Electron localization function for transition-metal compounds

 The analysis of the electron localization function of molecules and solids needs to involve the atomic core regions as well to reveal a more detailed insight into the bonding situation. Received: 20 February 2002 /Accepted: 14 June 2002 /Published online: 19 August 2002     

Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.     

A principle of linear covariance for quantum mechanics and the electronic structure theory of molecules and other atom clusters

Quantum mechanical equations should look the same in any non-orthonormal or orthonormal basis frame when properly formulated so as to be fully covariant under the largest group indicated. Non-orthonormal frames are crucial especially for the quantum theory of chemistry. Various methods such as valence-bond, localized orbital, molecular orbital, etc. result from a single formulation using the principle of linear covariance which is stated, proved, and exemplified. Molecular quantities with the full inclusion of overlaps are derived with the same ease as without overlaps.     

Electron localization and delocalization indices for solids

The electron localization and delocalization indices obtained by the integration of exchange‐correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Local structure of the chemical bond in metal azides calculated in a basis set of Wannier functions

The local structure of the chemical bond in molecular ion crystals of alkaline and heavy metal azides (MN₃, M = Li, Tl, Ag) is discussed in terms of Wannier functions. Various schemes of localization are considered in relation to the peculiarities of electronic structure, and hybridization effects, leading to anion-cation complexes in compounds with covalent bonds, are analyzed.     

Nonorthogonal ultralocalized functions and fitted Wannier functions for local electron correlation methods for solids

Despite the formal exponential decay behavior of Wannier functions (WFs), their spatial extent, which is a key parameter determining the computational cost of local correlation calculations for solids, is still rather large. The problems with the localization of the WFs can partly be attributed to their mutual orthogonality. Possibilities of reduction of the spatial extent of the WFs without losing the accuracy of the calculations are investigated. A method for generation of nonorthogonal ultralocalized functions based on maximization of their Löwdin populations is developed. A scheme for fitting of the WFs and nonorthogonal localized functions with a limited support is proposed. The calculations show that by combining both techniques one can obtain quite compact linearly independent localized functions, which may significantly decrease the computational cost in post-HF calculations.     

电子定域化函数的含义与函数形式

电子定域化函数(ELF)是研究电子结构的重要工具.本文介绍了电子定域性的概念,从电子对密度和动能密度两个角度详细讨论了ELF的物理意义与其函数形式的联系,并将ELF推广到自旋极化形式.通过实例分析,指出了参考项在ELF 中起到了关键性作用.对两种自旋极化形式的ELF 的比较发现:CheckDen 和TopMoD程序中使用的形式并不合理,明显低估了单电子区域的定域性.最后指出了一些文献由于对ELF函数的错误理解而在引用时出现的错误.     

Nuclear attraction and electron interaction integrals of exponentially decaying functions and the Poisson equation

Summary The technique proposed by O-Ohata and Ruedenberg (J Math Phys 7:547 (1966)) and by Silver and Ruedenberg (J Chem Phys 49:4306 (1968)) of computing nuclear attraction and electron interaction integrals by solving an inhomogeneous Laplace equation can also be applied ifB functions (Filter E, Steinborn EO (1978) Phys Rev A 18:1) are used as basis functions in atomic and molecular calculations. It is shown that because of the remarkable mathematical properties ofB functions the derivation of compact explicit expressions for the multicenter integrals mentioned above is particularly simple. These results are also of interest in the context of other exponentially decaying functions, since all the other commonly occurring exponentially decaying functions as, for instance, Slater functions or bound state hydrogen eigenfunctions can be expressed as simple linear combinations ofB functions. Consequently, their multicenter integrals can also be expressed in terms of multicenter integrals ofB functions.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

Electron group functions for the analysis of the electronic structures of molecules

The electronic structure of a vast majority of molecular systems can be understood in terms of electron groups and their wave functions. They serve as a natural basis for bringing intuitive chemical and physical concepts into quantum chemical calculations. This article considers the general electron group functions formalism as well as its simple geminal version. We try to characterize the wave function with the group structure and its capabilities in actual calculations. For this purpose we implement a variational method based on the wave function in the form of an antisymmetrized product of strongly orthogonal group functions and perform a series of electronic structure calculations for small molecules and model systems. The most important point studied is the relation between the choice of electron groups and the results obtained. We consider energetic characteristics as well as optimal geometry parameters. In view of practical importance, the structure of variationally optimized local one-electron states is considered in detail as well as intuitive characteristics of chemical bonds.     

氯代亚乙烯基双噁唑的合成、晶体结构及其电子光谱

由氯代丁烯二酰氯和α－氨基苯乙酮的盐酸盐经缩合、关环反应合成了标题化合物Ⅰ、Ⅱ．用元素分析、紫外光谱、红外光谱、质谱鉴定了其结构，并用Ｘ射线衍射法测定了Ⅰ的晶体结构，其空间群为Ｐ２１，晶胞参数α＝０．８４５０（２）ｎｍ，ｂ＝０．６９９４（１）ｎｍ，ｃ＝１．５４３２（５）ｎｍ，β＝１０２．３８（２）°，Ｚ＝２．由于在烯键碳原子上引入体积较大的氯原子，使Ⅰ和Ⅱ分子的平面性变差，其电子光谱相对于反式－１，２－双［２－５－苯基唑基）］乙烯（ＰＯＥＯＰ）有蓝移，且荧光量子产率明显下降。     

Generalized one-electron spin functions and self-similarity measures

A simple method for construction of eigenfunctions of one-electron spin angular momentum operators from products of the primitive one-electron spin functions is presented. Properties of these functions and their applications to the evaluation of some integrals met in theory of quantum similarity are briefly discussed.     

