Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

doi:10.1088/1674-1056/ad655a

中国物理B ›› 2024, Vol. 33 ›› Issue (10): 107101-107101.doi: 10.1088/1674-1056/ad655a

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

Guangdi Zhang(张广迪)¹, Li Mao(毛力)^1,2,†, and Hongxing Xu(徐红星)^1,2,3,4,‡

1 School of Physics and Technology, Wuhan University, Wuhan 430070, China;
2 Wuhan Institute of Quantum Technology, Wuhan 430205, China;
3 School of Microelectronics, Wuhan University, Wuhan 430072, China;
4 Henan Academy of Sciences, Zhengzhou 450046, China

收稿日期:2024-05-21 修回日期:2024-07-11 接受日期:2024-07-19 出版日期:2024-10-15 发布日期:2024-10-15
通讯作者: Li Mao, Hongxing Xu E-mail:maoli@whu.edu.cn;hxxu@whu.edu.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0211303) and the National Natural Science Foundation of China (Grant No. 91850207).

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

Guangdi Zhang(张广迪)¹, Li Mao(毛力)^1,2,†, and Hongxing Xu(徐红星)^1,2,3,4,‡

1 School of Physics and Technology, Wuhan University, Wuhan 430070, China;
2 Wuhan Institute of Quantum Technology, Wuhan 430205, China;
3 School of Microelectronics, Wuhan University, Wuhan 430072, China;
4 Henan Academy of Sciences, Zhengzhou 450046, China

Received:2024-05-21 Revised:2024-07-11 Accepted:2024-07-19 Online:2024-10-15 Published:2024-10-15
Contact: Li Mao, Hongxing Xu E-mail:maoli@whu.edu.cn;hxxu@whu.edu.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0211303) and the National Natural Science Foundation of China (Grant No. 91850207).

摘要/Abstract

摘要： In real space density functional theory calculations, the effective potential depends on the electron density, requiring self-consistent iterations, and numerous integrals at each step, making the process time-consuming. In our research, we propose an optimization method to expedite density functional theory (DFT) calculations for systems with large aspect ratios, such as metallic nanorods, nanowires, or scanning tunneling microscope tips. This method focuses on employing basis set to expand the electron density, Coulomb potential, and exchange-correlation potential. By precomputing integrals and caching redundant results, this expansion streamlines the integration process, significantly accelerating DFT computations. As a case study, we have applied this optimization to metallic nanorod systems of various radii and lengths, obtaining corresponding ground-state electron densities and potentials.

关键词: density functional theory, basis set, integrals precomputation, nanorod

Abstract: In real space density functional theory calculations, the effective potential depends on the electron density, requiring self-consistent iterations, and numerous integrals at each step, making the process time-consuming. In our research, we propose an optimization method to expedite density functional theory (DFT) calculations for systems with large aspect ratios, such as metallic nanorods, nanowires, or scanning tunneling microscope tips. This method focuses on employing basis set to expand the electron density, Coulomb potential, and exchange-correlation potential. By precomputing integrals and caching redundant results, this expansion streamlines the integration process, significantly accelerating DFT computations. As a case study, we have applied this optimization to metallic nanorod systems of various radii and lengths, obtaining corresponding ground-state electron densities and potentials.

Key words: density functional theory, basis set, integrals precomputation, nanorod

中图分类号: (Density functional theory, local density approximation, gradient and other corrections)

71.15.Mb

02.60.Pn (Numerical optimization) 81.16.-c (Methods of micro- and nanofabrication and processing)

Guangdi Zhang(张广迪), Li Mao(毛力), and Hongxing Xu(徐红星). Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems[J]. 中国物理B, 2024, 33(10): 107101-107101.

Guangdi Zhang(张广迪), Li Mao(毛力), and Hongxing Xu(徐红星). Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems[J]. Chin. Phys. B, 2024, 33(10): 107101-107101.

