New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

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     

Ab Initio High Pressure Investigations of InI

The high pressure behaviour of InI is studied by DFT‐calculations and compared with experimental data. The existence of a 5s² electron pair in In⁺ represents an unfavourable bonding situation for high symmetry structures because of effective closed shell repulsion. Since cations with a ns² electron pair are highly polarizable and the electronic situation is more favourable in the low symmetry structure InI prefers a TlI‐type structure at ambient pressure. A pressure induced transition to the more densely packed high symmetry CsCl‐type structure takes place at about 19 GPa according to our calculations. At ambient pressure the interactions are predominantly ionic. However with increasing pressure the distances between In⁺ cations in the TlI‐type structure diminish drastically, mainly due to the changing space requirement of the lone electron pair. Apart from ionic interactions further bonding interactions between the In⁺ cations occur. At elevated pressure the electron localization function (ELF) as well as the band structure diagrams suggest metallic bonding between the In⁺ within the zigzag chain, i. e. increasing bonding interactions between the In⁺ cations due to the electron pair and its s‐p‐mixing. At ambient pressure In‐In interactions are rather weak and the space requirement of the lone electron pair mainly determines the characteristic arrangement of the ions. At elevated pressure the In‐In interactions become stronger and stabilise themselves additionally the specific structural arrangement.     

Ab Initio and Quantum Chemical Topology studies on the isomerization of HONO to HNO2. Effect of the basis set in QCT

The article focus on the isomerization of nitrous acid HONO to hydrogen nitryl HNO₂. Density functional (B3LYP) and MP2 methods, and a wide variety of basis sets, have been chosen to investigate the mechanism of this reaction. The results clearly show that there are two possible paths: 1) Uncatalysed isomerisation, trans‐HONO → HNO₂, involving 1,2‐hydrogen shift and characterized by a large energetic barrier 49.7 ÷ 58.9 kcal/mol, 2) Catalysed double hydrogen transfer process, trans‐HONO + cis‐HONO → HNO₂ + cis‐HONO, which displays a significantly lower energetic barrier in a range of 11.6 ÷ 18.9 kcal/mol. Topological analysis of the Electron Localization Function (ELF) shows that the hydrogen transfer for both studied reactions takes place through the formation of a ‘dressed’ proton along the reaction path. 1 Use of a wide variety of basis sets demonstrates a clear basis set dependence on the ELF topology of HNO₂. Less saturated basis sets yield two lone pair basins, V₁(N), V₂(N), whereas more saturated ones (for example aug‐cc‐pVTZ and aug‐cc‐pVQZ) do not indicate a lone pair on the nitrogen atom. Topological analysis of the Electron Localizability Indication (ELI‐D) at the CASSCF (12,10) confirms these findings, showing the existence of the lone pair basins but with decreasing populations as the basis set becomes more saturated (0.35e for the cc‐pVDZ basis set to 0.06e for the aug‐cc‐pVTZ). This confirms that the choice of basis set not only can influence the value of the electron population at the particular atom, but can also lead to different ELF topology. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.     

Nature of the ring-closure process along the rearrangement of octa-1,3,5,7-tetraene to cycloocta-1,3,5-triene from the perspective of the electron localization function and catastrophe theory

We analyze the behavior of the energy profile of the ring‐closure process for the transformation of (3Z,5Z)‐octa‐1,3,5,7‐tetraene 5 to (1Z,3Z,5Z)‐cycloocta‐1,3,5‐triene 6 through a combination of electron localization function (ELF) and catastrophe theory (CT). From this analysis, concepts such as bond breaking/forming processes, formation/annihilation of lone pairs, and other electron pair rearrangements arise naturally through the reaction progress simply in terms of the different ways of pairing up the electrons. A relationship between the topology and the nature of the bond breaking/forming processes along this rearrangement is reported. The different domains of structural stability of the ELF occurring along the intrinsic reaction path have been identified. The reaction mechanism consists of six steps separated by fold and cusp catastrophes. The transition structure is observed in the third step, d(C1? C8) = 2.342 Å, where all bonds have topological signature of single bonds (C? C). The “new” C1? C8 single bond is not formed in transition state and respective catastrophe of the ELF field (cusp) is localized in the last step, d(C1? C8) ≈ 1.97 Å, where the two monosynaptic nonbonding basins V(C1) and V(C8) are joined into single disynaptic bonding basin V(C1,C8). The V(C1,C8) basin corresponds to classical picture of the C1? C8 bond in the Lewis formula. In cycloocta‐1,3,5‐triene 6 the single C1? C8 bond is characterized by relatively small basin population 1.72e, which is much smaller than other single bonds with 2.03 and 2.26e. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Lone electron pair (E) role on the crystal structures and the mechanism of high ionic conductivity of PbSnF4E2. Stereochemical and ab initio investigations

The F^– anion mobility of archetype fast ionic conductor PbSnF₄ formerly investigated by neutron diffraction with temperature is revisited based on a joint stereochemical and DFT investigation. It is mainly shown that a rapid exchange between F anions at the different tetragonal lattice sites is enhanced within the polyhedra enclosing the lone pair E in a dynamic change of coordination from octahedral to square pyramidal as for Sn(II). E stereoactivity in the interspaces along c direction is illustrated by the electron localization function ELF isosurface representations and followed by the non linear change of the c lattice constant with temperature.     

