电子结构方法中带结构特征值问题的统一视角（英文）

在(相对论)电子结构方法中,四元数矩阵特征值问题和计算激发能的线性响应(Bethe-Salpeter)特征值问题是两个经常出现的结构特征值问题.尽管前一个问题已被十分仔细地研究,后一个问题在一般形式下,即不假设电子Hessian正定性的复矩阵情况,并没有得到完全的理解.鉴于它们非常相似的数学结构,本文从一个统一的角度研究了这两个问题,揭示了它们特征向量的"李群"结构,为将来设计对角化算法和数值优化方法提供了一个统一的框架.利用和处理四元数矩阵特征值问题相同的归约算法,本文给出了表征线性响应问题特征值(实数、纯虚、或复数)的充分必要条件.这一结果可以看作是实矩阵情况下已知条件的自然推广.     

采用多重网格法进行电子结构的计算

采用多重网格法(MG)和对称性理论以及密度泛函理论中著名的Kohn-Sham 方程,开发了一种计算具有一定对称性的原子簇的电子结构的方法,并对H₂ 分子的基态能进行了实际的计算,并与用其他理论计算得到的结果进行了比较。     

N、△重子谱中负能级分量的作用

利用瞬时近似的Bethe-Salpeter方程,并且考虑了Dirac旋量中负能级分量对单胶子交换势的修正,对N、△重子谱进行了计算.结果发现负能级分量的考虑对势参数,尤其是对αs有显著的影响,但对整个N、△重子谱的改变不大.     

五对角阵逆特征值问题的一个数值解法及其应用

给出一个由谱数据构造实对称五对角阵的数值方法及其在梁的振动逆问题中的应用。     

Si中B-空位复合缺陷的电子结构

本文对Si中B-空位(BV)缺陷的电子结构,提出一个“五个空杂化轨道”的简化理论模型。用紧束缚的Koster-Slater格林函数方法,算得的空位最近邻原子的超精细相互作用常数,以及电子波函数在远离空位的几率分布都同电子-核子双共振实验结果相符合。理论确定的深能级位置同深能级瞬态谱的实验值相比拟。协调了现有BV°缺陷的实验资料,支持了B原子位于空位的次近邻,BV°缺陷处于B^-V⁺电荷态的结论。 关键词：     

铜氧化物超导体的电子结构

本文主要很据光电子能谱和电子能量损失谱的实验结果，综述目前对铜氧化物超导体的铜原子的价态、强电子相关作用、反铁磁性、空穴导电及其对称性和费米面的性质等电子结构问题的认识．     

石墨烯纳米带电子结构的紧束缚法研究

在推导出的一般复式格子的π电子紧束缚能量色散关系的基础上,通过假定石墨烯纳米带的电子横向限制势为无穷大硬壁势,导出石墨烯纳米带的能量色散关系及石墨烯纳米带或为金属或为半导体的条件.结果表明：石墨烯纳米带的电子结构与其几何构型（对称性及宽度）密切相关,所以通过控制几何构型,可将其调制成金属或不同带隙的半导体.这意味着石墨烯纳米带对于发展新型纳米器件具有重要意义. 关键词： 石墨烯纳米带 复式格子 紧束缚模型 电子结构     

高温超导体MgB_2的电子结构研究

用第一性原理能带理论计算了高温超导体MgB-2的电子结构.计算得出的电子能带说明MgB-2是一种宽能带化合物,价带主要由Mg和B原子s和p的杂化形成.费米能级处的态密度N(EF)是0.72(states/eV).根据这些结果,初步推断出MgB-2的超导电性的微观机制不可能是电子-声子耦合的BCS模型,而是有待于探索的新机制.     

固态镓的电子结构

本文采用第一性原理分子动力学方法,在让原子得到充分弛豫后,计算了固体镓的电子结构。结果与实验相符合。通过计算总能随体积的变化,讨论了零温下固体镓的相稳定性。结果表明在α-Ga中,最近邻原子之间存在共价性从而导致电阻各向异性,而镓的其它相均为良好的金属。 关键词：     

富勒稀C36的电子结构与电子传导

本文采用基于第一性原理的密度泛函理论和非平衡格林函数方法研究了C36分子的电子结构和电子传导特性．本文以Au(1,1,1)为电极分别建立了4个电子输运模型,分别计算了他们的电子传输概率、伏安曲线,同时分析了产生这些分子器件电子输运性质的原因．研究计算结果发现, C36的电子输运主要发生在分子壳上,当左、右电极分别连接在第6号和第35号碳原子两端时,C36的电子输运性能最好,伏安曲线显示该分子具有半导体特性．     

Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems

We propose two variants of tailored finite point (TFP) methods for discretizing two dimensional singular perturbed eigenvalue (SPE) problems. A continuation method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE. We study the analytical solutions of two special cases of the SPE, and provide an asymptotic analysis for the solutions. The theoretical results are verified in the numerical experiments. The numerical results demonstrate that the proposed schemes effectively resolve the delta function like of the eigenfunctions on relatively coarse grid.     

