 4 is devoted to a detailed exposition of the currently available approximations for the exchange-correlation functional, based on two exact representations of this quantity. The most important virial relations valid for density functionals are summarized in Chap. 5. The discussion of the exchange-correlation functional is then resumed in Chap. 6, in which the concept of orbital-dependent functionals is introduced. This chapter also serves as a demonstration of the firstprinciples character of DFT, in that it shows that the true exchange-correlation energies and potentials can be systematically approached by use of orbital-dependent functionals. On the other hand, the discussion of the existence theorem, of the basic