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10计算材料物理-第四章_图文

计算材料物理
专题 结构搜索和预测2

Why is Structure Prediction Hard?
Energy

Local minima
Global minimum True structure Atomic positions

? Accurate Potential Energy Surface ---- ab initio ? Huge number of local minima ---- how?

随机抽样方法
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Random Sampling methods involve in the random generation of a large number of structures on PES; AIRSS (ab initio random structure searching)

http://www.cmmp.ucl.ac.uk/~ajm/airss/airss.html http://iopscience.iop.org/0953-8984/23/5/053201

翻越势垒方法
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模拟退火算法(simulated annealing; SA) 盆地跳算法(Basin-hopping) minima hopping metadynamics algorithm

模拟退火算法

minima hopping

Basin hopping

metadynamics

演化(进化)算法
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遗传算法(genetic algorithms; GA) 粒子群优化算法(particle swarm optimization; PSO) 蚁群优化算法(ant colony optimization; ACO)

遗传算法

Swarm Intelligence 群体智能
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Swarm可被描述为一些相互作用相邻个体的集合体,蜂 群、蚁群、鸟群都是Swarm的典型例子。 鱼聚集成群可以有效地逃避捕食者,因为任何一只鱼发 现异常都可带动整个鱼群逃避。 蚂蚁成群则有利于寻找食物,因为任一只蚂蚁发现食物 都可带领蚁群来共同搬运和进食。 一只蜜蜂或蚂蚁的行为能力非常有限,它几乎不可能独 立存在于自然世界中,而多个蜜蜂或蚂蚁形成的Swarm 则具有非常强的生存能力,且这种能力不是通过多个个 体之间能力简单叠加所获得的。 社会性动物群体所拥有的这种特性能帮助个体很好地适 应环境,个体所能获得的信息远比它通过自身感觉器官 所取得的多,其根本原因在于个体之间存在着信息交互 能力。

粒子群优化算法 ( Particle Swarm Optimization)
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1995年由J. Kennedy, R. C. Eberhart等人提出 该算法最初是受到鸟群活动的规律性启发,进而利用群体 智能建立的一个简化模型。粒子群优化算法利用群体中的 个体对信息的共享使整个群体的运动在问题求解空间中产 生从无序到有序的演化过程,从而获得最优解。 PSO同遗传算法类似,是一种基于迭代的优化算法。系统 初始化为一组随机解,通过迭代搜寻最优值。但是它没有 遗传算法用的交叉(crossover)以及变异(mutation),而是 粒子在解空间追随最优的粒子进行搜索。同遗传算法比较, PSO的优势在于简单容易实现并且没有许多参数需要调整。 目前已广泛应用于函数优化,神经网络训练,模糊系统控 制以及其他遗传算法的应用领域。

结构搜索和预测程序
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AIRSS
Ab initio Random Structure Searching

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GASP
Genetic Algorithm for Structure and Phase Prediction

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CALYPSO
Crystal structure AnaLYsis by Particle Swarm Optimization

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USPEX
Universal Structure Predictor: Evolutionary Xtallography

http://www.cmmp.ucl.ac.uk/~ajm/airss/airss.html

Chris J Pickard

State University of New York at Buffalo

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XtalOpt is a free and truly open source evolutionary algorithm designed to predict crystal structures. It is implemented as an extension to the Avogadro molecular editor. XtalOpt runs on a workstation and supports using GULP, VASP, pwSCF (Quantum ESPRESSO), and CASTEP for geometry optimizations.

http://xtalopt.openmolecules.net/wiki/index.fcgi/ http://avogadro.cc/wiki/Main_Page David C. Lonie, Eva Zurek; XtalOpt: An Open-Source Evolutionary Algorithm for Crystal Structure Prediction, Computer Physics Communications 182 (2011) pp. 372-387

http://xtalopt.openmolecules.net/globalsearch/docs/tut-xo.html

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The Genetic algorithm for structure prediction – GASP – predicts the structure and composition of stable and metastable phases of crystals, molecules, atomic clusters and defects from firstprinciples. The GASP program is interfaced to many energy codes including: VASP, LAMMPS, MOPAC, Gulp, JDFTx and can efficiently run on parallel architectures.