参考文献

[1] Engel E 2011 Density functional theory (Berlin: Springer) pp. 109-169
[2] Li Z Z 2002 Solid State Theory (Beijing: Higher Education Press) pp. 329-341 (in Chinese)
[3] Burke K 2012 J. Chem. Phys. 136 150901
[4] Argaman N and Makov G 2000 Am. J. Phys. 68 69
[5] Runge E and Gross E K 1984 Phys. Rev. Lett. 52 997
[6] Marques M A and Gross E K 2004 Annu. Rev. Phys. Chem. 55 427
[7] Jia W L, Cao Z Y, Wang L, Fu J Y, Chi X B, Gao W G and Wang L W 2013 Comput. Phys. Commun. 184 9
[8] Jia W L, Fu J Y, Cao Z Y, Wang L, Chi X B, Gao W G and Wang L W 2013 J. Comput. Phys. 251 102
[9] Nitsche M A, Ferreria M, Mocskos E E and Gonzalez Lebrero M C 2014 J. Chem. Theory Comput. 10 959
[10] Ratcliff L E, Degomme A, Flores-Livas J A, Goedecker S and Genovese L 2018 J. Phys.: Condens. Matter 30 095901
[11] Das S, Motamarri P, Subramanian V, Rogers D M and Gavini V 2022 Comput. Phys. Commun. 280 108473
[12] Politzer P and Seminario J M 1995 Modern density functional theory: a tool for chemistry (Amsterdam: Elsevier) pp. 3-11
[13] Ghosh S K and Pal T 2007 Chem. Rev. 107 4797
[14] Romero I, Aizpurua J, Bryant G W and De Abajo F J G 2006 Opt. Express 14 9988
[15] Schuller J A, Barnard E S, Cai W, Jun Y C, White J S and Brongersma M L 2010 Nat. Mater. 9 193
[16] Baumberg J J, Aizpurua J, Mikkelsen M H and Smith D R 2019 Nat. Mater. 18 668
[17] Benz F, Schmidt M K, Dreismann A, Chikkaraddy R, Zhang Y, Demetriadou A, Carnegie C, Ohadi H, De Nijs B, Esteban R, Aizpurua J and Baumberg J J 2016 Science 354 726
[18] Hao E and Schatz G C 2004 J. Chem. Phys. 120 357
[19] Xu H X, Bjerneld E J, Kll M and Brjesson L 1999 Phys. Rev. Lett. 83 4357
[20] Michaels A M, Jiang J and Brus L 2000 J. Phys. Chem. B 104 11965
[21] Chen H J, Shao L, Li Q and Wang J F 2013 Chem. Soc. Rev. 42 2679
[22] Pines D 1953 Phys. Rev. 92 626
[23] Hopfield J 1958 Phys. Rev. 112 1555
[24] Elson J and Ritchie R 1971 Phys. Rev. B 4 4129
[25] Waks E and Sridharan D 2010 Phys. Rev. A 82 043845
[26] Li Z P and Xu H X 2007 J. Quant. Spectrosc. Radiat. Transfer 103 394
[27] Flatau P J, Fuller K A and Mackowski D W 1993 Appl. Opt. 32 3302
[28] Futamata M, Maruyama Y and Ishikawa M 2003 J. Phys. Chem. B 107 7607
[29] Mao L, Li Z P, Wu B and Xu H X 2009 Appl. Phys. Lett. 94 243102
[30] Zuloaga J, Prodan E and Nordlander P 2009 Nano Lett. 9 887
[31] Suo P F, Mao L, Shi J and Xu H X 2022 Nanomaterials 12 1746

