基态和单态第一激发态的联氨单分子分解反应的密度泛函研究

本文运用密度泛函B3LYP/6-311+G(3df,2p)方法研究了联氨分子的电子结构和能量,并系统分析了联氨分子的分解反应,计算绘制了单分子联氨在基态和单态第一激发态下沿N-N分解反应的势能曲线。本文计算发现联氨分子在这两种电子态下的离解能分别是：基态58.8 kcal/mol,单态第一激发态495.5 kcal/mol。基态分子分解反应是吸热反应,而单态第一激发态分解反应是放热反应。计算发现单态第一激发态的激发能是554.2 kcal/mol。结合这两种电子态下联氨分子的红外振动频率分析,本文认为,在非强制断键的情况下,联氨分子沿N-N键均裂而生成两个NH2自由基的可能性很小。     

基态和单态第一激发态的联氨单分子分解反应的密度泛函研究

本文运用密度泛函B3LYP/6-311+G(3df,2p)方法研究了联氨分子的电子结构和能量,并系统分析了联氨分子的分解反应,计算绘制了单分子联氨在基态和单态第一激发态下沿N-N分解反应的势能曲线。本文计算发现联氨分子在这两种电子态下的离解能分别是：基态58.8 kcal/mol,单态第一激发态495.5 kcal/mol。基态分子分解反应是吸热反应,而单态第一激发态分解反应是放热反应。计算发现单态第一激发态的激发能是554.2 kcal/mol。结合这两种电子态下联氨分子的红外振动频率分析,本文认为,在非强制断键的情况下,联氨分子沿N-N键均裂而生成两个NH2自由基的可能性很小。     

石墨烯量子点的磁性及激发态性质

利用密度泛函理论在B3LYP/6-31G(d)基组水平上研究了具有zigzag边界的石墨烯量子点,结果表明不同大小的石墨烯量子点的基态都是具有磁性的自旋三重态.其磁性一方面来源于zigzag边界上占有凸出位置的碳原子,另一方面来源于带有孤对电子的碳原子.从整体上看,除6b结构外,其他结构的能隙随着苯环数量的增加逐渐减小,而附加电荷却使体系能隙明显减小.用含时密度泛函理论(TD-DFT)对能隙为3.83 eV的由六个苯环排列成的三角形结构进行了激发态的计算,发现第十七激发态强度最大,能量为3.93 eV,对 关键词： 石墨烯量子点 磁性 能隙 激发态     

氯乙烯在外电场下的激发态结构研究

采用密度泛函B3P86方法在6-311G基组上优化了不同外电场作用下氯乙烯分子的基态几何结构、电偶极矩和分子的总能量,然后利用杂化CIS-DFT方法(CIS-B3P86)在相同基组下探讨了无电场时氯乙烯分子前9个激发态的激发能、波长和振子强度和外电场对氯乙烯分子激发态的影响规律.结果表明,分子的几何构型与外电场大小有着强烈的依赖关系.随着外电场的增大,分子总能量先增大后减小,电偶极矩μ先减小后增大.激发能随电场增加快速减小,表明在外电场作用下,氯乙烯分子易于激发和离解.激发态波长随电场的增大而不断增大,且其电子跃迁光谱都集中在紫外区.     

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Fluctuations in the level density of a fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many-body density of states, related to shell effects, are obtained. The fluctuations depend nontrivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single-particle motion.     

Theoretical study of the migration of the hydrogen atom adsorbed on aluminum nanowire

We study the behavior of a hydrogen atom adsorbed on aluminum nanowire based on density functional theory. In this study, we focus on the electronic structure, potential energy surface (PES), and quantum mechanical effects on hydrogen and deuterium atoms. The activation energy of the diffusion of a hydrogen atom to the axis direction is derived as 0.19 eV from PES calculations. The probability density, which is calculated by including quantum effects, is localized on an aluminum top site in both cases of hydrogen and deuterium atoms of the ground state. In addition, some excited states are distributed between aluminum atoms on the surface of the nanowire. The energy difference between the ground state and these excited states are below 0.1 eV, which is much smaller than the activation energy of PES calculations. Thus using these excited states, hydrogen and deuterium atoms may move to the axial direction easily. We also discuss the electronic structure of the nanowire surface using quantum energy density defined by one of the authors.     

