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.     

Understanding reaction mechanisms in organic chemistry from catastrophe theory applied to the electron localization function topology

Thom's catastrophe theory applied to the evolution of the topology of the electron localization function (ELF) gradient field constitutes a way to rationalize the reorganization of electron pairing and a powerful tool for the unambiguous determination of the molecular mechanisms of a given chemical reaction. The identification of the turning points connecting the ELF structural stability domains along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a chemical transformation, such as multiple bond forming/breaking processes, ring closure processes, creation/annihilation of lone pairs, transformations of C-C multiple bonds into single ones. The reaction mechanism of some relevant organic reactions: Diels-Alder, 1,3-dipolar cycloaddition and Cope rearrangement are reviewed to illustrate the potential of the present approach.     

Maximum probability domains from Quantum Monte Carlo calculations

Although it would be tempting to associate the Lewis structures to the maxima of the squared wave function |Psi|2, we prefer in this paper the use of domains of the three-dimensional space, which maximize the probability of containing opposite-spin electron pairs. We find for simple systems (CH4, H2O, Ne, N2, C2H2) domains comparable to those obtained with the electron localization function (ELF) or by localizing molecular orbitals. The different domains we define can overlap, and this gives an interesting physical picture of the floppiness of CH5+ and of the symmetric hydrogen bond in FHF-. The presence of multiple solutions has an analogy with resonant structures, as shown in the trans-bent structure of Si2H2. Correlated wave functions were used (MCSCF or Slater-Jastrow) in the Variational Quantum Monte Carlo framework.     

Comparison of the electron localization function and deformation electron density maps for selected earth materials

The electron localization function (ELF) and experimental and theoretical deformation electron density maps are compared for several earth materials and one representative molecule. The number and arrangement of the localized one-electron probability density domains generated in a mapping of the ELF correspond to the number and arrangement of the localized electron density domains generated in a mapping of the deformation electron density distribution, a correspondence that suggests that the two fields are homeomorphically related. As a homeomorphic relationship has been established previously between the Laplacian of the electron density distribution and the ELF, the relationship suggests that the deformation electron density distribution is also homeomorphically related to the Laplacian of the distribution.     

Electronic fluxes during diels‐alder reactions involving 1,2‐benzoquinones: mechanistic insights from the analysis of electron localization function and catastrophe theory

By means of the joint use of electron localization function (ELF) and Thom's catastrophe theory, a theoretical analysis of the energy profile for the hetero‐Diels‐Alder reaction of 4‐methoxy‐1,2‐benzoquinone 1 and methoxyethylene 2 has been carried out. The 12 different structural stability domains obtained by the bonding evolution theory have been identified as well as the bifurcation catastrophes (fold and cusp) responsible for the changes in the topology of the system. This analysis permits finding a relationship between the ELF topology and the evolution of the bond breaking/forming processes and electron pair rearrangements through the reaction progress in terms of the different ways of pairing up the electrons. The reaction mechanism corresponds to an asynchronous electronic flux; first, the O1? C5 bond is formed by the nucleophilic attack of the C5 carbon of the electron rich ethylene 2 on the most electrophilically activated carbonyl O1 oxygen of 1 , and once the σ bond has been completed, the formation process of the second O4? C6 bond takes place. In addition, the values of the local electrophilicity and local nucleophilcity indices in the framework of conceptual density functional theory accounts for the asychronicity of the process as well as for the observed regioselectivity. © 2012 Wiley Periodicals, Inc.     

An electron localization function investigation of bonding in some simple four‐coordinate nitrogen and phosphorus compounds

The bonding in some simple four‐coordinate species involving nitrogen and phosphorus has been studied by the electron localization function (ELF) approach and compared to that in their conventionally singly and doubly bonded counterparts. Despite evidence suggesting the presence of a conventional multiple bond in certain cases of the four‐coordinate species, the ELF study shows this not to be the case. Rather, the situation is better pictured as, for example, in the case of H₃PCH₂as where both ionic and covalent interactions are present, a type of bond we term cov‐ionic. While the ionic interaction is generally strong, the covalent part can be weak, as in the case of the four‐coordinate nitrogen compounds, or strong, as in the case of the four‐coordinate phosphorus species. The quantum mechanically determined properties of the cov‐ionic bonded compounds are consistent with this picture. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:341–352, 2000     

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.     

