通过价层电子密度分析展现分子电子结构

迄今已有众多实空间函数被提出用来揭示化学上感兴趣的分子电子结构特征,例如化学键、孤对电子和多中心电子共轭。在这些分析方法中,电子定域化函数(ELF)、电子密度的拉普拉斯(∇²ρ)和变形密度(ρ_def)被广泛用于实际研究。众所周知,分析分子的总电子密度无法像以上提及的方法那样展现出与分子电子结构有关的丰富的信息。但是,在本文中,通过数个实例以及通过与ELF、∇²ρ和ρ_def的对比,我们指出若只关注价层电子密度分布,分子电子结构特征也是可能被探究的。我们发现对大多数情况,对非常简单的价层电子密度的分析也可以给出与ELF、∇²ρ和ρ_def分析类似的信息,并且这种分析具有计算复杂度更低的额外优点。我们希望本文的工作可以使得化学家们关注长期被忽视的价层电子密度所具有的重要价值。也值得注意的是,价层电子密度分析并非完全没有缺点,当这种方法无法提供丰富信息的时候,研究者仍需借助于其它类型的分析手段。     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997     

Estimating π binding energy of N‐Heterocyclic carbenes: The role of polarization

In this work, the tuneability of the π acceptor or donor properties of a set of N‐heterocyclic carbenes (NHCs) with a wide spectrum of electronic characteristics is established by means of density functional theory and energy decomposition analysis (EDA) tools. Even though the main orbital interaction contribution to the NHC coordination is the σ donation, a significant contribution of the π interactions to the bond is observed. By means of carefully selected coordination sites, different contributions to the π interactions could be identified and isolated. It includes not only the well known back donation and donation interactions, but also the intrafragment polarization, which has not been considered in previous studies. This can be obtained through the use of the extended transition state method for EDA combined with the natural orbitals for chemical valence and the constrained space orbital variation analysis. The contributions vary with the position of the heteroatoms and the presence of exocyclic substituents; the donation/backdonation π interactions between NHC and the coordination site can range between 2 and 61% of the total π orbital interactions, while the rest is owed to intrafragment polarization. Our results do not only contribute to the understanding of the electronic structure of NHC‐based complexes, giving ways to improve their catalytic properties, but also provide comprehension on the modelization methods used to study their donor–acceptor interactions. © 2015 Wiley Periodicals, Inc.     

Chemical bonding in refractory transition metal compounds with 8, 9, and 10 valence electrons

The chemical bonding in the refractory transition metal compounds TiC, TiN, and VN is investigated by experimental and theoretical techniques. High-precision X-ray diffraction is used to determine the electron densities in these three compounds experimentally. The X-ray structure factors and the respective valence electron densities are used twice, once to understand the chemical bonding and once to relate the experimental charge densities to those obtained from band structure calculations. These calculations, which in general are in very good agreement with experimental data, utilize the linearized augmented plane wave (LAPW) method. Theory and experiment lead to a detailed analysis of the chemical bonding in these compounds with 8, 9, and 10 valence electrons. By decomposition of the theoretical charge density into contributions from different states (energy regions), it was possible to show the strong covalent nonmetal p-metal d interaction, which is otherwise apparent only in TiC, but not in TiN or VN. In the latter two compounds the additional electrons occupy mainly metal d states with t_2g symmetry, so that in the total valence charge densities the most important bonding feature is covered. In addition to covalent interactions all compounds have a metallic bonding contribution as well as a considerable charge transfer from the metal to the nonmetal site. This mixture in chemical bonding accounts for the unusual combination of properties such as ultrahardness, high melting points, and good conductivity.     

Sublattice Method in Chemical Bond Theory for Dolomite Crystals

The distribution of valence and difference densities in crystalline CaMg(CO₃)₂ was calculated within the framework of the local density functional theory. It is shown that the terminal maxima of difference density located beyond the oxygen atom nuclei have different values due to the polarizing influence of the cations.     

Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin‐polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 2016 Wiley Periodicals, Inc.     

Density matrices from position and momentum densities

Summary One-electron density matrices, which are representable in single-centers-orbital basis sets, have been investigated with respect to their reconstruction from densities. The maximum allowed dimension for reconstruction from a combination of position & momentum density dependent properties is only slightly bigger than the dimension in the case of position (or momentum) densities only. Since for a given one-particle basis of dimensionM, the number of one-matrix elements which can be determined is also of orderM only, while the total number of one-matrix elements is of orderM ², it is in general necessary to introduce severe constraints and restrictions. The accuracy demands on the data and algorithms increase exponentially for linearly increasing size of basis set.     

