Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Electron Affinities of the Early Lanthanide Monoxide Molecules

The photoelectron imagings of LaO^-, CeO^-, PrO^-, and NdO^- at 1064 nm are reported. The well resolved photoelectron spectra allow the electron a±nities to be determined as 0.99(1) eV for LaO, 1.00(1) eV for CeO, 1.00(1) eV for PrO, and 1.01(1) eV for NdO, respectively. Density functional calculations and natural atomic orbital analyses show that the 4f electrons tend to be localized and suffer little from the charge states of the molecules. The photodetached electron mainly originates from the 6s orbital of the metals. The ligand field theory with the δ=2 assumption is still an effective method to analyze the ground states of the neutral and anionic lanthanide monoxides.     

Density functional theory on phase space

Forty‐five years after the point de départ [Hohenberg and Kohn, Phys Rev, 1964, 136, B864] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the electron density still eludes us—and possibly will do so forever [Schuch and Verstraete, Nat Phys, 2009, 5, 732]. In what follows we examine a formulation in the same spirit with phase space variables. The validity of Hohenberg–Kohn–Levy‐type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation‐exchange functionals on phase space. A new proof of the overbinding property of the Müller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the Thomas–Fermi model. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

AlnO2±团簇结构的几何特征与稳定性

采用密度泛函理论(DFT)的B3LYP方法,在6-311G**水平上对AlnO2±(n=1-10)团簇的几何和电子结构进行了理论计算.讨论了混合团簇的基态结构与振动频率,以及电荷转移与分子轨道.结果表明,AlnO2±(n>1)团簇的基态结构都是2个较小的AlmO(m相似文献   

A study with a complete-active-space self-consistent-field plus density functional theory combination: The low-lying bound states of N<Subscript>2</Subscript>

The use of a large set of correlation energy functionals, in a post-self-consistent-field procedure, is analyzed for the calculation of the potential-energy curves of the ground state and some excited states in the case of the N₂ molecule. The results show the improvement of the molecular properties, such as dissociation energies, equilibrium bond distances and harmonic vibrational frequencies, (when some of the tested functionals are used), together with the problems that the use of density functional theory functionals applied to multideterminantal wave functions implies. AcknowledgementPartial financial support by the Spanish MCYT, through project BQU2001-0883, is gratefully acknowledged.     

Ab initio investigation of the magnetic states of Ca2MnO4 and Ca2MnO3.5

An analysis of the electronic and magnetic properties of Ca₂MnO₄ and Ca₂MnO_3.5 is carried out within local spin density functional theory using the augmented spherical wave method. From energy differences between the hypothetic magnetic configurations both systems are found to be insulating antiferromagnets in the ground state with a 1 eV gap. However we identify an intermediate half metallic ferromagnetic state with the Hund’s rule expected moments for Mn^IV (3 μ_B) and Mn^III (4 μ_B, high spin HS configuration), respectively. The latter result of moment magnitude finds support in recent experimental evidence of Mn^III bismuth oxide as a ferromagnet in its ground state. This is characterized by a small density of states (DOS) magnitude of itinerant states in spin (↑) channel pointing to a metallic-like behavior as it is experimentally evidenced. For both Ca₂MnO₄ and Ca₂MnO_3.5 the chemical bonding characteristics are resolved for the two spin channels. Relationship to colossal magnetoresistive compounds is proposed.     

