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随着超级计算机硬件和数值算法迅速发展, 使得目前利用密度泛函理论研究上千个原子体系的电子能带和结构等性质变得可行. 数值原子轨道基组由于其基组较小和局域等特性, 可以很好地与电子结构计算中的线性标度算法等的新算法结合, 用来研究较大尺寸的物理体系. 本文详细介绍了一款中国科学技术大学量子信息重点 实验室自主开发的基于数值原子轨道基组的第一性原理计算软件 Atomic-orbital Based Ab-initio Computation at UStc. 大量的测试结果表明: 该软件具有很好的准确性和较高的并行效率, 可以用于包含1000个原子左右的系统的电子结构和原子结构的研究以及分子动力学模拟计算.With the rapid development of supercomputers and the advances of numerical algorithms, nowadays it is possible to study the electronic, structural and dynamical properties of complicated physical systems containing thousands of atoms using density functional theory (DFT). The numerical atomic orbitals are ideal basis sets for large-scale DFT calculations in terms of their small base size and localized characteristic, and can be mostly easily combined with linear scaling methods. Here we introduce a first-principles simulation package “Atomic-orbital Based Ab-initio Computation at UStc (ABACUS)”, developed at the Key Laboratory of Quantum Information, University of Science and Technology of China. This package provides a useful tool to study the electronic, structural and molecular dynamic properties of systems containing up to 1000 atoms. In this paper, we introduce briefly the main algorithms used in the package, including construction of the atomic orbital bases, construction of the Kohn-Sham Hamiltonian in the atomic basis sets, and some details of solving Kohn-Sham equations, including charge mixing, charge extrapolation, smearing etc. We then give some examples calculated using ABACUS: 1) the energy orders of B20 clusters; 2) the structure of bulk Ti with vacancies; 3) the density of states of a model protein; 4) the structure of a piece of DNA containing 12 base pairs, 788 atoms. All results show that the results obtained by ABACUS are in good agreement with either experimental results or results calculated using plane wave basis.
[1] Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864
[2] Kohn W, Sham L J 1965 Phys. Rev. 140 A1133
[3] Goedecker S 1999 Rev. Mod. Phys. 71 1085
[4] Lin L, Lu J F, Car R E W 2009 Phys. Rev. B 79 115133
[5] Lin L, Chen M H, Yang C, He L X 2013 J. Phys.: Condens. Matter 25 295501
[6] Soler J M, Artacho E, Gale J D, García A, Junquera J, Ordejón P, Sánchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
[7] Ozaki T 2003 Phys. Rev. B 67 155108
[8] Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X G, Reuter K, Scheffler M 2009 Comput. Phys. Commun. 180 2175
[9] Chen M H, Guo G C, He L X 2010 J. Phys.: Condens. Matter 22 445501
[10] Chen M H, Guo G C, He L X 2011 J. Phys.: Condens. Matter 23 325501
[11] Hamann D R, Schlter M, Chiang C 1979 Phys. Rev. Lett. 43 1494
[12] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal Corso A, Fabris S, Fratesi G, de Gironcoli S, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Smogunov A, Umari P, Wentzcovitch R M 2009 J. Phys.: Condens. Matter 21 395502
[13] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[14] Grimme S 2006 J. Comput. Chem. 27 1787
[15] Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207
[16] Kleinman L, Bylander D M 1982 Phys. Rev. Lett. 48 1425
[17] Portal D S, Artacho E, Soler J M 1995 Solid State Communications 95 685
[18] Li P F, Liu X H, Chen M H, Lin P Z, Ren X G, Lin L, He L doi:10.1016/j.commatsci.2015.07.004
[19] Frigo M, Johnson S G 2005 Proc. IEEE 93 216
[20] Pulay P 1980 Chem. Phys. Lett. 73 393
[21] Kerker G P 1981 Phys. Rev. B 23 3082
[22] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[23] Alfè D 1999 Comput. Phys. Commun. 118 31
[24] Methfessel M, Paxton A T 1989 Phys. Rev. B 40 3616
[25] (Cleveland: CRC Press) pp411-422
[26] Wang J Y, Zhu S G, Xu C F 2002 Biology Chemistry (Beijing: Higher Education Press) p489
[27] Chattopadhyay B, Mukherjee M 2011 J. Phys. Chem. B 115 1760
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[1] Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864
[2] Kohn W, Sham L J 1965 Phys. Rev. 140 A1133
[3] Goedecker S 1999 Rev. Mod. Phys. 71 1085
[4] Lin L, Lu J F, Car R E W 2009 Phys. Rev. B 79 115133
[5] Lin L, Chen M H, Yang C, He L X 2013 J. Phys.: Condens. Matter 25 295501
[6] Soler J M, Artacho E, Gale J D, García A, Junquera J, Ordejón P, Sánchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
[7] Ozaki T 2003 Phys. Rev. B 67 155108
[8] Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X G, Reuter K, Scheffler M 2009 Comput. Phys. Commun. 180 2175
[9] Chen M H, Guo G C, He L X 2010 J. Phys.: Condens. Matter 22 445501
[10] Chen M H, Guo G C, He L X 2011 J. Phys.: Condens. Matter 23 325501
[11] Hamann D R, Schlter M, Chiang C 1979 Phys. Rev. Lett. 43 1494
[12] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal Corso A, Fabris S, Fratesi G, de Gironcoli S, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Smogunov A, Umari P, Wentzcovitch R M 2009 J. Phys.: Condens. Matter 21 395502
[13] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[14] Grimme S 2006 J. Comput. Chem. 27 1787
[15] Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207
[16] Kleinman L, Bylander D M 1982 Phys. Rev. Lett. 48 1425
[17] Portal D S, Artacho E, Soler J M 1995 Solid State Communications 95 685
[18] Li P F, Liu X H, Chen M H, Lin P Z, Ren X G, Lin L, He L doi:10.1016/j.commatsci.2015.07.004
[19] Frigo M, Johnson S G 2005 Proc. IEEE 93 216
[20] Pulay P 1980 Chem. Phys. Lett. 73 393
[21] Kerker G P 1981 Phys. Rev. B 23 3082
[22] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[23] Alfè D 1999 Comput. Phys. Commun. 118 31
[24] Methfessel M, Paxton A T 1989 Phys. Rev. B 40 3616
[25] (Cleveland: CRC Press) pp411-422
[26] Wang J Y, Zhu S G, Xu C F 2002 Biology Chemistry (Beijing: Higher Education Press) p489
[27] Chattopadhyay B, Mukherjee M 2011 J. Phys. Chem. B 115 1760
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