Maximum-entropy analysis of momentum densities in diatomic molecules

The one-particle density in momentum space γ(p) is studied for diatomic molecules by using the maximum-entropy technique. The knowledge of one or more momentum expectation values <p"> provides approximations on the density γ(p) for any value of the momentum, which are convergent when increasing the number of known moments. Other unknown expectation values are estimated in terms of the constructed maximum-entropy densities. A numerical study of the quality of the approximations is carried out by means of experimental and theoretical data for the momentum expectation values involved. Experimental errors are also taken into account to have an idea of the sensibility of the results to the information from which they are obtained. © 1997 John Wiley & Sons, Inc.     

Electron localization function in full-potential representation for crystalline materials

The electron localization function (ELF) is implemented in the first-principles, all-electron, full-potential local orbital method. This full-potential implementation increases the accuracy with which the ELF can be computed for crystalline materials. Some representative results obtained are presented and compared with the results of other methods. Although for crystal structures with directed bonding only minor differences are found, in simple elemental metals, there are differences in the valence region, which give rise to different ELF topologies.     

Electronic structure,magnetic properties,and mixed valence character of Ce2Ni3Si5 from first principles calculations

Cerium intermetallic compounds exhibit anomalous physical properties such as heavy fermion and Kondo behaviors. Here, an ab initio study of the electronic structure, magnetic properties, and mixed valence character of Ce₂Ni₃Si₅ using density functional theory (DFT) is presented. Two theoretical methods, including pure Perdew–Burke–Ernzerhof (PBE) and PBE + U , are used. In this study, Ce³⁺ and Ce⁴⁺ are considered as two different constituents in the unit cell. The formation energy calculations on the DFT level propose that Ce is in a stable mixed valence of 3.379 at 0 K. The calculated electronic structure shows that Ce₂Ni₃Si₅ is a metallic compound with a contribution at the Fermi level from Ce 4f and Ni 3d states. With the inclusion of the effective Hubbard parameter (U _eff), the five valence electrons of 5 Ce³⁺ ions are distributed only on Ce³⁺ 4f orbitals. Therefore, the occupied Ce³⁺ 4f band is located in the valence band (VB) while Ce⁴⁺ 4f orbitals are empty and Located at the Fermi level. The calculated magnetic moment in Ce₂Ni₃Si₅ is only due to cerium (Ce³⁺) in good agreement with the experimental results. The U _eff value of 5.4 eV provides a reasonable magnetic moment of 0.981 for the unpaired electron per Ce³⁺ ion. These results may serve as a guide for studying present mixed valence cerium‐based compounds. © 2017 Wiley Periodicals, Inc.     

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca₆H₉[N(SiMe₃)₂]₃(pmdta)₃ (pmdta=N,N,N′,N′′,N′′-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n−1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.     

Stoichiometric Valence and Structural Valence—Two Different Sides of the Same Coin: “Bonding Power”

Two valencies instead of one! Stoichiometric valence and structural valence are two distinct properties of atoms. The former, ^stoichV, is derived from the composition of a compound and has integer values; the latter, ^structV, depends on the structure of a compound and has non‐integer values. The scheme shows a representation of valence states of antimony and oxidation of Sb^III to Sb^V, as a function of the eccentricity parameter Φ _i.

     

Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.     

Second-order quantum similarity measures from intracule and extracule densities

The calculation of quantum similarity measures from second-order density functions contracted to intracule and extracule densities obtained at the Hartree-Fock level is presented and applied to a series of atoms, (He, Li, Be, and Ne), isoelectronic molecules (C₂H₂, HCN, CNH, CO, and N₂), and model hydrogen-transfer processes (H₂/H⁺, H₂/Hot, H₂/H⁻). Second-order quantum similarity measures and indices are found to be suitable measures for quantitatively analyzing electron-pair density reorganizations in atoms, molecules, and chemical processes. For the molecular series, a comparative analysis between the topology of pairwise similarity functions as computed from one-electron, intracule, and extracule densities is carried out and the assignment of each particular local similarity maximum to a molecular alignment discussed. In the comparative study of the three hydrogen-transfer reactions considered, second-order quantum similarity indices are found to be more sensitive than first-order indices for analyzing the electron-density reorganization between the reactant complex and the transition state, thus providing additional insights for a better understanding of the mechanistic aspects of each process. Received: 7 July 1997 / Accepted: 29 October 1997     

Densities and Apparent Molar Volumes of Aqueous H<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>BO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript> Solutions at Temperatures from 296 to 573 K and at Pressures up to 48 MPa