氟硼二吡咯类pH荧光探针PET光谱特性的理论计算

氟硼二吡咯(BODIPY)类pH荧光探针分子是基于光诱导电子转移(PET)的荧光探针分子, 识别基团氮原子上引入不同取代基可呈现不同的光学灵敏度. 本文应用密度泛函理论(DFT)及含时密度泛函理论(TD-DFT)方法对六种含不同取代基的探针分子进行了几何构型优化及激发态计算, 探讨了不同取代基对PET效应影响. 计算结果表明: 基态时这些探针分子的最高占有分子轨道(HOMO)和最低未占有分子轨道(LUMO)都在荧光母体BODIPY的π, π^*轨道, 而识别基团上氮原子孤对电子所在的轨道为HOMO-1轨道. 但是在激发态, 当氮原子上有两个取代基时, HOMO-1→LUMO跃迁的激发能都小于荧光团的HOMO→LUMO跃迁, 这将有可能产生PET效应并导致荧光熄灭, 而当氮原子上有一个取代基时不会出现这种现象. 通过激发态结构优化可以发现, 无论识别基团氮原子上有一个还是两个取代基, N原子的轨道对称性都发生变化, 由sp³→sp², 孤对电子占据在p轨道上, 其轨道能级升高至荧光团的HOMO和LUMO轨道之间, 将导致不同程度的PET效应, 与实验结果一致.     

Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Origin‐independent sum over states simulations of magnetic and electronic circular dichroism spectra via the localized orbital/local origin method

Although electronic and magnetic circular dichroism (ECD, MCD) spectra reveal valuable details about molecular geometry and electronic structure, quantum‐chemical simulations significantly facilitate their interpretation. However, the simulated results may depend on the choice of coordinate origin. Previously (?těpánek and Bou?, J. Comput. Chem. 2013, 34, 1531), the sum‐over‐states (SOS) methodology was found useful for efficient MCD computations. Approximate wave functions were “resolved” using time‐dependent density functional theory, and the origin‐dependence was avoided by placing the origin to the center of mass of the investigated molecule. In this study, a more elegant way is proposed, based on the localized orbital/local origin (LORG) formalism, and a similar approach is also applied to generate ECD intensities. The LORG‐like approach yields fully origin‐independent ECD and MCD spectra. The results thus indicate that the computationally relatively cheap SOS simulations open a new way of modeling molecular properties, including those involving the origin‐dependent magnetic dipole moment operator. © 2015 Wiley Periodicals, Inc.     

A general,recursive, and open‐ended response code

We present a new implementation of a recent open‐ended response theory formulation for time‐ and perturbation‐dependent basis sets (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) at the Hartree–Fock and density functional levels of theory. A novel feature of the new implementation is the use of recursive programming techniques, making it possible to write highly compact code for the analytic calculation of any response property at any valid choice of rule for the order of perturbation at which to include perturbed density matrices. The formalism is expressed in terms of the density matrix in the atomic orbital basis, allowing the recursive scheme presented here to be used in linear‐scaling formulations of response theory as well as with two‐ and four‐component relativistic wave functions. To demonstrate the new code, we present calculations of the third geometrical derivatives of the frequency‐dependent second hyperpolarizability for HSOH at the Hartree–Fock level of theory, a seventh‐order energy derivative involving basis sets that are both time and perturbation dependent. © 2014 Wiley Periodicals, Inc.     

铁原子与氮分子间的相互作用——单端位构型

用杂化密度泛函B3LYP方法在6-311+G(d)基组水平上研究了Fe 原子与N2分子相互作用的单端位构型的直线形和弯曲形两种结构的平衡几何结构、电子结构、轨道布局及红外光谱等性质. 计算结果表明, 由于强的σ-σ电子对互斥作用, 基组态4s²3d⁶的Fe原子不能与N2分子发生化学作用; 当Fe 原子呈现可与N2之间发生σ-π授予反馈作用的激发组态时, Fe 与N2分子之间可形成稳定的结构; 在得到的多个电子态中, 能量最低的是直线形的1³∑^-, 比Fe(a⁵D)和N2(¹∑⁺g )能量高21.6 kJ·mol-1, 同时存在几个能量相近的电子态, 如1³∏、1³Φ; 弯曲形都是不稳定态, 可能是连接直线形和单侧双配位构型的过渡态; 单端位构型产物相对于基态的反应物均是热力学不稳定的; 单端位构型中Fe对N2的活化作用很小, N—N 键长增加不超过7 pm.     

