Ayers Paul W, Yang Weitao
Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
J Chem Phys. 2006 Jun 14;124(22):224108. doi: 10.1063/1.2200884.
We provide a rigorous proof that the Hohenberg-Kohn theorem holds for spin densities by extending Lieb's Legendre-transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital's energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund's rules and holes below the Fermi level.
我们通过将李布的勒让德变换公式扩展到自旋密度，给出了 Hohenberg-Kohn 定理对自旋密度成立的严格证明。由此产生的自旋密度泛函理论解决了几个棘手问题。最重要的是，本文给出了沿绝热连接曲线任意点处自旋势的显式构造，从而为在 Kohn-Sham 密度泛函理论（DFT）中使用自旋密度的交换关联泛函提供了形式基础。考虑了这一结果对无限制 Kohn-Sham DFT 计算的实际影响，并讨论了费米能级以下空穴的存在性。我们认为，一个轨道的能量会随着其占据数的增加而趋于升高，这为确定 Kohn-Sham DFT 中占据数的计算算法提供了基础，并有助于解释洪德规则的起源以及费米能级以下空穴的成因。
