Machine-learning And Graph-theory-based Crystal Structure Prediction Methods And Their Applications

The structure of a material is the basis for understanding its physical and chemical properties.Experimental methods,such as X-ray diffraction and neutron diffraction,can determinate the structures of materials.But in some cases like high pressures,experimental measurements solely can not provide the complete structural informa-tion.So it is important to develop theoretical structure prediction methods.It can not only assist experimental determination of the structures,but also predict the structures in advance and guide experiments.In recent ten years,structure prediction methods developed rapidly and have wide applications.However,most of the current structure prediction works still focus on relatively small systems and structure predictions for large systems are demanding.The difficulties derive mainly from two reasons:one is high time cost of first principle calculations and the other is the exponentially grow-ing complexity of global structure determination.Therefore,developments of more efficient structure prediction methods combined with new theoretical tools is of great importance.The reseach of machine learning(ML)is very hot recently and its applications in physics,chemistry and material science also attract much attention.Among the applica-tions,the reseach of machine learning force field is developing rapidly.Machine learn-ing force fields can achieve much higher accuracy than classical force fields with less human interventions and the time cost is much less than that of first principle calcula-tions.The combination of machine learning and crystal structure prediction is expected to solve the problem of high time cost of local optimizations.Graph theory has been applied to crystallography long ago,but its applications in condensed matter physics and material science are rare.In recent works,graph theory is proved to be a powerful tool for finding crystals with specific coordination numbers.The applications of graph theory can effectively reduce the complexity of searching space.However,current works are still limited to specific structure prediction prob-lems.It is worthy to expand the applications of graph theory in general crystal structure prediction problems.Based on graph theory and machine learning,we developd novel crystal structure prediction methods.We also studied machine learning force fields and applications of graph theory in high throughout structure screening.Moreover,using first principle calculations and crystal structure prediction,we investigated the pressure-induced sta-bilization of noble gas compounds,containing helium-methane compounds and noble gas compounds with alkali oxides and alkali sulfides.The main results of the thesis are as follows:1.The performance of a machine learning force field is determined by its descrip-tor and regression parameters when the training dataset is fixed.However,most of the previous works only optimized the regression parameters during the training process.Here,we implemented the descriptor in a differentiable way so we can optimize both descriptor and regression parameters simultaneously.We found that machine learning force fields with optimized descriptors have some advantages compared with the ones without descriptor optimization,especially when the training dataset is small.Machine learning force fields are able to reproduce the first principle results of phonon and dy-namical simulations.It indicates the capability of ML potentials to do multiple tasks.Moreover,based on descriptors of machine learning force fields,we proposed and im-plemented a crystal structure prediction method combining evolutionary algorithm and Bayesian optimization.The method uses Gaussian Process Regression models to select the structures for the next generation and improves the searching effectiveness.2.Recently,a lot of works focus on high throughout screening of low-dimensional structures in databases using geometry criteria.However,the existence of self-penetrating nets may lead to incorrect results by previous methods.In stead of these methods,we use the quotient graph to analysis the topologies of structures and compute their dimen-sionalities.Based on the quotient graph,we can calculate not only the dimensionality correctly but also the multiplicity of self-penetrating structures.We screened the Crys-tallography Open Database using the method and found hundreds of structures with different dimensionalities and high multiplicities up to eleven.Moreover,we proposed two crossover-mutation schemes based on quotient graph to improve the evolutionary crystal structure prediction method.The first one can automatically identify molecules in crystals and search for molecular crystals efficiently without setting molecular ge-ometry in advance.The other is based on the first scheme,but it uses a community detection algorithm to decompose extended systems.For example,the algorithm can correctly split?-B into B₁₂clusters.So the second scheme is able to reduce the com-plexity of search space effectively and improve the searching efficiency.The test results indicate that these schemes have great advantages compared with the starndard scheme in different systems.3.Using first principle calculations and crystal structure prediction,we inves-tigated the possibility of trapping helium or larger neon guest atoms under pressure within alkali-metal oxide and sulfide structures.We found stable helium and neon-bearing compounds at very low pressures,and some of them are even stable at ambient pressure.The chemical interactions between the host oxide or sulfide and the guest noble-gas atoms are weak,and the compounds might be useful for gas storage.4.Both helium and methane are major components of giant icy planets,such as Uranus and Neptune.We have investigated the possibility of chemical reactions between helium and methane at high pressures.Our structure searching methods and first-principles calculations predict that a He₃CH₄compound is stable over a wide range of pressures from 55 to 155 GPa and a He CH₄compound becomes stable around 105GPa.The insertion of helium atoms changes the original packing of pure methane molecules and also largely hinders the polymerization of methane at higher pressures.After analyzing the diffusive properties of He₃CH₄,in addition to a plastic methane phase,we have discovered an unusual phase which exhibits coexistence of diffusive helium and plastic methane.In addition,the range of the diffusive behavior within the helium-methane phase diagram is found to be much narrower than that of previously predicted helium-water compounds.This may be due to the weaker van der Waals in-teractions between methane molecules compared to those in helium-water compounds,and the helium-methane compound melts more easily.