Expedite random structure searching using objects from Wyckoff positions.

Random structure searching has been proved to be a powerful approach to search and find the global minimum and the metastable structures. A true random sampling is in principle needed yet it would be highly time-consuming and/or practically impossible to find the global minimum for the complicated systems in their high-dimensional configuration space. Thus the implementations of reasonable constraints, such as adopting system symmetries to reduce the independent dimension in structural space and/or imposing chemical information to reach and relax into low-energy regions, are the most essential issues in the approach. In this paper, we propose the concept of "object" which is either an atom or composed of a set of atoms (such as molecules or carbonates) carrying a symmetry defined by one of the Wyckoff positions of space group and through this process it allows the searching of global minimum for a complicated system to be confined in a greatly reduced structural space and becomes accessible in practice. We examined several representative materials, including Cd3As2 crystal, solid methanol, high-pressure carbonates (FeCO3), and Si(111)-7 × 7 reconstructed surface, to demonstrate the power and the advantages of using "object" concept in random structure searching.

[1]  Chris J Pickard,et al.  Ab initio random structure searching , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[2]  R. Needs,et al.  Perspective: Role of structure prediction in materials discovery and design , 2016 .

[3]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Quan Li,et al.  Materials discovery via CALYPSO methodology , 2014, Journal of physics. Condensed matter : an Institute of Physics journal.

[5]  Dinabandhu Das,et al.  Cocrystallization with Acetylene: Molecular Complex with Methanol , 2008 .

[6]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[7]  X. Qi,et al.  Topological insulators and superconductors , 2010, 1008.2026.

[8]  Hong Guo,et al.  Electronic properties of Si(111)- 7 × 7 and related reconstructions: Density functional theory calculations , 2012 .

[9]  R. Needs,et al.  Structures and stability of calcium and magnesium carbonates at mantle pressures , 2014, 1407.3369.

[10]  Yanchao Wang,et al.  Crystal structure prediction via particle-swarm optimization , 2010 .

[11]  J. Zaanen,et al.  Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. , 1995, Physical review. B, Condensed matter.

[12]  Andre K. Geim,et al.  The rise of graphene. , 2007, Nature materials.

[13]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[14]  B. Maté,et al.  Phases of solid methanol. , 2009, The journal of physical chemistry. A.

[15]  A. Oganov,et al.  High-pressure phases of CaCO3: Crystal structure prediction and experiment , 2006 .

[16]  Q. Gibson,et al.  The crystal and electronic structures of Cd(3)As(2), the three-dimensional electronic analogue of graphene. , 2014, Inorganic chemistry.

[17]  Chunzhong Wang,et al.  First-principles study of pressure-induced magnetic transition in siderite FeCO3 , 2012 .

[18]  Q. Williams,et al.  A high-pressure infrared and X-ray study of FeCO3 and MnCO3: comparison with CaMg(CO3)2-dolomite , 2004 .

[19]  J. Behler,et al.  Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential. , 2008, Physical review letters.

[20]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[21]  I. Swainson,et al.  Phase Transitions in Solid Methanol , 2002 .

[22]  Q. Gibson,et al.  The crystal and electronic structures of Cd(3)As(2), the three-dimensional electronic analogue of graphene. , 2013, Inorganic chemistry.

[23]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[24]  S. Goedecker Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. , 2004, The Journal of chemical physics.

[25]  W. Vos,et al.  Structure of crystalline methanol at high pressure , 1998 .

[26]  H. Scheraga,et al.  Global optimization of clusters, crystals, and biomolecules. , 1999, Science.

[27]  O. A. Utas,et al.  Synthesis of two-dimensional TlxBi1−x compounds and Archimedean encoding of their atomic structure , 2016, Scientific Reports.

[28]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[29]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[30]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[31]  S. Tong,et al.  Low‐energy electron diffraction analysis of the Si(111)7×7 structure , 1988 .

[32]  Biswas,et al.  Simulated annealing of silicon atom clusters in Langevin molecular dynamics. , 1986, Physical review. B, Condensed matter.