Self-energy effect in a relativistic bound state problem

A modification of the Wick-Cutkosky equation for the relativistic bound state of two scalar particles interacting through the exchange of a massless scalar field within the ladder approximation has been considered by incorporating the self-energy diagrams in the integral kernel. An exact analytical solution of the equation is obtained at vanishing total energy and it is shown that the self-energy effects generally diminish the eigenvalues in agreement with the findings of Liet al, who, however solved the equation numerically for the case of massive scalar exchange. An additional feature of the modified equation is that it preserves the 0(5) symmetry at zero total energy as was first noted by Cutkosky for the scalar bound state equation without self-energy effects.     

Electronic structures and thermoelectric properties of La or Ce-doped Bi2Te3 alloys from first principles calculations

Thermoelectric properties of La or Ce-doped Bi₂Te₃ alloys were systematically investigated by ab initio calculations of electronic structures and Boltzmann transport equations. The Seebeck coefficient of p-type LaBi₇Te₁₂ and La₂Bi₆Te₁₂ was larger than that of Bi₂Te₃, because La doping increased the effective mass of carriers. On the other hand, the electrical conductivity of LaBi₇Te₁₂ and La₂Bi₆Te₁₂ decreased, which caused a reduction of power factor of these La-doped Bi₂Te₃ alloys in comparison with Bi₂Te₃. The influence of Ce doping on the band structure and thermoelectric properties of Bi₂Te₃ was similar to that of La doping. The theoretical calculation provided an insight into the transport properties of La or Ce-doped Bi₂Te₃-based thermoelectric materials.     

A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices $M$, $D$ and $K$ for the quadratic pencil $Q(\lambda)=\lambda^2M+\lambda D+K$, so that $Q(\lambda)$ has a prescribed subset of eigenvalues and eigenvectors. This method can determine the solvability of the inverse eigenvalue problem automatically. We then consider the least squares model for updating a quadratic pencil $Q(\lambda)$. More precisely, we update the model coefficient matrices $M$, $C$ and $K$ so that (i) the updated model reproduces the measured data, (ii) the symmetry of the original model is preserved, and (iii) the difference between the analytical triplet $(M, D, K)$ and the updated triplet $(M_{\text{new}}, D_{\text{new}}, K_{\text{new}})$ is minimized. In this paper a computationally efficient method is provided for such model updating and numerical examples are given to illustrate the effectiveness of the proposed method.     

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.     

锇杂苯的电子结构及芳香性

使用密度泛函理论及片段轨道相互作用分析方法 ,研究了典型的锇杂苯的电子结构和芳香性 .结果表明 ,锇碳六员环具有较好的环平面性及键的离域性 ,占据的锇dxz轨道与碳环的 3π空轨道之间的反馈π键相互作用 ,使得环上离域π电子数满足H櫣ｃｋｅｌ的 4n +2规则 ,计算的环外质子化学位移、同键反应芳香性稳定化能、绝对硬度和磁化率增量数据均表明锇杂苯具有芳香性     

Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics

In this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.     

二氧化钒的电子结构及光学性质计算

本文使用基于量子力学第一性原理的CASTEP程序包,计算了单斜结构和金红石结构的二氧化钒(VO2)的电子结构、介电常数、吸收系数、折射率等光学性质。介电函数的虚部、吸收光谱、折射率等它们的峰值位置存在一一对应关系,这表明了它们之间存在着内在的联系,它们都与电子从价带到导带的跃迁吸收有关,这为从物理本质上理解二氧化钒的光学性质提供了重要的依据。计算结果与实验结果符合得很好。     

单杠结构差分离散系统的振动反问题

研究组合结构中的杆-梁-杆组合单支结构,或称单杠结构的模态反问题,从数学上证明单杠结构差分离散系统固有振动的刚度矩阵的符号振荡性,并导出其频率和振型的一些定性性质.在此基础上,探讨由两组位移或应变振型及相应频率构造物理参数的条件和方法,给出两个计算实例.讨论结构参数关于其几何对称轴具有对称性的条件下的模态反问题,并给出计算实例.计算结果表明,上述反问题提法合理,解法正确.