Random Strategy For Crystal Structure Prediction Based On Group And Graph Theory

Functional materials are very important for solving energy crisis,environmental problems and information needs.As the most basic concept in condensed matter physics,crystal structure is a mathematical description for crystal materials.It determines almost all the physical and chemical properties of materials,and is the basis in theoretical predicting of material properties.The development of computer hardware and software,as well as the development of condensed matter physics theory,especially the emergence of large-scale high-performance computing cluster and density functional theory based first principles method,endow people the ability to analyze the crystal structures of materials based on experimental data and predict potential crystal structures with computer,which helps to accelerate the experimental exploring for new functional materials and reduces the development time and costs.In the past decades,many theories,methods and software have been developed in crystal structure predicting.They play an important role by helping theorists to analyze crystal structure of old phase and guiding the experimenters to explore new possible material phases.Because of the time-consuming of energy calculation,as the atomic number increase,the state space of structure becomes very large,and the corresponding high-dimensional energy surface becomes very complex,which leads to the difficulty for existing structural prediction methods based on random sampling strategy or evolutionary strategy.The structural prediction of large-scale system is still challenging.Therefore,developing new crystal structure prediction methods is necessary.In this paper,we propose a new method for crystal prediction based on random strategy combining with group and graph theory and develop the corresponding code RG2.RG2 generates random initial structures according to symmetry and establishes its quotient graph according to"proximity principle"with distance matrix.It then optimizes the initial structure by keeping"quotient graph",in which way it can efficiently generate reasonable crystal structure with well-defined structural feature.Our method transforms the structure prediction in real space into quotient graph prediction in logical space.The quotient graph is considered as a criterion to eliminate the unreasonable initial structures,and the requirement of"quotient graph"conservation is used as"geometric potential"to quickly optimize the initial structure,crossing the real barrier,to the nearby low energy local state.RG2 provides 3 random searching mode:normal random mode,frame random mode and initial structure random mode,and can help users to predict new crystal structure,edge or surface reconstruction,interface reconstruction or super lattice,defect or doping configurations,phase transition and path.RG2 can be used to solve problems in condensed matter physics and computational materials science in crystal structure predicting and functional materials designing.We also studied the possibility and performance of our new method with RG2 in several different systems:1.Three dimensional all sp~3 carbon crystals:we use RG2 to randomly search the structures in space groups 75 to 230,and get 281 new diamond-like structures,among which 129 are more than 40 atoms per cell,35 are more than 100,and 5 are more than 200;The search results demonstrate the search ability and efficiency of RG2.In addition,RG2find three new 3D 4-coordination periodic networks which are all stable as group IV elemental crystals.Among them,I-43d as carbon crystal is a super-hard transparent material with the largest band gap in the known carbon structure.2.Two dimensional planar all sp~2 carbon crystals:the extended RG2 is used to systematically search for 2D graphene allotropes,and many new low-energy 2D sp~2carbons were found,including the Dirac-cone semi-metal SW-graphene with“magic-stability”,and the intrinsic type-III Dirac-cone semi-metal SW40 with remarkable stability.We then use RG2 to systematically search 2D sp~2 carbons through a high-throughput searching,and got 1116 new graphene allotropes.Based on optimized TB parameters with excellent portability,we then calculate the band structure of all the new structures and the known old ones.The results show that there are 206(16 old)semi-metals,269(28 old)semiconductors and 761(76 old)metals.Especially,we find 2new Dirac-nodal-loop semi-metals,which have never been reported in 2D sp~2 carbons.3.Two dimensional sp-sp~2 carbon structures:by considering the mixed sp-sp~2 bonds in 2D carbons,RG2 find 48 new 2D graphyne allotropes.We then calculated their stabilities and basic physical properties by first principles method.The results show that there are four new graphyne allotropes possess energetic stability superior than the experimentally synthesized three allotropes,which indicate that they are possible targets for future experiments.These results further verify the applicability of RG2 in searching for mixed coordination crystal structures.