A series of clusters Ni4P are designed to simulate the amorphous alloy Ni80P20. After the cluster models are computed by DFT, several stable structures are gained. Their geometric, electronic and catalytic properties ...A series of clusters Ni4P are designed to simulate the amorphous alloy Ni80P20. After the cluster models are computed by DFT, several stable structures are gained. Their geometric, electronic and catalytic properties have been analyzed and discussed. It is proved that cluster Ni4P can reflect the amorphous alloy Ni80P20 very well from the geometry parameters. We find the deformed triangle dipyramid with quadruplet state （configuration 1^（4）） is the most stable structure for cluster Ni4P, which is the most possible local structure in amorphous alloy Ni80P20. And the transition energy between two isomers with the same multiple state is higher than the one with the different. Bond Ni-P plays a very important role in offering the system stability for cluster Ni4E P is the electron donor, and Ni is the accepter in cluster Ni4P, which is in accordance with the experiment results. The 3d orbital populations and Fermi levels of clusters Ni4 have been decreased with the addition of atom E Based on the research of Fermi levels of clusters Ni4P to approach the Fermi level of H2 and their density of state （DOS）, the highest catalytic active property in cluster Ni4P is owned to configuration 1^（4）.展开更多
A hypersurface x: M→S^(n+1) without umbilic point is called a Mbius isoparametric hypersurface if its Mbius form Φ=-ρ^(-2)∑_i(ei(H)+∑_j(h_(ij)-Hδ_(ij))e_j(logρ))θ_i vanishes and its Mbius shape operator S=ρ^(...A hypersurface x: M→S^(n+1) without umbilic point is called a Mbius isoparametric hypersurface if its Mbius form Φ=-ρ^(-2)∑_i(ei(H)+∑_j(h_(ij)-Hδ_(ij))e_j(logρ))θ_i vanishes and its Mbius shape operator S=ρ^(-1)(S-Hid) has constant eigenvalues. Here {e_i} is a local orthonormal basis for I=dx·dx with dual basis {θ_i}, II=∑_(ij)h_(ij)θ_iθ_J is the second fundamental form, H=1/n∑_i h_(ij), ρ~2=n/(n-1)(‖II‖~2-nH^2) and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in S^(n+1) is a Mbius isoparametric hypersurface, but the converse is not true. In this paper we classify all Mbius isoparametric hypersurfaces in S^(n+1) with two distinct principal curvatures up to Mbius transformations. By using a theorem of Thorbergsson [1] we also show that the number of distinct principal curvatures of a compact Mbius isoparametric hypersurface embedded in S^(n+1) can take only the values 2, 3, 4, 6.展开更多
文摘A series of clusters Ni4P are designed to simulate the amorphous alloy Ni80P20. After the cluster models are computed by DFT, several stable structures are gained. Their geometric, electronic and catalytic properties have been analyzed and discussed. It is proved that cluster Ni4P can reflect the amorphous alloy Ni80P20 very well from the geometry parameters. We find the deformed triangle dipyramid with quadruplet state （configuration 1^（4）） is the most stable structure for cluster Ni4P, which is the most possible local structure in amorphous alloy Ni80P20. And the transition energy between two isomers with the same multiple state is higher than the one with the different. Bond Ni-P plays a very important role in offering the system stability for cluster Ni4E P is the electron donor, and Ni is the accepter in cluster Ni4P, which is in accordance with the experiment results. The 3d orbital populations and Fermi levels of clusters Ni4 have been decreased with the addition of atom E Based on the research of Fermi levels of clusters Ni4P to approach the Fermi level of H2 and their density of state （DOS）, the highest catalytic active property in cluster Ni4P is owned to configuration 1^（4）.
基金Partially supported by NSFCPartially supported by TU Berlin, DFG, SRF, SEM+2 种基金Partially supported by Qiushi Award. 973 Project, RFDPthe Jiechu GrantPartially supported by DFG, NSFC and Qiushi Award
文摘A hypersurface x: M→S^(n+1) without umbilic point is called a Mbius isoparametric hypersurface if its Mbius form Φ=-ρ^(-2)∑_i(ei(H)+∑_j(h_(ij)-Hδ_(ij))e_j(logρ))θ_i vanishes and its Mbius shape operator S=ρ^(-1)(S-Hid) has constant eigenvalues. Here {e_i} is a local orthonormal basis for I=dx·dx with dual basis {θ_i}, II=∑_(ij)h_(ij)θ_iθ_J is the second fundamental form, H=1/n∑_i h_(ij), ρ~2=n/(n-1)(‖II‖~2-nH^2) and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in S^(n+1) is a Mbius isoparametric hypersurface, but the converse is not true. In this paper we classify all Mbius isoparametric hypersurfaces in S^(n+1) with two distinct principal curvatures up to Mbius transformations. By using a theorem of Thorbergsson [1] we also show that the number of distinct principal curvatures of a compact Mbius isoparametric hypersurface embedded in S^(n+1) can take only the values 2, 3, 4, 6.