The physical nature of the lone pair

Despite the large number of experimental and theoretical studies on the size, shape, and orientation of lone pairs and their resulting stereochemical character, lone pairs still remain poorly defined in terms of quantitative observable properties of a molecule. Using the conformation of saturated molecules and barriers to internal rotation, experimental chemists have arrived at conflicting sizes and orientations for lone pairs. Most theoretical attempts to define lone pair properties have centered on such non-observables as localized molecular orbitals or have been based on studies on isolated molecules.The use of observable properties to construct a consistent set of physical models to analyze the physical nature of lone pairs is discussed. Much as one probes an electric field with a test charge, probes such as H⁺, H^–, He and H could be used to probe regions of molecules such as NH₃ and H₂O where lone pairs are often postulated to exist.Ab initio quantum mechanical studies can be analyzed using electron density (and resulting changes during interaction), total pair density of electrons, the electrostatic potential about the molecule and bond energy analysis to study lone pair properties. A simple study of NH₃ using an H⁺ probe is presented to clarify the approach.     

On the Quantum Chemical Nature of Lead(II) “Lone Pair”

We study the quantum chemical nature of the Lead(II) valence basins, sometimes called the lead “lone pair”. Using various chemical interpretation tools, such as molecular orbital analysis, natural bond orbitals (NBO), natural population analysis (NPA) and electron localization function (ELF) topological analysis, we study a variety of Lead(II) complexes. A careful analysis of the results shows that the optimal structures of the lead complexes are only governed by the 6s and 6p subshells, whereas no involvement of the 5d orbitals is found. Similarly, we do not find any significant contribution of the 6d. Therefore, the Pb(II) complexation with its ligand can be explained through the interaction of the 6s² electrons and the accepting 6p orbitals. We detail the potential structural and dynamical consequences of such electronic structure organization of the Pb (II) valence domain.     

Localization function study of excitation processes in a set of small isoelectronic molecules

Electron localization function (ELF) theory is used to characterize changes that occur upon excitation from ground singlet to first excited triplet states in a series of isoelectronic 16‐electron molecules including H₂CCH₂, HNCH₂, H₂CO, HNNH, HNO, and O₂ (ground triplet to excited singlet). ELF allows one to visualize lone pair or nonbonding electrons, and in these cases the π→π* or n→π excitation processes involved lead to an effective 90° rotation of the electronic structure about one heavy atom center and consequent distortion towards pyramidal symmetry about both heavy atom centers. The heavy atom bond lengths change very little in those cases where effectively two‐center three‐electron bonds can be formed (HNNH, HNO, and O₂) while a significant lengthening occurs in those cases where hydrogen atoms prevent such interactions (H₂CCH₂, HNCH₂, and H₂CO). It is shown that both ELF basin populations and atoms‐in‐molecules (AIM) delocalization indices reflect expected bond orders for conventional single and double bonds provided one compares the ratio of the molecular quantities rather than their absolute magnitudes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1702–1711, 2001     

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.     

Application of the electron localization function to radical systems

An application of the topological electron localization function (ELF) analysis to free radical systems is presented. A separation of the ELF function into its α‐spin and β‐spin contributions has been performed. Methyl and phenyl radicals, ortho‐, meta‐, and para‐benzyne biradicals, and their corresponding radical anions have been chosen with the aim to validate the new ELF_α and ELF_β proposed functions. The results show that the ELF separation yields complementary information about the localization of the unpaired electron. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The role of non-bonding electron pairs in intermetallic compounds

The Electron Localisation Function, ELF pictorially visualises chemists' intuitive ideas of single and multiple bonds as well as non-bonding electron pairs in molecules. The power of the representation of chemical bonds via ELF is that on the one hand covalent, polar, and ionic bonds are distinguishable, and that on the other hand ELF can be calculated for molecules and solids. This enables us to transfer the ideas of chemical bonding from molecular to intermetallic compounds. Localised two-electron-two-centre bonds and lone pairs are present in solid-state valence compounds (Zintl phases) as expected by the 8-N rule. In solids, lone pairs are generally more contracted than in molecules due to 'lone-pair repulsion'. In intermetallic compounds localised electrons predominantly occur in the form of lone pairs. Lattice vibrations influence the strength of lone pair interactions and non-bonded interactions lead to an exchange of delocalised and localised electrons. Such a mechanism of local electron pair formation gives rise to ideas of a chemical view of the phenomenon of superconductivity in intermetallic compounds.     

