Ab initio structure and vibrational frequencies of lithium aromatic sulfonyl imide salts

The structure and vibrational frequencies of an aromatic lithium sulfonyl imide, i.e., lithium bis(4-nitrophenylsulfonyl)imide (LiNPSI) has been studied using self-consistent ab initio Hartree–Fock and hybrid density functional methods. These calculations engender two linkage isomers, which correspond to the local minima on the potential-energy surface. In the lowest-energy isomer, the ligand binds to the metal ion through two oxygens, one from each of the different SO₂ groups on the central nitrogen and forms a six-membered ring. Another LiNPSI isomer, wherein the anion coordinates through oxygen and nitrogen atoms and which is 55.9 kJmol⁻¹ higher in energy, has also been obtained. The S–N–S bond angle in the free anion as well as in the LiNPSI complex turns out to be nearly 121°. A comparison of the vibrational spectra of the free NPSI anion and that of the LiNPSI complex reveals that the SO₂ stretching vibrations at 1,239 and 1,205 cm⁻¹ can be used to differentiate between the two linkage isomers of the complex. The stronger complexation ability of the NPSI anion, compared to that for (CF₃SO₂)₂N⁻ has been explained in terms of the charge density within the molecular electrostatic potential isosurface encompassing both SO₂ groups of the anion. Received: 20 February 2002 / Accepted: 25 March 2002 / Published online: 3 June 2002     

Perspective on “Self-consistent equations including exchange and correlation effects”

 The paper by Kohn and Sham (KS) is important for at least two reasons. First, it is the basis for practical methods for density functional calculations. Second, it has endowed chemistry and physics with an independent particle model with very appealing features. As expressed in the title of the KS paper, correlation effects are included at the level of one-electron equations, the practical advantages of which have often been stressed. An implication that has been less widely recognized is that the KS molecular orbital model is physically well-founded and has certain advantages over the Hartree–Fock model. It provides an excellent basis for molecular orbital theoretical interpretation and prediction in chemistry. Received: 16 February 1999 / Accepted: 22 June 1999 / Published online: 9 September 1999     

Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

The Physical and Electronic Structure of M<Subscript>2</Subscript> Quadruply Bonded Complexes: A Density Functional Theory Study

The electronic structures and the physical properties (vertical excitation energies, vibrational stretching frequencies, and bond lengths) of a variety of M–M quadruply bonded (M = Mo, W) complexes are investigated using density functional theory (DFT). By utilizing a variety of pure and hybrid exchange-correlation (XC) functionals and a number basis sets, we are able to recommend a theoretical methodology for most efficiently probing the electronic structures of homoleptic M₂(O₂CR)₄ and bridged M₂(O₂C-X-CO₂)M₂ (R = organic group, typically H; X = conjugated organic group) complexes.

石墨烯条带的电子结构与性质:电场及长度效应

在密度泛函理论(DFT)和含时密度泛函理论(TDDFT)的基础上对宽度上含有8个zigzag链的石墨烯条带(8-ZGNR)的基态和激发态的性质进行了理论研究,着重考察了条带长度及电场的影响.B3LYP杂化泛函的计算结果显示:在基态上,8-ZGNR的最低能量态并不具有磁性,随着长度的增加,才会显示出反铁磁的性质.静电场的加入使8-ZGNR显示出反铁磁性和半金属性.在激发态上,诱导电子会随着外激光脉冲的变化而发生移动和变化,但是相比而言,α自旋电子更容易被激发而产生较明显的诱导电子密度,而β自旋电子则更容易脱离外激光场的控制而产生非绝热现象.     

ESIPT和TICT荧光发射的电子结构特征及发射能计算

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)相结合的计算方案对八种结构相似的水杨酰苯胺衍生物及其类似物第一激发单重态(S1)进行考察, 证实它们的荧光发射分属分子内质子转移(ESIPT)和分子扭转-电荷转移(TICT)两种不同机制且结论与已知实验事实相符. ESIPT发光的化合物在电子跃迁前后无明显的电荷转移发生, 发射能计算的适用泛函是OLYP和BLYP等无Hartree-Fock(HF)交换成分的纯泛函; TICT发光的化合物在电子跃迁前后发生明显的电荷转移, 其适用泛函为含约37% HF交换成分的混合型泛函(例如mPW1B95和MPW1K). 按上述原则来选择适用泛函, 即可在TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上正确预测水杨酰苯胺衍生物和类似物的发射能, 平均精度可达0.2 eV. 兼具质子转移与电荷转移双反应通道的化合物, 两者的竞争遵从能量最小原理, 结果使荧光发射仅选择其中一个通道进行. 泛函的选择只与实际发生的反应有关, 与并未实际发生的反应通道无关. 附加的八个算例进一步表明, 此成功的计算方案可望推广应用于其它类型的ESIPT和TICT荧光有机物.     

