带隙问题:第一性原理电子能带理论研究现状

电子能带结构是材料最基本的性质之一,对于材料的实际应用具有深刻影响。电子能带结构的理论描述一直以来都是第一性原理理论方法中最具挑战性的问题之一。作为材料理论计算“标准模型”的密度泛函理论,在局域密度近似或广义梯度近似下,存在着著名的“带隙问题”:半导体材料的理论带隙与实验值相比存在着显著的系统性误差。近年来,以改进对带隙的描述为主要目标之一,密度泛函理论领域有很多重要发展。同时,对于带隙问题,与密度泛函理论紧密相关但又有本质区别的另外一类理论方法是基于格林函数的第一性原理多体微扰理论,其中最为流行的GW方法是当前描述材料的电子能带结构最为准确的第一性原理方法,但一直以来都受限于计算量太大而无法应用于更复杂的体系。本文综述了密度泛函理论和格林函数多体理论在电子能带结构问题上的基本原理、最新进展以及存在的挑战性问题。希望通过比较两种理论框架的异同,为未来可能的发展思路提供启发。     

研究激发态的多体格林函数理论

本文介绍的多体格林函数理论是一种建立在一套格林函数(包括单粒子格林函数和双粒子格林函数)方程基础上的,用以研究物质激发态性质的第一性原理方法。该理论包括计算准粒子性质的GW方法和描述电子-空穴对运动的Bethe-Salpeter方程。GW方法可以以很高的精度计算轨道能量、能带结构、准粒子寿命等物理量;Bethe-Salpeter方程则在研究激发能、光吸收谱、激发态动力学等光学性质上有广泛的应用前景。多体格林函数理论通过自能算符描述电子之间以及电子与空穴之间的交换关联作用。本文将详细阐述该理论的基本概念和原理,并对其在各种材料中的应用做简要介绍。     

单分子器件电子输运性质的理论研究

对当前单分子器件的理论和实验的研究进展作了简短评述,并简要介绍电子输运理论,最后给出一个基于非平衡态格林函数电子输运理论的全自洽方法,研究单个水分子在Au(111)电极之间的输运性质的计算实例.研究结果表明由于水分子与电极之间存在较强的杂化作用,水分子的分立能级间距大,在小偏压范围内,水分子的特征已经被淹没在杂化能级之中.体系的电势变化主要发生在水分子局域区间,其电子输运行为主要是一个单通道过程.     

扩展苯基衍生物分子器件的电子输运的理论研究

通过结合杂化密度泛函和前线轨道理论与弹性散射格林函数方法研究了三种苯基衍生物分子器件的电子输运性质. 基于杂化密度泛函方法计算扩展分子电子结构的基础上, 计算了苯基衍生物三分子结的输运性质. 计算结果表明, 在低偏压下, 电流与电压呈线性变化; 分子结的电阻的对数与苯环的数目呈线性增加关系.     

基于块相关框架的多参考微扰理论和多参考耦合簇理论

传统单参考电子相关方法已经发展成熟,但很多时候无法正确描述共价键解离、双(多)自由基和激发态等电子之间相关性非常强的体系。近年来发展的多参考微扰理论和多参考耦合簇理论以多个行列式的线性组合为参考波函数,采用不同的方式有效考虑电子之间的动态相关,对强关联体系的描述取得了显著的改进。但根据理论出发点和精度要求的不同发展出了许多多参考理论,仍无一个公认的、令人满意的方案。本文将结合与常见电子相关方法在理论框架和计算精度上的比较,详细阐述块相关理论的基本原理,并介绍基于块相关的"另类"多参考电子相关方法。最后本文还简单展望了多参考电子相关方法今后的发展趋势。     

分子结的非弹性隧道谱和电子-振动的耦合

研究了分子结的非弹性隧道谱, 给出了基于微扰理论近似的非平衡格林函数. 深入研究了非弹性隧道谱和电子-振动耦合常数的相互关系. 同时, 还计算了OPV和OPE分子结的IETS, 计算结果与有关的实验结果具有很好的可比性.     

电子定域函数(ELF)理论方法简介——一种描述化学键的新模型

电子定域函数理论可以清晰和定量化描述理论化学研究的基本对象——化学键,已在原子、分子及固体体系中得到广泛应用。本文系统介绍了电子定域函数(ELF)理论方法的基本物理思想;对ELF函数的一些特点如数值稳定性、ELF与分子中的原子理论(AIM理论)方法的异同及ELF的拓扑分析进行了说明;对电子定域函数在研究原子壳层结构、化学键的性质、孤对电子的位置、反应过程化学键的断裂和生成等方面的应用进行了介绍。     

氢键对分子器件电学特性的影响

利用密度泛函理论和弹性散射格林函数方法,研究了被不同官能团取代后的联苯分子的电输运特性.计算结果表明,由于氢键的影响,使得分子的电子结构发生了变化,特别是对电子在分子结内的跃迁几率影响较大,从而直接影响了分子器件的伏安特性.     

