我的老师告诉我的关于密度泛函理论的谎言：用Hubbard二聚体看穿它们
Lies My Teacher Told Me About Density Functional Theory: Seeing Through Them with the Hubbard Dimer
摘要：
最现实的中等相关材料的计算开始于基态密度泛函理论（DFT）计算。虽然Kohn-Sham DFT每年在大约40，000篇科学论文中使用，但其基本基础并没有得到广泛的重视。在这一章中，我们分析了DFT的固有特性，在其最简单的形式，使用不对称哈伯德二聚体作为一个说明性的模型。我们首先通过DFT的核心原则，解释确切的基态密度泛函产生和不产生。考虑到系统的相对简单性，几乎所有精确的交换相关泛函的性质都很容易可视化和绘制。关键概念包括Kohn-Sham方案，XC势的相关性变得非常强的行为，导数不连续性和KS间隙和真实电荷间隙之间的差异，以及如何使用含时DFT提取光激发。通过这篇文章的结尾和伴随的练习，读者将提高他们解释和形象化DFT概念的能力，以及更好地理解别人可能出错的地方。
英文摘要：
Most realistic calculations of moderately correlated materials begin with a ground-state density functional theory (DFT) calculation. While Kohn-Sham DFT is used in about 40,000 scientific papers each year, the fundamental underpinnings are not widely appreciated. In this chapter, we analyze the inherent characteristics of DFT in their simplest form, using the asymmetric Hubbard dimer as an illustrative model. We begin by working through the core tenets of DFT, explaining what the exact ground-state density functional yields and does not yield. Given the relative simplicity of the system, almost all properties of the exact exchange-correlation functional are readily visualized and plotted. Key concepts include the Kohn-Sham scheme, the behavior of the XC potential as correlations become very strong, the derivative discontinuity and the difference between KS gaps and true charge gaps, and how to extract optical excitations using time-dependent DFT. By the end of this text and accompanying exercises, the reader will improve their ability to both explain and visualize the concepts of DFT, as well as better understand where others may go wrong.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
