全纯密度泛函理论
Holomorphic Density Functional Theory
摘要：
用Hartree-Fock（HF）或Kohn-Sham密度泛函理论（KS-DFT）表示的自洽场（SCF）近似都有可能产生多个解。然而，使用HF或KS-DFT确定的多个解决方案之间的正式关系仍然是未知的。通过引入一个参数化的泛函，我们研究了HF或KS-DFT的多个SCF解之间的联系。使用氢分子和电子转移模型，我们连续地将多个解从HF势映射到KS-DFT描述。我们发现，多个解决方案可以合并和消失的功能的变化，形成一个直接的类比，真正的HF解决方案消失沿分子结构的变化。为了克服这种消失的解决方案，我们开发了一个复杂的分析扩展DFT -“全纯DFT”的方法-，允许每个SCF定态解析继续在所有的分子结构和交换相关泛函。
英文摘要：
Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham Density Functional Theory (KS-DFT) both have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parametrised functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT - the "holomorphic DFT" approach - that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals.
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