PdYn±(n=0, 1, 2, 3)分子离子的结构与稳定性

在Pd和Y原子相对论有效原子实势和基函数SDD下, 使用密度泛函理论B3LYP方法对PdYn±(n=0, 1, 2, 3)分子离子的势能曲线与稳定性进行计算研究, 结果表明, PdY分子和PdY−, PdY2−, PdY3−与PdY+分子离子的基态电子状态分别为X2Σ、X1Σ、X2Σ、X1Σ、X1Σ, 能稳定存在, 势能函数可用Murrell-Sorbie函数表达, 并计算得到相应的力常数与光谱数据; PdY2+和PdY3+分子离子的基态分别为X2Σ和X1Σ, 是亚稳定态, PdY3+分子离子的三重态是排斥态, 不能稳定存在.     

Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.     

Chemistry with ADF

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order‐N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency‐dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF‐typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation‐strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time‐dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001     

硅杂环戊二烯衍生物电子结构与光谱性质的理论研究

采用密度泛函理论(DFT)B3LYP/6-31G*方法, 对2,5位取代的硅杂环戊二烯(Silole)系列衍生物进行几何结构优化, 通过计算得到电离能、电子亲和势、空穴抽取能及电子抽取能等相关能量, 并使用TD-DFT方法研究其吸收光谱, 分析相关能量及光谱的变化规律. 采用单组态相互作用(CIS/6-31G*)方法优化得到它们的最低单重激发态(S1)结构, 在此基础上, 使用TD-DFT方法计算对应的发射光谱. 分析2,5位芳基取代硅杂环戊二烯衍生物(DADPS)激发态与基态的结构差异及原因, 研究前线分子轨道的分布情况, 并讨论发光特征及载流子传输性能. 研究结果表明, 激发态结构弛豫主要发生在Silole环和直接与2,5位芳基相连的部位; 前线轨道主要分布在Silole环和2,5位芳基上; 二吡咯取代物有望成为空穴传输材料, 二噻吩取代物和二呋喃取代物有望在发光器件中表现出较高的发光效率.     

Singlet excitation energies of thiophene derivatives of fluorene: TD‐DFT study

Fluorene‐thiophene (FT)‐based oligomers and polymers and their derivatives are good candidates for organic blue light‐emitting diodes. In this work, the intrinsic properties of the ground and excited states of FT monomer and its derivatives are studied. The ground‐state optimized structures and energies are obtained using molecular orbital theory and density functional theory (DFT). The ground‐state potential energy curves or surfaces of FT and its derivatives are also obtained. All derivatives are nonplanar in their electronic ground states. The character and energy of the first 20 singlet–singlet electronic transitions are investigated by applying the time‐dependent density functional theory (TD‐DFT) approximations to the correspondingly optimized ground‐state geometries. The lowest singlet state is studied with the configuration interaction (singles) approach (CIS). Excitation energies are red shifted when the FT unit or its derivatives are extended longitudinally. CIS results suggest geometry relaxation in the first singlet excited state. When available, a comparison is made with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Generalized Christoffel–Darboux formulae and the frontier Kohn–Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.     

最优化“调控”区间分离密度泛函理论的研究进展

发展精确、高效的交换-关联泛函一直是密度泛函理论工作者所追求的神圣目标。传统密度泛函被证实在计算原子或分子体系的某些基态和激发态性能时存在困难,而且预测不具有普适性;另一方面,一些高水平方法如耦合簇（CC）理论和基于格林函数（G）和屏蔽库仑作用（W）近似的多体微扰理论（MBPT）,尽管相对精确但往往需要消耗昂贵的计算成本,因而其研究体系的尺寸和实用性受到了很大的限制。近年来,“最优化”调控区间分离泛函的发展在一定程度上使得上述问题得到改善,尤其是在消耗较少的计算成本前提下能够达到与高水平方法相媲美的预测精度,引起了越来越多的关注。本文首先简要回顾了密度泛函领域的理论背景,在区间分离密度泛函理论的基础上,重点介绍了最优化“调控”的概念;并且结合近期的理论工作对其在实际计算时的表现进行评价;最后,就最优化“调控”方法的前景和应用进行了展望。