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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/density-functional-theory
课程评论：没有评论
课程名称：密度泛函理论 概述：本课程旨在全面介绍密度泛函理论（DFT）。DFT 目前是研究相互作用电子的最广泛使用的方法，其应用范围涵盖从原子到固体系统，从原子核到量子流体。本课程将介绍 DFT 的基本概念、基础及基本思想，特别强调使 DFT 成为模拟量子力学系统主流方法的特点和原因。 本课程适合具有基本量子力学知识的学生和研究人员，不要求有模拟或固态物理的经验。我们将在需要时提供简明的数学背景。 课程大纲： 1. **从多体问题到密度泛函理论** 本周将介绍密度泛函理论的基本概念，首先讨论多体问题，如何使用电子密度进行重新表述。我们将重点关注与密度直接相关的观测量，最后讨论霍亨贝格-科恩定理，课程结束时将进行历史回顾，追溯引入密度泛函的首步。 2. **从密度到科恩-沙姆世界** 第二周将介绍科恩-沙姆世界，这一既奇特又高效的环境中，独立粒子由能给出准确密度的方程控制。尽管独立粒子所感受到的势能未知且可能存在病态问题，该理论在原则上成立。模块最后也将给予简要的历史观点。 3. **近似与策略** 第三周将探讨 DFT 的一些实用方面，尤其是对未知交换关联势的近似策略。还将讨论带隙的概念以及通过自洽方法解决科恩-沙姆方程的实用方案。
Name:From the Many-Body problem to Density Functional Theory
Description:This week will introduce the Density Functional Theory concepts. The week starts from an introduction to the many-body problem, and how things could be reformulated using the electron density. We will focus on observables, in particular those most directly related to the density. Finally we will discuss the Hohenberg-Kohn theorems. A little historical detour is taken at the end, where we will follow the footprints of the first steps to introduce a functional of the density in quantum problems.
Name:From density to the Kohn-Sham world
Description:This second week introduces the Kohn-Sham world, a weird and very efficient world in which independent particles are governed by equations that give the exact density. At least, in principle, for the potential felt by the independent particle is unknown, as well as pathological. Again, a brief historical point of view ends the module.
Name:Approximations and strategies
Description:This third week tackles some more practical aspects of DFT. In particular the strategies for approximating the unknown exchange-correlation potential. Two other important points are the concept of band-gap and the practical scheme to solve the KS equations, via a self-consistent approach.
The aim of this course is to give a thorough introduction to Density Functional Theory (DFT). DFT is today the most widely used method to study interacting electrons, and its applicability ranges from atoms to solid systems, from nuclei to quantum fluids. In this course, we introduce the most important concepts underlying DFT, its foundation, and basic ideas. We will in particular stress the features and reasons that lead DFT to become the dominant method for simulating quantum mechanical systems. The course is intended for students and researchers with knowledge of basic quantum mechanics. No experience in simulation or solid-state physics is required. We try to give a concise mathematical background when particular concepts are needed.
