Single electron densities: a new tool to analyze molecular wavefunctions

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.     

Application of the topological analysis of the electronic localization function to archetypical [Pb(II)Ln]p complexes: The bonding of Pb2+ revisited

The coordination of neutral ligands (L = OC, HCN, NH₃, PH₃, SH₂, HNCO and H₂O) to Pb²⁺ is investigated and analyzed by means of the topological analysis of the Electronic Localization Function (ELF). It is shown that the mean charge density of the V(Pb) basin (〈ρ〉_V(Pb)) can reach a ligand‐independent limiting value from n = 6, a coordination number from which the [PbL_n]²⁺ complexes adopt holodirected structures. The investigations performed on anionic series (L = HS^?, OH^?, CN^?, F^?, Cl^?, and Br^?) lead to optimized stable structures in which the coordination number does not exceed n = 4, even in the presence of a model aqueous solvent. This different behavior with respect to the neutral ligand series is interpreted by means of natural populations and electrostatic repulsions. The main result of this contribution is that stable Pb(II) complexes could be those exhibiting reasonable values of 〈ρ〉_V(Pb), namely those not exceeding the saturation plateau evidenced in the present piece of work. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic and kinetic potentials and electron density allowed partitioning any molecules and crystals into atomic - and potential-based -basins; -basins explicitly account for the electron exchange effect, which is missed for -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of - and -basins. The gap between - and -basins represents the charge transfer, while the gap between - and -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of -, -, and - basin boundaries between interacting atoms was proposed. The position of -boundary between - and -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's -basin penetrates oxygen atom's -basin, while for covalent bonds a -boundary closely approaches a -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the -basin of an electron occupier atom.     

Understanding lead chemistry from topological insights: the transition between holo- and hemidirected structures within the [Pb(CO)n]2+ model series

In this contribution, we focus to the currently unknown [Pb(CO)(n)](2+) model series (n=1 to 10), a set of compounds which allows us to investigate in-depth the holo- and hemidirectional character that lead complexes can exhibit. By means of DFT computations performed using either relativistic four-component formalisms coupled to all-electron basis sets for [Pb(CO)](2+), [Pb(OC)](2+) and [Pb(CO)(2)](2+), or scalar relativistic pseudopotentials for higher n values, the structure and the energetics of these species are investigated. The results are complemented by Constrained Space Orbital Variations (CSOV) and Electron Localization Function (ELF) comprehensive analyses in order to get better insights into the poorly documented chemical fundamentals of the Pb(2+) cation. Whereas the discrimination between holo- and hemidirected structures is usually done according to the geometry, we here provide a quantitative indicator grounded on (V(Pb)), the mean charge density of the valence monosynaptic V(Pb) ELFic basin associated to the metal cation. Free-enthalpy relying discussions show, moreover, that those gas-phase complexes having n=7, 8 or 9 may be experimentally instable and should dissociate into [Pb(CO)(6)](2+) and a number of CO ligands. According to second-order differences in energy, it is anticipated that the n=3 or 6 structures should be the most probable structures in the gas phase. Gathering all data from the present theoretical study allows us to propose some concepts that the versatile structural chemistry of Pb(2+) complexes could rely on.     

Comparative Analysis of Electron‐Density and Electron‐Localization Function for Dinuclear Manganese Complexes with Bridging Boron‐ and Carbon‐Centered Ligands

Bonding in borylene‐, carbene‐, and vinylidene‐bridged dinuclear manganese complexes [MnCp(CO)₂]₂X (X=B‐tBu, B=NMe₂, CH₂, C?CH₂) has been compared by analyses based on quantum theory of atoms in molecules (QTAIM), on the electron‐localization function (ELF), and by natural‐population analyses. All of the density functional theory based analyses agree on the absence of a significant direct Mn? Mn bond in these complexes and confirm a dominance of delocalized bonding via the bridging ligand. Interestingly, however, the topology of both charge density and ELF related to the Mn‐bridge‐Mn bonding depend qualitatively on the chosen density functional (except for the methylene‐bridged complex, which exhibits only one three‐center‐bonding attractor both in ??²ρ and in ELF). While gradient‐corrected functionals provide a picture with localized two‐center X? Mn bonding, increasing exact‐exchange admixture in hybrid functionals concentrates charge below the bridging atom and suggests a three‐center bonding situation. For example, the bridging boron ligands may be described either as substituted boranes (e.g., at BLYP or BP86 levels) or as true bridging borylenes (e.g., at BHLYP level). This dependence on the theoretical level appears to derive from a bifurcation between two different bonding situations and is discussed in terms of charge transfer between X and Mn, and in the context of self‐interaction errors exhibited by popular functionals.     

价层电子对互斥理论的改进——计算中心原子价层电子对数的新方法

对氢、卤素、氧族元素作配位原子时提供的价电子数做了合理的解释,并推导出计算中心原子价层电子对数的新方法,该方法不需要书写路易斯结构式再确定成键电子对数和孤电子对数,也不必规定不同族的原子作配位原子时提供的价电子数,只需要根据公式即可直接得到中心原子的价层电子对数。     

Activation of C–H bond in methane by Pd atom from the bonding evolution theory perspective

We report detailed study focused on the electron density redistribution during the simple oxidative addition reaction being the crucial stage of various catalytic processes. The bonding evolution theory based on the electron localization function and Thom's catastrophe theory shows that activation of methane's C? H bond by Pd atom consist of six elementary steps. The important feature revealed is the pronounced reorganization of Pd's outer core maxima corresponding to N‐shell electrons of metal. Electronic rearrangements identified in this model reaction are likely to be the case in the more complex reactions of the same type involving transition metal compounds and, in principle, can be observed by modern ultrafast spectroscopy and diffraction techniques. © 2013 Wiley Periodicals, Inc.     