[33]  Qiang Zhu,et al.  Constrained evolutionary algorithm for structure prediction of molecular crystals: methodology and applications. , 2012, Acta crystallographica. Section B, Structural science.

[34]  Hans Wondratschek,et al.  Bilbao Crystallographic Server: I. Databases and crystallographic computing programs , 2006 .

[35]  A. Laio,et al.  Predicting crystal structures: the Parrinello-Rahman method revisited. , 2002, Physical review letters.

[36]  I. Zeljkovic,et al.  Large single crystal growth, transport property, and spectroscopic characterizations of three-dimensional Dirac semimetal Cd3As2 , 2015, Scientific Reports.

[37]  A. V. Matetskiy,et al.  Atomic structure and electronic properties of the two-dimensional (Au ,Al )/Si (111 )2 ×2 compound , 2015 .

[38]  Joel A. Kubby,et al.  Scanning tunneling microscopy of semiconductor surfaces , 1996 .

[39]  T. Ohta,et al.  Quasiparticle dynamics in graphene , 2007 .

[40]  G. A. Steigmann,et al.  The crystal structure of Cd3As2 , 1968 .

[41]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[42]  Nikolaus Hansen,et al.  USPEX - Evolutionary crystal structure prediction , 2006, Comput. Phys. Commun..

[43]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[44]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[45]  J. Kuo,et al.  Structure prediction of the solid forms of methanol: an ab initio random structure searching approach. , 2016, Physical chemistry chemical physics : PCCP.

[46]  T. Harman,et al.  Cd3As2—A Noncubic Semiconductor with Unusually High Electron Mobility , 1959 .

[47]  K. Takayanagi,et al.  Structural analysis of Si(111)‐7×7 by UHV‐transmission electron diffraction and microscopy , 1985 .

[48]  A. A. Alekseev,et al.  Electronic band structure of a Tl/Sn atomic sandwich on Si(111) , 2015 .

[49]  Chris J Pickard,et al.  High-pressure phases of silane. , 2006, Physical review letters.

[50]  Xin Zhao,et al.  New layered structures of cuprous chalcogenides as thin film solar cell materials: Cu2Te and Cu2Se. , 2013, Physical review letters.

[51]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[52]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[53]  Yanming Ma,et al.  First-principles structural design of superhard materials. , 2013, The Journal of chemical physics.

[54]  Li Zhu,et al.  CALYPSO: A method for crystal structure prediction , 2012, Comput. Phys. Commun..

[55]  Saïd Salhi,et al.  Strategies for increasing the efficiency of a genetic algorithm for the structural optimization of nanoalloy clusters , 2005, J. Comput. Chem..

[56]  Jooyoung Lee,et al.  Ab initio materials design using conformational space annealing and its application to searching for direct band gap silicon crystals , 2016, Comput. Phys. Commun..

[57]  A. Saranin,et al.  Effect of Surface Potential Relief on Forming Molecular Arrays: Tryptanthrin Adsorbed on Various Si(111) Reconstructions , 2010 .

[58]  A. A. Alekseev,et al.  Low-temperature one-atom-layer 7×7-In phase on Si(111) , 2016 .

[59]  V. Prakapenka,et al.  High-Pressure Orthorhombic Ferromagnesite as a Potential Deep-Mantle Carbon Carrier , 2015, Scientific Reports.

[60]  F. Stillinger Exponential multiplicity of inherent structures , 1999 .

[61]  Scott Kirkpatrick,et al.  Optimization by simulated annealing: Quantitative studies , 1984 .

[62]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[63]  Hans Wondratschek,et al.  Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups. , 2006, Acta crystallographica. Section A, Foundations of crystallography.

[64]  Mohamed E. El-Hawary,et al.  A Survey of Particle Swarm Optimization Applications in Electric Power Systems , 2009, IEEE Transactions on Evolutionary Computation.

[65]  Artem R. Oganov,et al.  Structure prediction and its applications in computational materials design , 2015 .

[66]  A. Oganov,et al.  Evolutionary crystal structure prediction as a tool in materials design , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[67]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[68]  K. Knight,et al.  Thermal expansion of gypsum investigated by neutron powder diffraction , 1996 .