用电子定域函数研究主族原子的壳层结构

采用电子定域函数(ELF)方法对第一到第四周期主族元素的壳层结构进行了研究。计算得到了各壳层半径及壳层内的电荷数,探讨了原子序数与壳层半径间的关系。结果有助于学生更好地理解原子的壳层结构。     

Fourier analysis,correlation functions and nonadiabatic electron transfer: Wavepackets and exact representations

Summary We investigate the validity of several common approximations in the analysis of nonadiabatic intramolecular electron transfer rate constants. Utilizing the Fourier representation of the golden rule form, we study the evolution of the vibrational correlation function that represents the density-of-states-weighted Franck-Condon factor. In particular, we test the validity of the perturbation theoretic golden rule form and of the Gaussian wavepacket representation for the vibrational wavefunctions against numerically exact quantum mechanical propagations. Although specific cases are found in which both of these break down, for a wide range of conditions (including anharmonic behavior and frequency changes), both the Gaussian wavepacket representation and the golden rule are excellent approximations.     

Diagonal coefficient representation of density functions and quantum similarity measures

Quantum similarity measures within a new theoretical point of view are described for arbitrary order density functions, with the aid of attached pseudo-wave functions, in a vector semispace structure associated with a Minkowski metric.     

On the correlation between the bifurcation values of the electron localization function and the nuclear independent chemical shift in aromatic and heteroaromatic compounds

In this work, for a representative set of 24 aromatic molecules, that includes hydrocarbons, hetero and charged rings, we explore the correlations between two aromaticity indexes. One of these indexes is based on the bifurcation values of the σ and π electron localization function (ELF), while the other one is the nuclear independent chemical shift (NICS). We observe that the quality of the possible correlations between these two kinds of indexes strongly depends on the kind of rings and on the particular indexes that are considered.     

新型有机电子受体氟代苝酰亚胺的合成与表征

设计和合成了一种新型有机电子受体N,N′-二(五氟代苯基)-3,4,9,10-苝四羧基二酰亚胺(DFPP),利用傅里叶红外光谱和核磁共振谱等方法表征了DFPP的分子结构,用紫外-可见吸收光谱、循环伏安法和电子自旋共振谱等手段证明了DFPP中极低的最低未占有轨道(LUMO)能级为-4.37eV.另外,还发现了DFPP薄膜的独特聚集态结构,五氟代苯基正好处于相邻分子苝环的正上方或正下方.     

Electron localization function and electron localizability indicator applied to study the bonding in the peroxynitrous acid HOONO

The ground‐state electronic structure of peroxynitrous acid (HOONO) and its singlet biradicaloid form (HO ··· ONO) have been studied using topological analysis of the electron localization function (ELF), together with the electron localizability indicator (ELI‐D), at the DFT (B3LYP, M05, M052X, and M06), CCSD, and CASSCF levels. Three isomers of HOONO (cis‐cis, cis‐perp, and trans‐perp) have been considered. The results show that from all functionals applied, only B3LYP yields the correct geometrical structure. The ELF and ELI‐D‐topology of the O? O and central N? O bonds strongly depends on the wave function used for analysis. Calculations carried out at CAS (14,12)/aug‐cc‐pVTZ//CCSD(T)/aug‐cc‐pVTZ level reveal two bonds of the charge‐shift type: a protocovalent N? O bond with a basin population of 0.82–1.08e, and a more electron depleted O? O bond with a population of 0.66–0.71e. The most favorable dissociation channel (HOONO → HO + ONO) corresponds to breaking of the most electron‐deficient bond (O? O). In the case of cis‐ and trans‐HO ··· ONO, the ELF, ELI‐D, and electron density fields results demonstrate a closed‐shell O ··· O interaction. The α‐spin electrons are found mainly (0.64e) in the lone pairs of oxygen V_{i = 1,2} (O) from the OH group. The β‐spin electrons are delocalized over the ONO group, with the largest concentration (0.34e) on the lone pair of nitrogen V(N). © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Photo-Induced Intermolecular Electron Transfer-Effect of Acceptor Molecular Structures

Photo-induced electron transfer versus molecular structure of acceptors is investigated using ultrafast time-resolved transient grating spectroscopy. Typical laser dyes Rhodamine 101 (Rh101) and Rhodamine 6G (Rh6G) in electron donor solvent-aniline are adopted as the objects. The forward electron transfer time constant from aniline to the excited singlet state of two Rhodamine dyes and subsequent back electron transfer from two dyes to aniline are measured. The experimental results denote that Rh6G presents faster electron transfer rates with aniline in both forward electron transfer and back electron transfer processes. With chemical calculation and qualitative analysis, it is found that the flexible molecular geometry of Rh6G leads to stronger electron coupling with donor solvent and further gives rise to larger electron transfer rates.