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CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) is an efficient structure prediction method and its same-name computer software. The CALYPSO package is protected by the Copyright Protection Center of China with the registration No. 2010SR028200 and classification No. 61000-7500. Freely distributed on Academic use under the regulations termed in the CALYPSO_LICENCE.

http://www.calypso.cn/

马琰铭 教授 吉林大学 超硬材料国家重点实验室

王彦超

吕健

朱黎

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WHAT IS THE FEATURE? Predictions of the energetically stable/metastable structures at given chemical compositions and external conditions (e.g., pressure) for clusters, 2D layers, surfaces, and 3D crystals. Design of novel functional materials, e.g., superhard materials. Options for the structural evolutions using global or local PSO. Structure searches with automatic variation of chemical compositions. Structure predictions with fixed cell parameters, or fixed space groups, or fixed molecules. CALYPSO is currently interfaced with GAUSSIAN, DFTB+, VASP, CASTEP, Quantum Espresso, GULP, SIESTA and CP2K codes. The interface with other total energy codes can also be implemented by users' request.

CALYPSO

History of CALYPSO
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The CALYPSO team independently initialized the idea of applying PSO algorithm into structure prediction in 2006 (Ma and Wang) first application of PSO algorithm into structure prediction of 3D crystals by Wang, Lv, Zhu & Ma in 2010, 2D layers by Wang, Miao, et al, in 2012 2D surface reconstruction by Lu et al, in 2014 Structure searching efficiencies of isolated systems have been substantially improved by the CALYPSO team (Lv, Wang, Zhu & Ma) in 2012, where the success of this application has been backed up with the introduction of various efficient techniques (e.g., bond characterization matrix for fingerprinting structures, symmetry constraints on structure generation, etc.).

Major Techniques Employed
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Structural evolution through PSO algorithm. PSO is best-known for its ability to conquer large barriers of energy landscapes by making use of the swarm intelligence and by self-improving structures. Both global and local PSO algorithms have been implemented. The global PSO has the advantage of fast convergence, while local PSO is good at avoiding premature convergence and thus enhance the capability of CALYPSO in dealing with more complex systems.

Major Techniques Employed
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Symmetry constraints during structure generation to reduce searching space and enhance the structural diversity. Structural characterization techniques to eliminate similar structures, define nonflying areas, enhance searching efficiency, and divide energy surfaces for local PSO searching. (i) bond characterization matrix technique (ii) atom-centered symmetrical function technique

Major Techniques Employed
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Introducing new structures per generation with controllable percentage to enhance structural diversity. Interface to a number of local structural optimization codes varying from highly accurate DFT methods to fast semiempirical approaches that can deal with large systems. Local structural optimization enables the reduction of noise of energy surfaces and the generation of physically justified structures.

methodologies in CALYPSO
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Crystal structure prediction: Yanchao Wang, Jian Lv, Li Zhu, and Yanming Ma Crystal Structure Prediction via Particle Swarm Optimization Phys. Rev. B 82, 094116 (2010) Yanchao Wang, Jian Lv, Li Zhu, and Yanming Ma CALYPSO: A method for crystal structure prediction Comput. Phys. Commun. 183, 2063 (2012) Cluster structure prediction: Jian Lv, Yanchao Wang, Li Zhu, and Yanming Ma Particle-swarm structure prediction on clusters J. Chem. Phys. 137, 084104 (2012) Two-Dimensional layer structure prediction: Yanchao Wang, Maosheng Miao, Jian Lv, Li Zhu, Ketao Yin, Hanyu Liu, and Yanming Ma An effective structure prediction method for layered materials based on 2D particle swarm optimization algorithm J. Chem. Phys. 137, 224108 (2012) Superhard Materials Design: Xinxin Zhang, Yanchao Wang, Jian Lv, Chunye Zhu, Qian Li, Miao Zhang, Quan Li and Yanming Ma First-principles structural design of superhard materials J. Chem. Phys. 138, 114101 (2013)

Generation of structures with the constraint of symmetry

Bond characterization matrix (BCM)
The average over all bonds formed by types A and B atoms can be derived by

In order to avoid the dependence on the choice of reference frame, it is important to consider the rotationally invariant combinations

the similarity of two structures can be quantitatively represented by the Euclidean distance between their BCMs

penalty function technique

a certain number of high-energy structures are rejected, and the remaining low energy structures

Introducing new structures to enhance diversity

Successful of CALYPSO
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The CALYPSO method, packed with the PSO algorithm and many enhancement techniques, is successful in solving numerous structural problems. As a result, CALYPSO has received world-wide attention. Till the middle of 2014, there are more than six hundreds registered users of CALYPSO, distributed over 40 different countries. In only 4 years, the success of CALYPSO code has been recorded in over 100 high-profile publications, including a number of papers in Nat. Chem., Nat. Commun., PNAS, PRL, JACS, Angew. Chem. Int. Edit., etc.

