On the significance of ELF basins

For perfectly localized orbitals, the basins of ELF are the domains in which the probability of finding a pair of electrons is maximal.     

AIM and ELF Analyses of Halogen Bonding in NCS:BrCl Complexes

The nature of halogen bonding in five complexes formed between the thiocyanate (NCS) radical and a BrCl molecule was analyzed by quantum theory of atoms in molecules (QTAIM) and electron‐localization function (ELF) in this paper. The calculated results show that the geometry of the halogen atom bonded at the N‐atom is stable than those bonded at S‐ or C‐atom. The molecular electrostatic potentials determine the geometries and stabilities of the complexes. The valence basin of the S‐ or N‐atom in the electron‐donating NCS radical is compressed and its population decreases during the process of formation of the halogen‐bonded complexes.     

Electron pairing and chemical bonds. Electron fluctuation and pair localization in ELF domains

This article reports the numerical comparison of the quantities characterizing the extent of electron fluctuation and pair localization in the domains determined by the direct minimization of electron fluctuation with the domains resulting from the partitioning of the molecules based on the topological analysis of the so-called electron localization function (ELF). Such a comparison demonstrates that the ELF partitioning can be regarded as a feasible alternative to computationally much more demanding direct optimization of minimum fluctuation domains. This opened the possibility of the systematic scrutiny of the electron pair model of the chemical bond, and as it was demonstrated, the previous pessimistic claims about the applicability of this model are not completely justified.     

Electron delocalization and bond formation under the ELF framework

A first approach to the relationship between the electron localization function (ELF) and electronic delocalization upon bond formation is provided. We show from first principles the ability of ELF at the bond critical points to act as an index of the electron reorganization involved in chemical bonding. Simultaneously, this index, that we shall call ELF delocalization index (EDI), constitutes a good measure of electron delocalization. We will show how the core of ELF is proportional to the Wiberg index under the valence bond approach. This relationship will be exploited for some representative examples where EDI is able to identify the stages of bond formation. Furthermore, a maximum in EDI along this process has been found to correlate with the molecular equilibrium configuration, allowing for a formulation of a ??maximal localization principle?? for the stable structure of covalent compounds in terms of ELF.     

Chiral aromaticities. AIM and ELF critical point and NICS magnetic analyses of Mobius-type aromaticity and homoaromaticity in lemniscular annulenes and hexaphyrins

An atoms-in-molecules (AIM) and electron localization function (ELF) critical point analysis is reported for two types of lemniscular system, each of which exhibits double-half-twist Mobius topology. This reveals that this type of conformation for [14]annulene 1 has, in addition to the obvious bond critical points (BCPs), two weaker transannular points in the central cross-over region. These can be interpreted in terms of local rings showing single-half-twist Mobius homoaromaticity in addition to the double-half-twist aromaticity revealed by the annulene as a whole. Another example of a single-half-twist Mobius homoaromatic 9 is suggested here to show aromatic properties as strong as its nonhomoaromatic analogue 8. The AIM critical points in 1 are relatively insensitive to the ring size (varied from 12 to 16), and only small changes are seen in the critical point properties when the pi-electron count is incremented from 4n+2 to 4n by dianion formation. These results are discussed in terms of the reported transformation of the 14-pi-electron octalene 10 by reduction/alkylation into 12, an isomer of 1. Another class of molecule that exhibits lemniscular topology is the phyrins. A transannular BCP in the central cross-over region for the double-half-twist aromatic [26]hexaphyrin 3 is revealed, which is not present for the double-half-twist antiaromatic [28]hexaphyrin 2. The NICS(rcp) for the former indicates strong Mobius homoaromaticity.     

The three-center-four-electron (3c-4e) bond nature revisited. An atoms-in-molecules theory (AIM) and ELF study

Theoretical calculations (B3LYP/6–311+ +G**) were performed on a series of formally hypervalent compounds showing linear three-center geometries. The bonding nature was analyzed by the electron density, ρ(r), and electron-localization function (ELF) topologies, including calculations of the AIM charges and NMR chemical shifts (GIAO method). In addition, a quantitative analysis was also performed of the localization and delocalization indexes, obtained from the electron-pair density in conjunction with the definition of an atom in a molecule. Furthermore, the populations and fluctuations in the ELF basins were also evaluated. The compounds studied presented linear (1–5), T-shaped (6–9), and bipyramidal structures (10–15). Our results support the 3c-4e model for the linear (1–5) structures, but reveal for the T-shaped (6–9) structures only a small contribution from this model. In addition, there is no evidence to support the 3c-4e bond scheme for the bipyramidal compounds (10–15). Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

ChemInform Abstract: The Electron Localization Function (ELF) in closo Boron Clusters

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Electron number probability distributions for correlated wave functions

Efficient formulas for computing the probability of finding exactly an integer number of electrons in an arbitrarily chosen volume are only known for single-determinant wave functions [E. Cances et al., Theor. Chem. Acc. 111, 373 (2004)]. In this article, an algebraic method is presented that extends these formulas to the case of multideterminant wave functions and any number of disjoint volumes. The derived expressions are applied to compute the probabilities within the atomic domains derived from the space partitioning based on the quantum theory of atoms in molecules. Results for a series of test molecules are presented, paying particular attention to the effects of electron correlation and of some numerical approximations on the computed probabilities.     