Densities of four aqueous H₃BO₃ solutions (0.062, 0.155, 0.315, and 0.529 mol-kg^–1) have been measured in the liquid phase with a constant volume piezometer immersed in a precisely controlled liquid thermostat. Measurements were made at temperatures between 296 and 573 K and pressures from 0.82 to 48 MPa. The total uncertainties of the density, pressure, temperature, and molality measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.0005 mol-kg^–1, respectively. The accuracy of the method was confirmed by PVT measurements on pure water for two isobars (30 and 39 MPa) at temperatures from 313 to 573 K. The experimental and calculated (IAPWS formulation) densities for pure water show excellent agreement which is within their experimental uncertainties (average absolute deviation, AAD=0.012%;). Apparent and partial molar volumes were derived using the measured densities for solutions and pure water, and these results were extrapolated to zero concentration to yield the partial molar volumes of the electrolyte (H₃BO₃) at infinite dilution. The temperature, pressure, and concentration dependencies of the apparent and partial molar volumes were studied. Small pressure and concentration effects on the apparent molar volumes were found at temperatures up to 500 K. The parameters of a polynomial type of equation of state for the specific volume V_sol(P, T, m) as a function of pressure, temperature, and molality were obtained with a least-squares method using the experimental data. The root-mean-square deviation between measured and calculated values from this polynomial equation of state is ±0.2 kg-m^–3 for density. Measured values of the solution densities and the apparent and partial molar volumes are compared with data reported in the literature.     

Theory of chemical bonds in metalloenzymes IV: Hybrid‐DFT study of Rieske‐type [2Fe?2S] clusters

The Rieske‐type [2Fe? 2S] cores of electron‐transfer (ET) proteins in the mitochondrial respiratory chain have unusual properties, such as redox potentials and spectroscopy. In this study, part IV of a series, the inherent molecular structures and characteristic electronic structures of the Rieske‐type [2Fe? 2S] clusters are investigated using broken‐symmetry hybrid density functional theory (BS‐HDFT). Geometry optimizations for the oxidized and reduced states were performed and their characteristic vibrational modes are assigned. Magnetic properties are investigated using model Hamiltonians to describe the electron delocalization and the unsymmetric property. The parameters of the model Hamiltonian, such as exchange coupling J, valence delocalization B, and potential energy difference Δ, are evaluated from the BS‐HDFT calculations. The valence localization and excitation energy (ΔE) of the Rieske‐type [2Fe? 2S] cluster are discussed. The chemical bond nature is characterized by chemical indices from natural orbital analysis. Our theoretical results are reasonably consistent with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Sulfur- and Selenium-Containing Compounds Potentially Exhibiting Al Ion Conductivity

We have created a set of crystalline model structures exhibiting straight lines of Al³⁺ connected to chalcogenides (O²⁻, S²⁻, and Se²⁻) connected to metal cations of varying valence (Sr²⁺, Y³⁺, Zr⁴⁺, Nb⁵⁺, and Mo⁶⁺). They were relaxed with density functional theory computations and analysed by Bader partitioning. As Al³⁺ ions are supposed to strongly interact with their atomic environment, we studied the electron density topology induced by higher-valent cations in the extended chemical neighbourhood of Al. In fact, we found a general decrease of ionic charges and an increasing displacement of the chalcogenides towards higher-valent ions for the heavier chalcogens. Therefore, we comprehensively screened S- and Se-containing compounds for candidates theoretically exhibiting low migration barriers for Al³⁺ ions by using Voronoi–Dirichlet partitioning and bond valence site energy calculations. The basis for this search is the Inorganic Crystal Structure Database. Indeed, we could extract six promising candidates with low Al³⁺ migration barriers. which are even lower than the barriers for any other element inside of these materials. This will encourage efforts towards preparing suitable Al³⁺ conductors.     

Intermediate Valence Behavior of Yb2Cu9Al8

Intermediate valence behavior is frequently observed in materials containing Ce, Yb, Eu, Sm, or Tm. In the current work, we report synthesis and characterization of Yb₂Cu₉Al₈ (Th₂Zn₁₇ structure type). Its intermediate valence behavior can be described by an excitation energy E_ex/k_B = 319 K and a spin fluctuation temperature T_sf = 60 K. The valence state of Yb is estimated to be close to 2.04 for the low-temperature region. The valence gradually evolves to the value of 2.80 at T = 400 K. The specific heat coefficient of γ_exp = 59 mJ · mol_Yb^–1 · K^–2 indicates a moderate effective mass enhancement, together with finite density of states at the Fermi level. The latter is also confirmed by the band structure calculations.