Simulation And Prediction Methods For Complex Crystal Structures

Complex crystal structure simulation helps us to understand the various physical and chemical properties of matter.The conventional Kohn-Sham density functional theory?KS-DFT?have long been considered inappropriate for simulating systems of ten thousand of atoms.Orbital-Free density functional theory does not need to deal with wave functions,and only the electron density can uniquely determine the ground-state properties of a many-electron system.The inherent quasi-linear scaling of OF-DFT makes it possible to carried out first-principles simulation for millions of atoms,and makes it the most promising theory for large-scale simulations.Most of the theoretical simulation of materials are based on crystal structures,so determining the crystal structure of a material is critical.Theoretical structure prediction not only helpful to understand experimental phenomena,but also guides experiments,and design and development of new materials.However,the potential energy surface of crystal structure is extremely complicated,and as the number of atoms in the system increases,the complexity of the potential energy surface increases exponentially.Therefore,predicting the ground state structure of the crystal by theory is enormously challenging.Researchers at home and abroad have developed a series of crystal structure prediction methods,which have achieved great success in small and medium scale material systems.However,they all have certain limitations,such as not able to overcome the very large energy barrier or trapped in the local minimum.So,it's difficult to predict crystal structures of complex systems.In summary,the simulation and prediction for complex crystal structures need to solve two key issues:1.Develop a first-principles simulation method and software that can efficiently simulate tens of thousands or millions of atoms;2.Develop a theoretical crystal structure prediction method for complex systems.In order to solve the problem of theoretical simulation of complex crystal structures,recently,we developed a real-space finite-difference method for the numerical solution of OF-DFT using a direct energy-minimization scheme for periodic systems and coded it into the ATLAS?Ab initio orbiTaL-free density functionAl theory Software?software package.The accuracy of our method is demonstrated through direct comparisons to results from KS-DFT simulations for periodic systems of Mg,Al,and Al₃Mg.In this thesis,we developed a quasi-linear scaling method for evaluating the ion–electron potential of crystalline solids,implemented the parallel version ATLAS and expended the functionality.Meanwhile,we proposed a complex crystal structure prediction method based on global swarm intelligent algorithm in combination with crystal symmetry rule?SABC?for the complex crystal structure and coded the method into CALYPSO package.The main results of the thesis are as follows:1.The inherent quasi-linear scaling of OF-DFT makes it the most promising theory for large-scale simulations.In general,all the interaction terms of OF-DFT have linear scaling except for the electrostatic interaction term for periodic systems.the electrostatic potential can be written as the sum of ion–ion,electron–electron,and ion–electron interaction terms.The ion-electron and electron-electron term with O?N log N?scaling under periodic boundary conditions,where N is the number of grid points in the system,making its computational cost also acceptable for large-scale simulations.However,the computational cost of the ion–electron potential term of crystalline solids is quadratic scaling with the number of atoms.What's more,conventional method needs calculation of the structure factor,which is also very time consuming.Therefore,the evaluation of the electrostatic potential therefore is the bottleneck in most OF-DFT programs for large system simulation.In this thesis,we developed a quasi-linear scaling method for evaluating the ion–electron potential of crystalline solids.This method is to replace the long-range ion–electron potential with an equivalent localized charge distribution and corresponding boundary conditions on the unit cell.Firstly,we can obtain pseudo-charge density from the pseudopotential.Due to the pseudo-charge density is only localized within the cutoff radius,the total ionic charge density was determined by not more than one atom.Based on the convolution theorem,we can obtain the ion-electron potential by a simple multiplication in reciprocal-space.So,the method shows quasilinear scaling with the number of atoms.Compared to conventional method,new approach shows better computational efficiency.In particular,the computational time required for the system containing 12,000 Mg atoms is decreased substantially from?18,000 s for the conventional method to?316 s for the new scheme,and the efficiency has increased nearly 60 times.2.Recently,we developed a real-space finite-difference method for the numerical solution of OF-DFT using a direct energy-minimization scheme for periodic systems and coded it into the ATLAS software package.However,the capability of only static calculations of the total energy in this ATLAS package severely limits its applicability,as the package cannot be used to simulate the atomistic processes of real systems.In particular,our previous ATLAS package only implemented a sequential scheme,impeding its application for simulations of large-scale systems.In order to take full advantage of the modern high-performance computing,we implemented parallel version ATLAS based on message passing interface and pencil decomposition scheme.Owing to the highly scalable parallel decomposition schemes,the parallel version ATLAS can scale well to thousands of cores,and shows high ability to simulate a system containing 4 million atoms by taking less than 1 hour with 2048 processors.Meanwhile,we expanded the functionality of ATLAS to have geometrical relaxation and molecular dynamics simulation included.For geometrical relaxation,the ATLAS has ability to perform fixed-cell optimization and variable-cell optimization.For the MD simulation module,we implemented three widely used NVE,NVT and NPT ensembles.And the simulated results are excellent agreement with the experimental data,which confirms the reliability of the MD simulation.The scalable parallel implementation of the ATLAS package with extensive capabilities holds considerable promise for simulation of large-scale systems with millions of atoms,and crucial to its future success and popularity.3.In this thesis,we proposed a complex crystal structure prediction method based on global swarm intelligent artificial bee colony algorithm in combination with crystal symmetry rule?SABC?for the complex crystal structure and coded the method into CALYPSO package.Owing to the role transformation of three kinds of bees,exploration and exploitation processes are carried out simultaneously in SABC method and can significantly improve the performance of structure prediction.Through the test for MgAl₂O₄ with 28 atoms/cell,the SABC shows high efficiency and success rate in comparison with other algorithms.Furthermore,the SABC algorithm can predict the complex crystal structure containing more than one hundred atoms of multiple atom types.This is validated by correctly reproducing some known complex structures,such as Y₂Ba₂Ca₄Fe₈O₂₁ with 148 atoms and five elements in simulated cell and the garnet pyrope(Mg₂₄Al₁₆Si₂₄O₉₆)with 160 atoms in the unit cell.In addition,the application of this developed method leads to discovery of structure of high-pressure phase of BiFeO₃,which is confirmed by X-ray diffraction experimental data.