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.     

Influence of core–valence separation of electron localization function

The electron localization function (ELF) shows too-high values when computed from valence densities only (instead of using the total density). This effect is mainly found when d electrons are present in the outermost shell of the core. Although no pronounced qualitative differences could be noticed in the examples studied up to now, it is found that the quantitative differences between the values of ELF obtained from the valence densities only or from the total densities can be large. We also show, for the first time, an example (the Be atom) where ELF is obtained directly from the density. This exemplifies the possibility of computing ELF from highly accurate calculations (or from experimental data). © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1431–1439, 1997     

Novel Tin Structure Motives in Superconducting BaSn5 – The Role of Lone Pairs in Intermetallic Compounds [1]

BaSn₅ is the tin richest phase in the system Ba/Sn and is obtained by stoichiometric combination of the elements. The compound peritecticly decomposes under formation of BaSn₃ and a Sn–Ba melt at 430 °C. The structure shows a novel structure motive in tin chemistry. Tin atoms are arranged in graphite‐like layers (honeycombs). Two such layers form hexagonal prisms which are centered by Sn. Consequently the central tin atom has the unusual coordination number 12. The two‐dimensional tin slabs which consist of two 3⁶ and one 6³ nets of Sn atoms are separated by 6³ nets of Ba atoms with Ba above the center of each tin hexagon. The structure of BaSn₅ can be rationalized as a variante of AlB₂ and thus also of the superconducting MgB₂. Temperature dependent magnetic susceptibility measurements show that BaSn₅ is superconducting with T_c = 4.4 K. Reinvestigation of the magnetism of the Ba richer phase BaSn₃ reveals for this compound a T_c of 2.4 K. LMTO band structure and density of states calculations verify the metallic behavior of BaSn₅. The van Hove scenario of high‐temperature cuprate superconductors is discussed for this ‘classical' intermetallic superconductor. An analysis of the electronic structure with the help of fat‐band projections and the electron localization function (ELF) shows that the van Hove singularity in the DOS originates from non‐bonding (lone) electron pairs in the intermetallic phase BaSn₅. The role of lone pairs in intermetallic phases is discussed with respect to superconducting properties.     

ns2np4 (n = 4, 5) lone pair triplets whirling in M*F2E3 (M* = Kr,Xe): Stereochemistry and ab initio analyses

The stereochemistry of ns²np⁴ (n = 4, 5) lone pair LP characterizing noble gas Kr and Xe (labeled M*) in M*F₂ difluorides is examined within coherent crystal chemistry and ab initio visualizations. M*²⁺ in such oxidation state brings three lone pairs (E) and difluorides are formulated M*F₂E₃. The analyses use electron localization function (ELF) obtained within density functional theory calculations showing the development of the LP triplets whirling {E₃} quantified in the relevant chemical systems. Detailed ELF data analyses allowed showing that in α KrF₂E₃ and isostructural XeF₂E₃ difluorides the three E electronic clouds merge or hybridize into a torus and adopt a perfect gyration circle with an elliptical section, while in β KrF₂ the network architecture deforms the whole torus into an ellipsoid shape. Original precise metrics are provided for the torus in the different compounds under study. In KrF₂ the geometric changes upon β → α phase transition is schematized and mechanisms for the transformation with temperature or pressure are proposed. The results are further highlighted by electronic band structure calculations which show similar features of equal band gaps of 3 eV in both α and β KrF₂ and a reorganization of frontier orbitals due to the different orientations of the F-Kr-F linear molecule in the two tetragonal structures.     

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.     

Optical Sensing of Cesium Using 1,3-Alternate Calix[4]-mono- and Di(anthrylmethyl)aza-crown-6

We have synthesized two derivatives of alkylanthracene covalently bonded to 1,3-alternate calix[4]aza-crown-6 at the nitrogen position to study the effect of alkali metal ion complexation on the emission properties of anthracene fluorophore. The mono- and dianthryl-substituted probes are weakly fluorescent because their emission is partially quenched by photoinduced electron transfer (PET) from the nitrogen lone pair to the excited singlet state of anthracene. Upon complexation of alkali metal ions (e.g. K⁺, Cs⁺) by the crown moiety, the nitrogen lone pair can no longer participate in the PET process causing an enhancement in the emission of anthracene fluorophore (fluorescent turn on). The maximum fluorescence enhancement observed upon complexation of cesium ions by mono- and dianthryl-substituted calix[4]aza-crown-6 relative to the uncomplexed form was 8.5- and 11.6-fold, respectively.