Bonding in the Si2H2 isomers: A topographical study

Chemical bonding in the isomers of the formally triply bonded Si₂H₂ system are studied from the point of view of electron localization function (ELF) bond basin populations and atoms‐inmolecules (AIM) delocalization indices. Calculation carried out at the B3LYP/6‐31 + G(d,p) and MP2 (FC)/6‐31 + G(d,p) level leads to ELF topographies and basin populations that are in good agreement with our intuitive chemical pictures of bonding in these molecules. One single, two double, and one triple silicon silicon bonds are found in the four isomers. It is shown that, with one AIM exception, ratios of basin populations and delocalization indices are consistent and useful in characterizing the nature of the chemical bonding involved. © 2002 John Wiley & Sons, Inc. Heteroatom Chem 13:53–62, 2002; DOI 10.1002/hc.1106     

Chemical bonding in TiSb(2) and VSb(2): a quantum chemical and experimental study

The chemical bonding in the isostructural intermetallic compounds TiSb2 and VSb2, crystallizing in the CuAl2 type, was investigated by means of quantum chemical calculations, particularly the electron localization function (ELF), as well as by Raman spectroscopy, Hall effect and conductivity measurements on oriented single crystals, and high-pressure X-ray powder diffraction. The homogeneity ranges of the compounds were determined by powder X-ray diffraction, WDXS, and DSC measurements. TiSb2 exhibits no significant homogeneity range, while VSb2 shows a small homogeneity range of approximately 0.3 at. %. According to the ELF calculations, the Sb atoms form dumbbells via a two-center two-electron bond, while the T atoms (T = Ti, V) build up chains along the crystallographic c-axis. Both building units are connected by covalent T-Sb-T three-center bonds, thus forming a three-dimensional network. The strength of the bonds involving Sb was determined by fitting a force constant model to the vibrational mode frequencies observed by polarized Raman measurements on oriented single crystals. The resulting bond order of the Sb2 dumbbells is 1, while the strength of the three-center bonds resembles a bond order of 1.5. The weak pressure dependence of the c/a ratio confirms the slightly different bonding picture in TiSb2 compared to that in CuAl2. Electrical transport measurements show the presence of free charge carriers, as well as a metal-like temperature dependence of the electrical resistivity.     

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.     

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.     

Electronic structure of germanium monohydrides Ge(n)H, n = 1-3

Quantum chemical calculations were applied to investigate the electronic structure of germanium hydrides, Ge(n)H (n = 1, 2, 3), their cations, and anions. Computations using a multiconfigurational quasi-degenerate perturbation approach (MCQDPT2) based on complete active space wave functions (CASSCF), multireference perturbation theory (MRMP2), and density functional theory reveal that Ge(2)H has a (2)B(1) ground state with a doublet-quartet gap of approximately 39 kcal/mol. A quasidegenerate (2)A(1) state has been derived to be 2 kcal/mol above the ground state (MCQDPT2/aug-cc-pVTZ). In the case of the cation Ge(3)H(+) and anion Ge(3)H(-), singlet low-lying electronic states are derived, that is, (1)A' and (1)A(1), respectively. The singlet-triplet energy gap is estimated to 6 kcal/mol for the cation. An "Atoms in Molecules" (AIM) analysis shows a certain positive charge on the Ge(n) (n = 1, 2, 3) unit in its hydrides, in accordance with the NBO analysis. The topologies of the electron density of the germanium hydrides are different from that of the lithium-doped counterparts. On the basis of our electron localization function (ELF) analysis, the Ge-H bond in Ge(2)H is characterized as a three-center-two-electron bond. Some key thermochemical parameters of Ge(n)H have also been derived.     

Unusual substituent effects on the bonding of iminoboranes

Substituent effects on iminoboranes XBNH, HBNX and XBNX (X = H, CH3, NH2, OH, F) have been analyzed in the framework of the NBO, AIM and ELF approaches, using B3LYP/6-311++G(d,p) optimized geometries and electron densities. Boron-substituted derivatives, XBNH, are more stable than the corresponding nitrogen-substituted isomers HBNX, with the energy difference increasing as the electron withdrawing character of the substituent increases. The BN linkage is not much affected by N-substitution, but it is significantly altered when the substituent is attached to the boron atom in both XBNH and XBNX series of compounds. Moreover, substituent effects on the structures of iminoboranes are opposite those observed for the corresponding isoelectronic acetylene derivatives. The ELF analysis indicates that electron-withdrawing substituents enhance the localization of electrons in a torus around the CC or the BN axis. As a result, although electron density is depleted at the bcp, the bond does not necessarily become weaker, since density increases around the periphery, a phenomenon named the "hole" effect. The dissimilarities between acetylene and iminoborane derivatives are primarily a consequence of the significant distortion of this torus in the latter, due to the large difference between the electronegativities of B and N, which leads to a large contribution of the X-B=:N-Y resonance structure in some cases. The "hole" effect is reflected in a reasonable correlation between the Laplacian of the electron density at the bcp and the BN bond length.