一种适于大尺度复杂纳米体系材料模拟的半经验哈密顿方法

虞明; 吴式玉

doi:10.7498/aps.64.187302

摘要

本文综述介绍了近来发展的一种具有可靠性、普适性和预测性的半经验哈密顿方法. 该哈密顿在原子轨道的线性组合(LCAO)框架下同时引入了电荷自洽及环境因素(SCED), 称之为SCED-LCAO哈密顿. 由于SECD-LCAO 哈密顿囊括了电荷自洽重组、电子屏蔽效应以及多体环境的影响, 使得该方法可以更加准确地描述在复杂结构重组中化学键的成键与断键过程. 其动力学计算可用于模拟大尺度复杂纳米体系的结构特性、电子性能以及复杂结构的重组过程. 我们已经用此方法成功地解释了不同种类碳团簇纳米结构的相对稳定性和bucky-diamond结构碳团簇的热力学相变, 揭示了碳管生长的初始机理, 系统地研究了碳化硅纳米线的构型与能量之间的关系及其电子性能, 发现了碳化硅笼状结构的特征, 尤其是碳化硅笼状结构的动力学自动组装功能, 并预示了bucky-diamond结构的碳化硅团簇存在的可能性. 最近, 该方法引入了与环境关联的轨道占据因素, 并成功地运用到研究具有三价电子特性的多构硼元素体系中, 准确地描述了硼元素的复杂化学成键特性、同类异性结构以及不同种类硼团簇纳米结构的相对稳定性.

关键词:

Abstract

The advent of the era of nano-structures has also brought about critical issues regarding the determination of stable structures and the associated properties of such systems. From the theoretical perspective, it requires to consider systems of sizes of up to tens of thousands atoms to obtain a realistic picture of thermodynamically stable nano-structure. This is certainly beyond the scope of DFT-based methods. On the other hand, conventional semi-empirical Hamiltonians, which are capable of treating systems of those sizes, do not possess the rigor and accuracy that can lead to a reliable determination of stable structures in nano-systems. During the last dozen years, extensive effort has been devoted to developing methods that can handle systems of nano-sizes on the one hand, while possess first principles-level accuracy on the other. In this review, we present just such a recently developed and well-tested semi-empirical Hamiltonian, referred in the literature as the SCED-LCAO Hamiltonian. Here SCED is the acronym for self-consistent/environment-dependent while LCAO stands for linear combination of atomic orbitals. Compared to existing conventional two-center semiempirical Hamiltonians, the SCED-LCAO Hamiltonian distinguishes itself by remedying the deficiencies of conventional two-center semi-empirical Hamiltonians on two important fronts: the lack of means to determine charge redistribution and the lack of involvement of multi-center interactions. Its framework provides a scheme to self-consistently determine the charge redistribution and includes multi-center interactions. In this way, bond-breaking and bond-forming processes associated with complex structural reconstructions can be described appropriately. With respect to first principles methods, the SCED-LCAO Hamiltonian replaces the time-consuming energy integrations of the self-consistent loop in first principles methods by simple parameterized functions, allowing a speed-up of the self-consistent determination of charge redistribution by two orders of magnitudes. Thus the method based on the SCED-LCAO is no more cumbersome than the conventional semi-empirical methods on the one hand and can achieve the first principle-level accuracy on the other. The parameters and parametric functions for SCED-LCAO Hamiltonian are carefully optimized to model electron-electron correlations and multi-center interactions in an efficient fitting process including a global optimization scheme. To ensure the transferability of the Hamiltonian, the data base chosen in the fitting process contains large amount of physical properties, including (i) the binding energies, the bond lengths, and the symmetries of various clusters covering not only the ground state but also the excited phases, (ii) the binding energies as a function of atomic volume for various crystal phases including also the high pressure phases, and (iii) the electronic band structures of the crystalline systems. In particular, the data bases for excited phases of clusters and high pressure phases in bulk systems are more important when performing molecular dynamics simulations where correct transferable phases are required, such as the excited phases. The validity and the robustness of the SCED-LCAO Hamiltonian have been tested for more complicated Si-, C-, and B-based systems. The success of the SCED-LCAO Hamiltonian will be elucidated through the following applications: (i) the phase transformations of carbon bucky-diamond clusters upon annealing, (ii) the initial stage of growth of single-wall carbon nanotubes (SWCNTs), (iii) the discovery of bulky-diamond SiC clusters, (iv) the morphology and energetics of SiC nanowires (NWs), and (v) the self-assembly of stable SiC based caged nano-structures. A recent upgrade of the SCED-LCAO Hamiltonian, by taking into account the effect on the atomic orbitals due to the atomic aggregation, will also be discussed in this review. This upgrade Hamiltonian has successfully characterized the electron-deficiency in trivalent boron element captured complex chemical bonding in various boron allotropes, which is a big challenge for semi-empirical Hamiltonians.

Keywords:

semi-empirical Hamiltonian /
charge self-consistency and redistribution /
environment-dependent effect /
large scale and complex nanostructures

作者及机构信息

虞明,
吴式玉

1.
美国肯塔基州路易斯维尔大学物理系, Louisville, Kentucky 40292

通信作者: 虞明, m0yu0001@louisville.edu

基金项目: 美国国家自然科学基金(批准号: NSF-DMR-0112824)、美国能源部研究基金(批准号: DE-FG02-00ER45832)、美国陆军(SMDC)研究基金(批准号: W9113M-04-C-0024) 和美国肯塔基州科学及工程基金(批准号: KSEF-753-RED-007)资助的课题.

Authors and contacts

Yu Ming,
Wu Shi-Yu

1.
Department of Physics and Astronomy, University of Louisville, Kentucky 40292, USA

Corresponding author: Yu Ming, m0yu0001@louisville.edu

Funds: Project supported by the US National Science Fundation (Grant No. NSF-DMR-0112824), the US Department of Energy (Grant No. DE-FG02-00ER45832), the US Army (SMDC) (Grant No. W9113M-04-C-0024), and the Kentucky Science and Engineering Fundation (Grant No. KSEF-753-RED-007).

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施引文献

[1]	Hehre W J, Radom L, Schleyer P V R, Pople J A 1986 Ab Initio Molecular Orbital Theory (New York: John Wiley & Sons)
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[52]	Xin Z H, Zhang C Y, Yu M, Jayanthi C S, Wu S Y 2014 Computat. Mater. Sci. 84 49
[53]	Yu M, Jayanthi C S, Wu S Y 2012 Nanotechnology 23 235705
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