USPEX (Universal Structure Predictor: Evolutionary Xtallography...and in Russian "uspekh" means "success" owing to the high success rate and many useful results produced by this method!) is a method developed jointly by Artem R. Oganov, Andriy O. Lyakhov, Colin W. Glass, Qiang Zhu, and others implemented in the same-name code. http://uspex.stonybrook.edu/uspex.html

Artem R. Oganov

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Prediction of the stable and metastable structures knowing only the chemical composition. Simultaneous searches for stable compositions and structures are also possible. Incorporation of partial structural information is possible ? constraining search to fixed experimental cell parameters, or fixed cell shape, or fixed cell volume, ? starting structure search from known or hypothetical structures, ? assembling crystal structures from predefined molecules, including flexible molecules. efficient constraint techniques, which eliminate unphysical and redundant regions of the search space. Cell reduction technique (Oganov & Glass, 2008). niching using fingerprint functions (Oganov & Valle, 2009; Lyakhov, Oganov, Valle, 2010).

Features of the USPEX

Features of the USPEX
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initialization using fully random approach, or using space groups and cell splitting techniques (Lyakhov, Oganov, Valle, 2010) on-the-flight analysis of results - determination of space groups (and output in CIF-format), calculation of the hardness, order parameters, etc. prediction of the structure of nanoparticles and surface reconstructions restart facilities, enabling calculations to be continued from any point along the evolutionary trajectory powerful visualization and analysis techniques implemented in the STM4 code (by M.Valle), fully interfaced with USPEX.

Features of the USPEX
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USPEX is interfaced with VASP, SIESTA, GULP, DMACRYS, CP2k, QuantumEspresso codes. Interfacing with other codes is easy. submission of jobs from local workstation to remote clusters and supercomputers is possible. options for structure prediction using the USPEX algorithm (default), random sampling, corrected particle swarm optimization, evolutionary metadynamics, minima hopping-like algorithm. Capabilities to predict phase transition mechanisms using evolutionary metadynamics, variable-cell NEB method, and TSP method. options to optimize physical properties other than the energy - e.g., hardness (Lyakhov & Oganov, 2011), density (Zhu et al., 2011), and various electronic properties.

methodologies in USPEX
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Oganov A.R., Glass C.W. (2006). Crystal structure prediction using evolutionary algorithms: principles and applications. J. Chem. Phys. 124, art. 244704 (pdf-file). Glass C.W., Oganov A.R., Hansen N. (2006). USPEX – evolutionary crystal structure prediction. Comp. Phys. Comm. 175, 713-720 (pdf-file). Oganov A.R., Ma Y., Lyakhov A.O., Valle M., Gatti C. (2010). Evolutionary crystal structure prediction as a method for the discovery of minerals and materials. Rev. Mineral. Geochem. 71, 271-298 (pdf-file). Lyakhov A.O., Oganov A.R., Valle M. (2010). How to predict very large and complex crystal structures. Comp. Phys. Comm. 181, 1623-1632 (pdf-file). Oganov A.R., Lyakhov A.O., Valle M. (2011). How evolutionary crystal structure prediction works - and why. Acc. Chem. Res. 44, 227-237 (pdffile). Lyakhov A.O., Oganov A.R., Stokes H.T., Zhu Q. (2013). New developments in evolutionary structure prediction algorithm USPEX. Comp. Phys. Comm. 184, 1172-1182 (pdf-file).

网络资源
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A. R. Oganov, ed. (2010). Modern Methods of Crystal Structure Prediction. Berlin: Wiley-VCH. ISBN 978-3-527-40939-6. http://uspex.stonybrook.edu/ http://www.nwpu.edu.cn/info/1161/10733.htm

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