CFCl3的理论和紫外光电子能谱研究

采用紫外光电子能谱(PES)和量子化学方法,研究了以CFCl3化合物为代表的系列化合物(CFCl3、CF2Cl2、CF3Cl、CCl4)不同离子态的电子结构和性质。结果表明,四种化合物CF3Cl、CF2Cl2、CFCl3、CCl4的第一电离能依次下降。结合从头算自洽场分子轨道(abinitioSCFMO)和外壳层格林函数法(OVGF)计算对化合物的PES进行了分析和指认,表明化合物的外层轨道中Cl的孤对电子成分对电离能存在明显的影响;外层格林函数法计算得到电离能与实验吻合很好;同时发现在外壳层格林函数法计算结果中由于考虑相关能,得到的分子轨道存在能级顺序的交错。     

两体扰动势和H2O通道反应的三原子体系解析势

提出了两体扰动势的概念.通过两体扰动势构造多原子相互作用体系解析势的理论方法,获得了非线性三原子H2O相互作用体系的解析势函数.用势能面正确描述了O(1D)+H2→H2O→OH+H通道反应的性质.理论分析和实验结果非常符合.该方法比较容易推广构造多原子相互作用体系解析势.     

Nonequilibrium superoperator GW equations

Hedin's equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green's function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green's function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.     

A theoretical study of molecular conduction. II. A Hartree-Fock approach to transmission probability

In this paper, we discuss molecular conductivity based on Green's function methods. In our calculations, we adopted the self-energy formalism to accommodate semi-infinite electrodes connected to a molecule, and the self-energy was obtained from the surface Green's function of the electrodes. We adopted the formalism of the surface Green's function derived by Sanvito et al. [Phys. Rev. B 59, 11936 (1999)] and Krstic et al. [Phys. Rev. B 66, 205319 (2002)], and although their formalisms for the surface Green's function were different, we were able to demonstrate that these formalisms are mathematically identical. We analyzed the electron transmission probability by using the spectrum expression of Green's function, instead of using the inverse matrix of the effective Hamiltonian that includes an isolated molecule and the electrodes. Finally, we calculated the transmission probability of benzenedithiol based on the Hartree-Fock method and analyzed the disappearance of the transmission probability due to the orbital interference.     

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.     

Benchmarking the performance of density functional theory based Green's function formalism utilizing different self-energy models in calculating electronic transmission through molecular systems

Electronic transmission through a metal-molecule-metal system is calculated by employing a Green's function formalism in the scattering based scheme. Self-energy models representing the bulk and the potential bias are used to describe electron transport through the molecular system. Different self-energies can be defined by varying the partition between device and bulk regions of the metal-molecule-metal model system. In addition, the self-energies are calculated with different representations of the bulk through its Green's function. In this work, the dependence of the calculated transmission on varying the self-energy subspaces is benchmarked. The calculated transmission is monitored with respect to the different choices defining the self-energy model. In this report, we focus on one-dimensional model systems with electronic structures calculated at the density functional level of theory.     

On the evolution equations for reduced density operators in quantum open systems

Evolution equations for transition probabilities of reduced density operators in quantum open systems are derived. Information contained in such equations is obtained from spectral resolutions and the role of memory kernels is elucidated within the scenario of many body theory as a function of the self-energy fields. As an analytical example of this formulation relaxation times for dissipative systems are evaluated in terms of the interaction between subsystems.     

General criteria for assessing the accuracy of approximate wave functions and their densities

Master equations for propagators in quantum open systems and their spectral resolutions are derived. The Zwanzig partitioning scheme along the superoperator algebra are used to derive equations of motion for partitioned operators in a Liouville space. The reservoir influence on the dynamical evolution of operators is shown to lead explicitly to dissipative effects arising from memory terms in the evolution equations of such operators. It is also shown that spectral representations may be written in a self-consistent analytic way by means of the self-energy fields for transition energies of the system by taking into account the lack of the complete knowledge about the reservoir. A kinematic fluid interpretation of the resultant equations is given and an explicit form of the “collision” superoperator is obtained. Finally, a simple example to illustrate the determination of self-energy fields for the system–reservoir interaction corrections is given. © 1995 John Wiley & Sons, Inc.