趋于线性标度的增长法:基于局域定域分子轨道的双电子积分（英文）  

Elongation toward linear scaling:Two electron integrals in regionally localized molecular orbital basis

作　　者：PRICE David R 彭亮[1] 李少鹏 顾凤龙[1] AOKI Yuriko PRICE David R;PENG Liang;LI Shaopeng;GU Fenglong;AOKI Yuriko(Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China;Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan;Japan Science and Technology Agency, CREST,Kawaguchi, Saitama 332-0012, Japan)

机构地区：[1]环境理论化学教育部重点实验室∥华南师范大学化学与环境学院,广东广州510006 [2]日本九州大学工学院材料科学系 [3]日本科学技术厅

出　　处：《中山大学学报（自然科学版）》2019年第1期91-102,共12页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(21403075,21673085);日本科技厅战略创造研究推进事业;中国博士后基金

摘　　要：基于哈特里-福克的增长法与量子快速多极展开方法相结合对大体系的计算可以达到线性标度。然而,只要把双电子积分从原子轨道转换到定域轨道,然后直接从定域分子轨道构建福克矩阵是更加简单的方法。增长法采用截断的手段剔除那些不需要转换的积分从而每一步增长法的计算量几乎不变,这些手段包括采用舒瓦茨不等式、分子轨道系数的筛选、以及利用杂化轨道等可进一步减少双电子转换的数目。对水分子链体系的测试证明线性标度是可以达到的。这个新方法表明如果一个相互作用区域不超过120个定域分子轨道,它就比从原子轨道构建福克矩阵的方法更有效率。Elongation Hartree-Fock (ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However, it is a simpler method to form the Fock matrix directly from localized molecular orbitals, which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step, almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality, molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.

关 键 词：线性表度 增长法 定域轨道 

分 类 号：O641.122[理学—物理化学]