Mn22+离子1s22s-1s2np的偶极跃迁能和振子强度

用全实加关联方法计算了类锂Mn22 离子1s22s-1s2np(2≤n≤9)的偶极跃迁能和振子强度.1s2np(2≤n≤9)态的精细结构通过计算自旋-轨道与自旋-其他轨道相互作用算符的期待值确定.依据单通道量子亏损理论,确定了Rydberg系列1s2np的量子数亏损.从而可以用这些作为能量的缓变函数的量子亏损,实现对任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离阈附近束缚态-束缚态跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将Mn22 离子的这一重要光谱特性的理论预言外推到整个能域.     

Efficient non-resonant intermolecular vibrational energy transfer

Molecular excited vibrational states are metastable states and we incorporate their finite lifetimes into the theory of vibrational energy transfer between weakly interacting molecules, i.e., at internuclear distances at which they do not have a chemical bond. Expressions for the effective lifetime of an initially vibrationally excited molecule in the presence of a neighbouring molecule are derived in closed form. These expressions allow one to analyse the physics behind the energy transfer. It is shown that due to different finite lifetimes of the isolated excited molecules, a very efficient vibrational energy transfer can take place between them even if their energies are rather off-resonance. Examples are discussed.     

量子激发态最陡下降微扰理论

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。 关键词：     

Analytical perturbations of wave functions and energy levels of vibrational states of molecules

A method for investigating the excited vibrational states of molecules based on the analytical perturbation theory for linear operators is proposed. According to this theory, the similarity transformation of the total projector and the construction of the transforming function allow obtaining analytical representations of eigenvectors, and in the course of reduction, eigenvalues of the perturbed operator. Theoretical statements and formulas of contributions of analytical perturbations are applied to the investigation of vibrational-rotational interactions, determination of wave functions, and corresponding energy values of excited vibrational states of molecules.     

Electronic transitions of fluorene, dibenzofuran, carbazole, and dibenzothiophene: From the onset of absorption to the ionization threshold

A comparative study of the electronic transitions of fluorene and its hetero-analogues dibenzofuran, carbazole, and dibenzothiophene was performed in a wide energy range. Gas phase, crystal phase, and linear dichroism electronic transmittance spectra were measured with synchrotron radiation. Electronic transitions to excited singlet states were predicted with time-dependent density functional theory, TD-B3LYP/6-31+G(d,p). Based on the experimental and theoretical results, symmetry assignments of electronic transitions in the vacuum and near-UV region are suggested. The correspondence between excited states in these molecules, similarities, and differences between their electronic spectra are discussed.     

Response function analysis of excited-state kinetic energy functional constructed by splitting k-space

Over the past decade, fundamentals of time-independent density functional theory for excited state have been established. However, construction of energy functionals for excited states remains a challenging problem. We have developed a method for obtaining these functionals by splitting k-space according to the occupation of orbitals. In this paper we demonstrate the accuracy of kinetic energy functional thus obtained for excited states with two sets of vacant orbitals. We then perform a response function analysis of the functional proposed and show why our method could be the method of choice for the construction of excited state energy functionals.     

Dynamics of Bose-Einstein condensates in one-dimensional optical lattices in the presence of transverse resonances

The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which takes these resonant modes into account and derive variational equations for large-scale dynamics. Several applications of the theory are discussed and a novel type of “triple soliton” is proposed, which consists of a superposition of a wavepacket at the upper band edge and two transversally excited wavepackets which are displaced in quasi-momentum space.     

Excited states for Coulomb systems in the Hartree-Fock approximation

In this paper, we define excited states for Coulomb systems in the Hartree-Fock approximation as minima of the Hartree-Fock energy on a set of constraints depending on excited states of the lower energy. There are several ways to define such a procedure: we study four of them and prove an existence result for these excited states.     

Derivation of the density functional theory from the cluster expansion

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.     

Generalization of the Kohn—Sham ϱ43 result for excited states

A form is derived for the “exchange energy” in the density functional theory of excited states.     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

分子近阈结构的理论研究

本文利用多重散射方法研究了分子的近阈结构,阐明了:1)激发电子与分子离子实的相互作用动力学特征;2)势形共振的物理起源。并与实验比较,标识了NO₂内壳层激发的实验谱。 关键词：