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.     

Revealing the Bonding Pattern from the Molecular Electron Density Using Single Exponential Decay Detector: An Orbital‐Free Alternative to the Electron Localization Function

We introduce a new tool (single exponential decay detector: SEDD) to extract information about bonding and localization in atoms, molecules, or molecular assemblies. The practical evaluation of SEDD does not require any explicit information about the orbitals. The only quantity needed is the electron density (calculated or experimental) and its derivatives up to the second order.     

The Electronic Structures and Chemical Bonding of Some Dinuclear and Trinuclear Low－valence Molybdenum Complexes Containing Thiolate Bridges

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改进的相对论量子化学计算ZORA方法

提出一种改进的ZORA(Zeroth-OrderRegularApproximationtotheDiracEquation)方法,其单电子方程为：[σ·p(c^2/2c^2-V~0)σ·p+V(r)]ψ=εψ。式中V~0为空间限域的势能函数：V~0(r=~A∑V~0^A(r~A),r~A=|r-R~A|,V~0^A(r~A)=V^A(r~A){1+exp[α(r~A-r~0^A]}^-^1。其中A表示分子的某个组成原子,R~A为A原子的位置矢量,V^A(r~A)为自由A原子的势函数,α和r~0^A为参数。改进的ZORA方法具有原来方法的所有优点,避免了原有ZORA方法因不满足标度变换不变性带来的缺陷,而且计算过程简单。具体计算表明,通过适当选择参数α和r~0^A,用本研究提出来的方法,在计算分子几何结构和键合能时,基本上消除了ZORA方法由于标度变换依赖性产生的误差。     

Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond

The novel functional electron localizability indicator is a useful tool for investigating chemical bonding in molecules and solids. In contrast to the traditional electron localization function (ELF), the electron localizability indicator is shown to be exactly decomposable into partial orbital contributions even though it displays at the single-determinantal level of theory the same topology as the ELF. This approach is generally valid for molecules and crystals at either the single-determinantal or the explicitly correlated level of theory. The advantages of the new approach are illustrated for the argon atom, homonuclear dimers N2 and F2, unsaturated hydrocarbons C2H4 and C6H6, and the transition-metal-containing molecules Sc(2)2+ and TiF4.     

Unusual bond formation in aspartic protease inhibitors: a theoretical study

The origin of the formation of the weak bond N|C...O involved in an original class of aspartic protease inhibitors was investigated by means of the electron localization function (ELF) and explicitly correlated wave-function (MRCI) analysis. The distance between the electrophilic C and the nucleophilic N centers appears to be controlled directly by the polarity and proticity of the medium. In light of these investigations, an unusual dative N-C bonding picture was characterized. Formation of this bond is driven by the enhancement of the ionic contribution C(+)-O(-) induced mainly by the polarization effect of the near N lone pair, and to a lesser extent by a weak charge delocalization N-->CO. Although the main role of the solvating environment is to stabilize the ionic configuration, the protic solvent can enhance the C(+)-O(-) configuration through a slight but cumulative charge transfer towards water molecules in the short N-C distance regime. Our revisited bond scheme suggests the possible tuning of the N-CO interaction in the design of specific inhibitors.     

The role of π electrons in the formation of benzene-containing lithium-bonded complexes

The intermolecular interactions in C₆H₆???LiX (X=OH, NH₂, F, Cl, Br, NC, CN) complexes are investigated by using second‐order Møller–Plesset perturbation theory (MP2) calculations and quantum theory of “atoms in molecules” (QTAIM) studies, and the role of π electrons is studied in the formation of these benzene‐containing lithium‐bonded complexes. The molecular electrostatic potentials of benzene and LiX determine the geometries of the lithium‐bonded complexes. The electron densities at the lithium bond critical points in the πC₆H₆???LiX complexes are obviously stronger than those in the σC₆H₆???LiX complexes, which indicates that the intermolecular interactions in the C₆H₆???LiX complexes are mainly attributable to π‐type interaction. The topological and energy properties at the lithium bond critical points in both the C₆H₆???LiX and πC₆H₆???LiX complexes are linear with the interaction energies, thereby showing the crucial role of the π electrons in the formation of these complexes. Electron localization function (ELF) analysis indicates that the formation of the lithium bonds leads to the reduction of the ELF π‐electron density and volume, and the reduction of the π‐electron volume is linear with the interaction energies with the correction coefficient 0.9949.     

Computational study of the process of hydrogen bond breaking: the case of the formamide-formic acid complex

MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) quantum calculations are used to study the formamide-formic acid complex (FFAC), a system bound by two hydrogen bonds, N--H...O and O--H...O, that forms a bond ring at equilibrium. When the intermolecular separation between monomers R increases, this ring opens at a distance for which the weaker N--H...O bond breaks remaining the stronger O--H...O bond. The computational study characterizes that process addressing changes of interaction energy DeltaE, structure and properties of the electron density rho(r) as well as spatial distributions of rho(r), the electrostatic potential U(r), and the electron localization function eta(r). It is shown that the spatial derivatives of DeltaE, the topology of rho(r), and qualitative changes noticed in U(r) = 0 isocontours allow to identify a precise distance R for which one can say the N--H...O hydrogen bond has broken. Both levels of theory predict essentially the same changes of structure and electron properties associated to the process of breaking and virtually identical distances at which it takes place.     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

Quantification of electron correlation effects: Quantum Information Theory vs Method of Increments

Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap (“sloppy”) DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one-body MoI calculations.