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类Hartree-Fock方程的数值方法

本站小编 Free考研考试/2021-12-27

林霖
加州大学伯克利分校数学系, 劳伦斯伯克利国家实验室, 美国伯克利, 加利福尼亚 94720
收稿日期:2019-02-28出版日期:2019-06-15发布日期:2019-05-18

作者简介:林霖,加州大学伯克利分校数学系副教授、劳伦斯伯克利国家实验室计算科学部研究员.2007年和2011年分别在北京大学和普林斯顿大学获学士和博士学位;2011-2013年在劳伦斯伯克利国家实验室从事博士后研究工作.主要研究领域为数值分析、计算量子化学、计算材料科学、多尺度建模和并行计算等方面.曾获DOE Early Career Award (2017-2022)、NSF CAREER Award (2017-2022)、SIAM Computational Science and Engineering (CSE) Early Career Prize (2017)和Alfred P.Sloan fellowship (2015-2017)等.截止目前,在SCI期刊上发表学术论文70余篇.
基金资助:美国国家自然科学基金DMS-1652330,美国能源部DE-SC0017867资助项目.


NUMERICAL METHODS FOR HARTREE-FOCK-LIKE EQUATIONS

Lin Lin
Department of Mathematics, University of California, Berkeley, and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Received:2019-02-28Online:2019-06-15Published:2019-05-18







摘要



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本文的主要目的是介绍近年来大基组下的类Hartree-Fock方程数值求解的一些进展.类Hartree-Fock方程出现在Hartree-Fock理论和含杂化泛函的Kohn-Sham密度泛函理论中,是电子结构理论中一类重要的方程.该方程在复杂的化学和材料体系的电子结构计算中有广泛地应用.由于计算代价的原因,类Hartree-Fock方程一般只被用在较小规模的量子体系(含几十到几百个电子)的计算.从数学角度上讲,类Hartree-Fock方程是一个非线性积分-微分方程组,其计算代价主要来自于积分算子的部分,也就是Fock交换算子.通过发展和结合自适应压缩交换算子方法(ACE),投影的C-DⅡS方法(PC-DⅡS)方法,以及插值可分密度近似方法(ISDF),我们大大降低了杂化泛函密度泛函理论的计算代价.以含1000个硅原子的体系为例,我们将平面波基组下的杂化泛函的计算代价降至接近不含Fock交换算子的半局域泛函计算的水平.同时,我们发现类Hartree-Fock方程的数学结构也为一类特征值问题的迭代求解提供了新的思路.
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