Use of ELF and AIM parameter ratios for bond order characterization of two‐, three‐, and four‐coordinate gallium hydrides

Calculations at the B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p) level involving the electron localization function (ELF) and atoms‐in‐molecules (AIM) methods have been carried out for two‐, three‐, and four‐coordinate gallium hydrides present in Na and Li salts and as the isolated dianionic species, for some isoelectronic germanium compounds, and for several neutral gallium hydrides. Using the ratio of delocalization indices and bond basin populations referenced to reasonable standards, formal bond orders are derived. While chemically expected bond orders are found in most cases, the situation in the [HGaGaH]²⁻ species appears to lie intermediate between bonds of order 2 and 3, and that for neutral trans‐bent HGaGaH is found to be best described as a bond of order 1. In these cases the larger bond order predicted by ELF bond basin populations evidently results from overlap of the bond basin into the lone pair (nonbonding) region of the molecule. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:175–185, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10120     

Electron pairing and chemical bonds: pair localization in ELF domains from the analysis of domain averaged Fermi holes

This article reports the application of a recently proposed formalism of domain averaged Fermi holes to the problem of the localization of electron pairs in electron localization function (ELF) domains and its possible implications for the electron pair model of chemical bond. The main focus was on the systems, such as H2O or N2, in which the "unphysical" population of ELF domains makes the parallel between these domains and chemical bond questionable. On the basis of the results of the Fermi-hole analysis, we propose that the above problems could be due to the fact that in some cases the boundaries of the ELF domains need not be determined precisely enough.     

Electron distribution in water by high-energy electron scattering

The differential cross-sections for high-energy electrons scattered from water have been measured over a wide range of momentum transfers. The effect of chemical binding was seen from the comparison between the experiment and the calculation for an independent-atom model. The ab initio calculation using SCF MO was carried out with respect to the elastic scattering. It was in a good agreement with the experiment and thus a reliable electron distribution in water was obtained.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

Fast topological analysis of 2D and 3D grids of data: application to the atoms in molecule (AIM) and the electron localization function (ELF)

The topological analysis of grids of data is used for determination of surfaces or volumes around maxima. The volumes are then related to chemical information such as atoms or bonds, and can be used for integration of local properties such as electronic population. The problem of global connectivity is reversed into the question of local connectivity yielding a linear scaling partition algorithm. Two packages are developed for a very fast analysis and partition of 2D or 3D grids of data, applications being made to C2H2, C2H4, C6H6, H2CO, and H2CS molecules using the Atoms in Molecule (AIM) or Electron Localization Function (ELF).     

On the nature of metal-carbon bonding: AIM and ELF analyses of MCH(n) (n = 1-3) compounds containing early transition metals

Ab initio and DFT calculations have been performed on a series of organometallic compounds, according to the formula MCH(n), where M = K, Ca, Sc, Ti, V, Cr, or Mn and n = 1-3. Various theoretical methods are compared, the B3LYP level yielding the same agreement with the experimental geometries available as the correlated MP2 and CISD methods, with the 6-311++G(3df,2p) basis set for C and H and Wachter's (15s11p6d3f1g)/[10s7p4d3f1g] basis set for transition metals. The main geometric and electronic features of the molecules studied are described, analyzing the M-C bonding characteristics in terms of the atoms in molecules theory (AIM) and the electron localization function (ELF). Although multiple bonding is expected from the Lewis bonding scheme, the results indicate an almost pure ionic bond for all of the systems studied. The net charge transfer from the metal to the carbon atom ranges from 0.5 to 1 e(-), and the electronic structure of the CH(n)(-) moiety is unaltered after the interaction with the metal cation, showing little or no effect on the shape of the electron pairing. The bond paths corresponding to a possible alpha-agostic bond for these systems are not present.     

Analysis of the probability distribution method for spectrum decomposition

The probability distribution method provides a new way for spectrum deconvolution, that is especially applicable in the case of poor counting statistics. Here it has been compared with the conventional least-squares curve-fitting method. A large number of spectrum regions of a few channels were generated to simulate a spectrum containing a low intensity peak on low background, and were evaluated by both methods, to establish which method provides an unbiased estimate of the peak area in the cases examined, and on what conditions.