Electronic Structure Characteristics of ESIPT and TICT Fluorescence Emissions and Calculations of Emitting Energies

A scheme of time-dependent density functional theory (TDDFT) combined with the single-excitation configuration interaction (CIS) approach was employed to investigate the first excited singlet state (S₁) for eight salicylanilide derivatives and analogues, which have similar structural formulas. The results showed that fluorescence-emitting mechanisms of these molecules were in two distinct manners (excited-state intramolecular proton transfer (ESIPT) and twisted intramolecular charge transfer (TICT)), which agreed with the well-known experiments. For ESIPT compounds with inconspicuous charge transfer (CT) during electron transition, pure functionals without Hartree-Fock (HF) exchange energy, such as OLYP and BLYP, were suitable to calculate emitting energies. For TICT compounds with large CT during electron transition, hybrid functionals with about 37% HF exchange energy, such as mPW1B95 and MPW1K, performed well. On condition that the exchange-correlation (XC) functionals were chosen properly according to the rules above, reliable emitting energies for salicylanilide derivatives and analogues could be obtained at the TDDFT/6-31G(d)//CIS/3-21G(d) level. The average accuracy reached about 0.2 eV. For the salicylanilides with both proton transfer (PT) and CT reaction channels, only one channel occurred actually according to the principle of energy minimum. This actual reaction decided proper XC functionals, whereas the reaction that did not occur actually was trivial. Eight appendent compounds were calculated to prove that this successful scheme is expected to be suitable for other ESIPT and TICT compounds.     

Attractive electron–electron interactions within robust local fitting approximations

An analysis of Dunlap's robust fitting approach reveals that the resulting two‐electron integral matrix is not manifestly positive semidefinite when local fitting domains or non‐Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four‐center two‐electron integrals based on the resolution‐of‐the‐identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair‐atomic resolution‐of‐the‐identity (PARI) approach, atomic‐orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree–Fock and Kohn–Sham calculations, the indefinite integral matrix causes nonconvergence in the self‐consistent‐field iterations. In these cases, the two‐electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb‐metric RI method. The speed‐up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple‐zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky‐decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. © 2013 Wiley Periodicals, Inc.     

含水Mg3Al-LDH-Cl的电子结构与成键特征

建立了Mg₃Al-LDH-Cl-nH₂O (n＝0～2)双层周期性计算模型. 选用密度泛函理论-赝势平面波法CASTEP, 从原子轨道布居、Mulliken电荷布居、态密度(DOS)等方面, 计算研究了含层间水情况下体系的电子结构及成键特征, 并探求了层间水分子含量及水分子的电子屏蔽效应对Mg₃Al-LDH-Cl-nH₂O材料电子结构的影响. 结果表明体系层板上 M—O同时具有共价键与离子键两种特征, 主客体之间以静电作用为主, 而层间客体之间的相互作用以氢键作用为主. 层间H₂O的电子屏蔽作用主要表现为对层间阴离子的影响以及对层板上二价金属阳离子的影响. 主体层板的电价成分和层间域的共价成分均随着水分子数目的增加而增加.     

LiVPO4F电子结构及电化学性质的第一性原理研究

采用密度泛函理论(DFT)结合投影缀加波(PAW)方法,对LiVPO₄F的晶体结构,电子结构和电化学属性进行了研究。从理论上获得了脱Li前后具体的晶格参数的变化。通过对其态密度的计算,发现在放电过程中,V在化合物中呈现离子态,发生+3/+4价态的转变,电子转移主要发生在V原子上;而P原子的状态比较稳定,并不发生大的电子的转移,磷酸根的空间结构也变化不大。同时LiVPO₄F的禁带宽度仅为1.63 eV,说明其在一定情况下具有良好的导电性,有利于放电过程中电子的输运。LiVPO₄F是铁磁相,磁矩为2μ_B,而VPO₄F为反铁磁相。此外,通过计算获得了LiVPO₄F的平均嵌锂电压为4.0 eV。     

Examination of several density functionals in numerical Kohn–Sham calculations for atoms