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xianyong Ding(丁献勇), Haoran Wei(魏皓然), Ruixiang Zhu(朱瑞翔), Xiaoliang Xiao(肖晓亮), Xiaozhi Wu(吴小志), and Rui Wang(王锐). Half-metallic ferromagnetic Weyl fermions related to dynamic correlations in the zinc-blende compound VAs[J]. 中国物理B, 2024, 33(9): 97103-097103.
[2]	C. S. Gomes, F. E. Jorge, and A. Canal Neto. All-electron basis sets for H to Xe specific for ZORA calculations: Applications in atoms and molecules[J]. 中国物理B, 2024, 33(8): 83101-083101.
[3]	Aming Lin(林啊鸣), Jing Shi(石晶), Su-Huai Wei(魏苏淮), and Yi-Yang Sun(孙宜阳). Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes[J]. 中国物理B, 2024, 33(8): 86601-086601.
[4]	Kaiyan Zhang(张凯彦), Peng Song(宋朋), Fengcai Ma(马凤才), and Yuanzuo Li(李源作). Rational molecular engineering towards efficient heterojunction solar cells based on organic molecular acceptors[J]. 中国物理B, 2024, 33(6): 68402-068402.
[5]	Zongli Sun(孙宗利), Yanshuang Kang(康艳霜), and Yanmei Kang(康艳梅). Local thermal conductivity of inhomogeneous nano-fluidic films:A density functional theory perspective[J]. 中国物理B, 2024, 33(4): 46503-046503.
[6]	Yuhui Song(宋玉慧), Yifei Cao(曹逸飞), Sichen Huang(黄思晨), Kaichao Li(李凯超), Ruhai Du(杜如海), Lei Yan(严蕾), Zhengkun Fu(付正坤), and Zhenglong Zhang(张正龙). Plasmon-induced nonlinear response on gold nanoclusters[J]. 中国物理B, 2024, 33(4): 44204-044204.
[7]	Yuhui Song(宋玉慧), Yirui Lu(芦一瑞), Axin Guo(郭阿鑫), Yifei Cao(曹逸飞), Jinping Li(李金萍), Zhengkun Fu(付正坤), Lei Yan(严蕾), and Zhenglong Zhang(张正龙). Microscopic mechanism of plasmon-mediated photocatalytic H₂ splitting on Ag-Au alloy chain[J]. 中国物理B, 2024, 33(3): 33101-033101.
[8]	Xiao-Dong Liu(刘晓东), Qi-Liang Lu(卢其亮), and Qi-Quan Luo(罗其全). Structure, electronic, and nonlinear optical properties of superalkaline M₃O (M = Li, Na) doped cyclo[18]carbon[J]. 中国物理B, 2024, 33(2): 23601-023601.
[9]	Jun Deng(邓俊), Jinbo Pan(潘金波), and Shixuan Du(杜世萱). Databases of 2D material-substrate interfaces and 2D charged building blocks[J]. 中国物理B, 2024, 33(2): 26101-026101.
[10]	Xin Qu(瞿鑫), Peng Xu(许鹏), Zhiyong Liu(刘志勇), Jintao Wang(王金涛), Fei Wang(王飞), Wei Huang(黄威), Zhongxin Li(李忠星), Weichang Xu(徐卫昌), and Xinguo Ren(任新国). Charge self-consistent dynamical mean field theory calculations in combination with linear combination of numerical atomic orbitals framework based density functional theory[J]. 中国物理B, 2024, 33(10): 107106-107106.
[11]	Zuo Li(李佐), Mingxia Shi(石明霞), Gang Yao(姚钢), Minlong Tao(陶敏龙), and Junzhong Wang(王俊忠). Epitaxial growth of ultrathin gallium films on Cd(0001)[J]. 中国物理B, 2024, 33(1): 18101-18101.
[12]	Su-Yu Xu(徐宿雨), Miao Yu(于淼), Dong-Yang Yuan(袁东阳), Bo Peng(彭博), Lei Yuan(元磊), Yu-Ming Zhang(张玉明), and Ren-Xu Jia(贾仁需). Physical mechanism of oxygen diffusion in the formation of Ga₂O₃ Ohmic contacts[J]. 中国物理B, 2024, 33(1): 17302-17302.
[13]	Man Liu(刘曼), Zishuang Cheng(程子爽), Xiaoming Zhang(张小明), Yefeng Li(李叶枫), Lei Jin(靳蕾),Cong Liu(刘丛), Xuefang Dai(代学芳), Ying Liu(刘影), Xiaotian Wang(王啸天), and Guodong Liu(刘国栋). Two-dimensional dumbbell silicene as a promising anode material for (Li/Na/K)-ion batteries[J]. 中国物理B, 2023, 32(9): 96303-096303.
[14]	Antônio Canal Neto, Francisco E. Jorge, and Henrique R. C. da Cruz. All-electron ZORA triple zeta basis sets for the elements Cs-La and Hf-Rn[J]. 中国物理B, 2023, 32(9): 93101-93101.
[15]	Lei-Lei Tang(唐雷雷), Shun-Ping Shi(史顺平), Yong Song(宋永), Jia-Bao Hu(胡家宝), Kai Diao(刁凯), Jing Jiang(蒋静), Zhan-Jiang Duan(段湛江), and De-Liang Chen(陈德良). Hydrogen evolution reaction between small-sized Zr_n (n = 2–5) clusters and water based on density functional theory[J]. 中国物理B, 2023, 32(6): 66106-066106.