Theoretical Study On Carbon Group Materials:Structure Search Of Si_xGe_yH_z And High-spin State In C₆₀H_n

There are structural diversity and unique properties in carbon group nanomaterials.The application of carbon group materials in high-performance devices can be expanded through structural optimization and performance design.The structural diversity induced by adsorp-tion and doping can effectively modulate the properties of the system,which also makes it difficult to study the systems systematically due to the large number of candidates.For the Si_xGe_yH_znanocrystals with sp³hybridization,the quantum confinement effect can induce the size-dependent luminescence properties of the system,and the distribution of Si/Ge atoms can further tune the optical properties.To stimulate the magnetic ordering of the fullerenes(C₆₀)with sp²hybridization,the surface adsorption of hydrogen atoms are introduced to result in the sp³hybridization of some carbon atoms,while the unpairedπelectrons will appear due to structural constraints in some specific systems,corresponding to the possible high-spin states.Therefore,molecular systems with magnetic moments can be designed by controlling the distri-bution of hydrogen atoms in the hydrogenated fullerene(C₆₀H_n).Combined the first-principles calculations with effective interaction models and structural recognition,we have investigated the structural stability and electronic properties of Si_xGe_yH_znanocrystals,and determined the largest magnetic moment that a C₆₀H_nmolecule can achieve for a given number of hydrogen atoms.The relevant research results will provide a theoretical reference for the design and de-velopment of carbon nanomaterials.In order to improve the efficiency of structural screening,we have developed a symmetry-based structural recognition method in clusters and crystals to enumerate possible candidates without duplicate ones.Based on the symmetry of the cluster,we use the distance matrix to find the atomic replacement operations corresponding to all the symmetry operations,and obtain the symmetry operation table of the cluster.The unique structures of adsorption and substitution in the cluster can be enumerated using the symmetry operation table.Combined with the efficient algorithms exploiting the group chain structure of finite groups,structures with the specific point group symmetry can be generated.Using the Hermite normal form,we obtain all unit cells of a given number of atoms,where the duplicate ones are removed,based on the symmetry of the crystal.The symmetry operation table of the unit cell can be used for the structure generation and recognition of the alloy structure.Through the method of cell expansion,we propose a general precedure of lattice matching and determine the possible matching lattice structure of silicene on Ag（111）surface.The development of related programs provides a foundation for structural search and material design.For the Si_xGe_yH_znanocrystals with different sizes and shapes,we have studied the ef-fects of Si/Ge atomic distribution on the structural stability and electronic properties.Based on the first-principles calculations,we have provided a bond energy model which can accurately and efficiently evaluate the energies of Si_xGe_yH_znanocrystals.Using the bond energy model to analyze the differences of various substitution sites,we have found that the Si atoms in the stable structures tend to be in the position where more H atoms are bonded,which perfectly explains the proportion and distribution of Si and Ge atoms corresponding to the stable struc-tures.Considering the free energy as a function of chemical potentials,we have obtained the phase diagram of Si_xGe_yH_znanocrystals,exploring the evolution of the stable structures with the environment.Through the calculations of Si_xGe_yH_znanocrystals,it is found that the gap of the system varies with different atomic distributions.However,the size effect is dominant,and the energy gap of the nanocrystals gradually decreases with the increasing of the system size（number of atoms）.When the number of atoms is the same,the gap distribution of differ-ent shape systems will gradually increase with the increasing of surface area.Furthermore,we have considered the temperature effect on the gap of the nanocrystals and obtained the optical properties of the stable structures at room temperature.Combining the first-principles method and the Hubbard model,we have found that there may be unpaired electrons in the hydrogenated fullerene C₆₀H_n,resulting in a high-spin elec-tronic state.In the C₆₀H_nsystem,since the first-principles calculation of the magnetic ground state depends heavily on the initial magnetic moment setting,we adopt the Hubbard model to determine the initial magnetic moment distribution for various systems.By calculating the mag-netic ground states of all 23 C₆₀H₂structures,we have found 9 structures with high spin states and one structure with an antiferromagnetic configuration.We have proposed an interaction model to predict the adsorption sites of hydrogen in C₆₀H_nwith the magnetic moment.Through the first-principles calculations for the case of n=3,4,we have confirmed that the model can describe the magnetic interaction of C₆₀H_nto a large extent.Screening the C₆₀H_n（n>4）by the magnetic interaction model,we have found the structures with the same number of unpaired electrons and adsorbed hydrogen atoms in a single molecule when n<6.Our results will provide a reference for the magnetic device design based on hydrogenated fullerene system in experiment.