Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chausse 149, 22761 Hamburg, Germany.
J Chem Phys. 2018 Oct 28;149(16):164103. doi: 10.1063/1.5037790.
A detailed account of the Kohn-Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.
这里给出了量子化学中 Kohn-Sham（KS）算法的详细描述，该描述在巴拿赫空间上的凸分析的非常一般的设置中严格制定。从 Levy-Lieb 型泛函出发，通过正则化将其凸和半连续扩展进行正则化以获得可微性。这一层额外的处理使我们能够严格地引入，与常见的未正则化方法相比，定义良好的 KS 迭代方案。然后证明了弱意义上的收敛性。这种广义形式适用于广泛的不同密度泛函理论，甚至可能适用于量子力学之外的模型。
