SCF algorithms for HF electronic calculations
SCF algorithms for HF electronic calculations
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DOI：
10.1007/978-3-642-57237-1_2
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
É. Cancès
中科院分区：
文献类型：
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作者：
É. Cancès
本文给出了求解Hartree-Fock问题的SCF算法的一些数学结果。在文章的第一部分，重点是两个经典的SCF程序，即Roothaan算法和电平移位算法。证明了Roothaan算法要么收敛于Hartree-Fock方程的解，要么在两个不是Hartree-Fock方程解的状态之间振荡，任何其他行为（两个以上状态之间的振荡，“混沌”行为，…）被排除在外。然后，电平移位算法被证明是收敛的足够大的移位参数，无论初始猜测。文章的第二部分详细介绍了一个新的算法最近推出的Le Bris和作者，所谓的最佳阻尼算法（ODA）的收敛特性。还提供了基本的数值模拟，指出研究中的各种算法的主要特点。
This paper presents some mathematical results on SCF algorithms for solving the Hartree-Fock problem. In the first part of the article the focus is on two classical SCF procedures, namely the Roothaan algorithm and the level-shifting algorithm. It is demonstrated that the Roothaan algorithm either converges towards a solution to the Hartree-Fock equations or oscillates between two states which are not solution to the Hartree-Fock equations, any other behavior (oscillations between more than two states, “chaotic” behavior, ... ) being excluded. The level-shifting algorithm is then proved to converge for large enough shift parameter, whatever the initial guess. The second part of the article details the convergence properties of a new algorithm recently introduced by Le Bris and the author, the so-called Optimal Damping Algorithm (ODA). Basic numerical simulations pointing out the principal features of the various algorithms under study are also provided.