We studied several exchange‐only and exchange–correlation energy density functionals in numerical, i.e., basis‐set‐free, nonrelativistic Kohn–Sham calculations for closed‐shell ¹S states of atoms and atomic ions with N electrons, where 2≤N≤120. Accurate total energies are presented to serve as reference data for algebraic approaches, as do the numerical Hartree–Fock results, which are also provided. Gradient‐corrected exchange‐only functionals considerably improve the total energies obtained from the usual local density approximation, when compared to the Hartree–Fock results. Such an improvement due to gradient corrections is not seen in general for highest orbital energies, neither for exchange‐only results (to be compared with Hartree–Fock results), nor for exchange–correlation results (to be compared with experimental ionization energies). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 227–241, 2001     

锂离子电池正极材料LiMnPO4的电子结构

采用基于密度泛函理论的第一性原理计算方法,计算了锂离子电池LiMnPO4正极材料的电子结构。计算结果表明:当Li+嵌入体系后,O和P的原子布居变化较小,电子向金属原子的转移明显得到加强。Li+和O2-有弱相互作用,当Li+离子脱出以后,氧原子所得到的电子数减小,导致布居减小。锂是以离子形式存在的于LiMnPO4正极材料中。在LiMnPO4和MnPO4体系中,Mn原子具有磁性,其磁矩分别为4.78μB和3.84μB,其余原子磁性近似为0。氧为负离子,带负电荷,而P和Mn则为正离子。O2p与P3s、P3p轨道发生有效重叠,并形成共价键,Mn3d和O2p之间能够有效地发生重叠并形成共价键。在放电过程中有电子从外电路进入正极,大部分电子所带电荷分布在Mn原子上。     

锂离子电池LiTi0.25Fe0.75SO4F正极材料的电子结构

采用密度泛函理论平面波赝势的方法,计算了LiFeSO₄F和LiTi_0.25Fe_0.75SO₄F正极材料的电子结构。计算结果表明：当锂嵌入材料后,S、O和F的原子布居变化较小,电子主要填充在过渡金属的3d轨道,导致过渡金属被还原,成为电化学反应的活性中心。在嵌锂态中,锂和氧（氟）之间形成了离子键,而过渡金属（Ti和Fe）与氧（氟）之间则形成了共价键,S-O键的共价性最强。态密度的计算结果则表明：Ti和Fe均保持高自旋排列结构;LiFeSO₄F的两个自旋通道的带隙分别为2.88和2.29 eV,其导电性很差;Ti掺杂使体系的带隙消失,显著地提高了正极材料的导电性;LiTi_0.25Fe_0.75SO₄F系统中Ti-O和Ti-F键均比纯相中的Fe-O和Fe-F键的共价性更强,因此Ti掺杂材料具有更好的结构稳定性。     

锂离子电池LiTi_(0.25)Fe_(0.75)SO_4F正极材料的电子结构

采用密度泛函理论平面波赝势的方法,计算了LiFeSO_4F和LiTi_(0.25)Fe_(0.75)SO_4F正极材料的电子结构。计算结果表明:当锂嵌入材料后,S、O和F的原子布居变化较小,电子主要填充在过渡金属的3d轨道,导致过渡金属被还原,成为电化学反应的活性中心。在嵌锂态中,锂和氧(氟)之间形成了离子键,而过渡金属(Ti和Fe)与氧(氟)之间则形成了共价键,S-O键的共价性最强。态密度的计算结果则表明:Ti和Fe均保持高自旋排列结构;LiFeSO_4F的两个自旋通道的带隙分别为2.88和2.29 e V,其导电性很差;Ti掺杂使体系的带隙消失,显著地提高了正极材料的导电性;LiTi_(0.25)Fe_(0.75)SO_4F系统中Ti-O和Ti-F键均比纯相中的Fe-O和Fe-F键的共价性更强,因此Ti掺杂材料具有更好的结构稳定性。     

Methoxy and Methyl Group Rotation: Solid‐State NMR 1H Spin‐Lattice Relaxation,Electronic Structure Calculations,X‐ray Diffractometry,and Scanning Electron Microscopy

We report solid‐state ¹H nuclear magnetic resonance (NMR) spin‐lattice relaxation experiments, X‐ray diffractometry, field‐emission scanning electron microscopy, and both single‐molecule and cluster ab initio electronic structure calculations on 1‐methoxyphenanthrene ( 1 ) and 3‐methoxyphenanthrene ( 2 ) to investigate the rotation of the methoxy groups and their constituent methyl groups. The electronic structure calculations and the ¹H NMR relaxation measurements can be used together to determine barriers for the rotation of a methoxy group and its constituent methyl group and to develop models for the two coupled motions.