Determination of substitutional sites in heterocycles from the topological analysis of the electron localization function (ELF)

The topological analysis of the electron localization function ELF has been carried out on five‐membered (C₄H₄NH, C₄H₄PH, C₄H₄O, C₄H₄S) and six‐membered (C₅H₅N, C₅H₅P) heterocycles. The bonding in these molecules is discussed on the basis of the valence basin populations. It is shown that the values of the ELF function at the (3,−1) critical points between disynaptic basins related to a given center provide a criterion to determine substitutional sites. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 509–514, 2000     

Charge-shift bonding--a class of electron-pair bonds that emerges from valence bond theory and is supported by the electron localization function approach

This paper deals with a central paradigm of chemistry, the electron-pair bond. Valence bond (VB) theory and electron-localization function (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair density plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RE(CS), and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contributions to the bond energy. The paper defines the atomic propensity and territory for CS bonding: Atoms (fragments) that are prone to CS bonding are compact electronegative and/or lone-pair-rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and involves: a) homopolar bonds of heteroatoms with zero static ionicity, b) heteropolar sigma and pi bonds of the electronegative and/or electron-pair-rich elements among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental manifestations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reactions as compared to hydrogen-transfers.     

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.     

The trinuclear gallium-bridged Ferrocenophane [{Fe(eta5-C5H4)2}3Ga2]: synthesis, bonding, structure, and coordination chemistry

The trinuclear ferrocenophane [{Fe(eta(5)-C(5)H(4))(3)}(2)Ga(2)] (3) featuring two sp(2)-hybridized gallium atoms in bridging positions between three ferrocene-1,1'-diyl units represents a novel type of ferrocene derivative. Compound 3 is obtained by thermal treatment of 1,1'-bis(dimethylgallyl)ferrocene (1) in nondonor solvents or in diethyl ether as solvent and subsequent thermal decomplexation. The [1.1]ferrocenophane [{Fe(eta(5)-C(5)H(4))(2)}(2){GaMe}(2)] (2) is an intermediate in the formation of 3. The reaction of 3 with an excess of trimethylgallium leads back to 1 and proves the reversibility of the multistep reaction sequence. Theoretical calculations reveal a carousel-type D(3h) structure for 3. The compound can best be described as being composed of three only weakly interacting ferrocenediyl units covalently connected by gallium atoms without any pi-bond contribution in the Ga--C bonds. Owing to steric constraints 3 cannot be reduced to the dianion 3(2-), which would feature a Ga--Ga bond. Compound 3 represents a stereochemically rigid difunctional Lewis acid allowing the formation of the adducts 3 a-3 d possessing linear donor-aceptor-aceptor-donor arrangements. Crystal structure data for 3 a-3 d show a symmetry-reduced chiral ferrocenophane core (D(3h)-->D(3)). A polymeric rodlike structure is observed for 3 b and 3 d caused by pi-stacking effects (3 b) or by a difunctional donor-acceptor interaction (3 d). In solution, the chirality of the adducts is lost by rapid interconversion of the enantiomers. A cyclic voltammogram of 3 b in pyridine reveals three quasi-reversible oxidation steps at -356, -154, and 8 mV, indicating only weak electron delocalization in the cationic species. The redox potentials of the pyridine adduct 3 b are compared with those of other pyridine-stabilized gallyl-sustituted ferrocene derivatives and with ferrocene itself.     

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     

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).     

A joint study based on the electron localization function and catastrophe theory of the chameleonic and centauric models for the Cope rearrangement of 1,5-hexadiene and its cyano derivatives

A novel interpretation of the chameleonic and centauric models for the Cope rearrangements of 1,5-hexadiene (A) and different cyano derivatives (B: 2,5-dicyano, C: 1,3,4,6-tetracyano, and D: 1,3,5-tricyano) is presented by using the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) on the reaction paths calculated at the B3LYP/6-31G(d,p) level. The progress of the reaction is monitorized by the changes of the ELF structural stability domains (SSD), each being change controlled by a turning point derived from CT. The reaction mechanism of the parent reaction A is characterized by nine ELF SSDs. All processes occur in the vicinity of the transition structure and corresponding to a concerted formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, respectively, together with an accumulation of charge density onto C(2) and C(5) atoms. Reaction B presents the same number of ELF SSDs as A, but a different order appears; the presence of 2,5-dicyano substituents favors the formation of C(1)-C(6) bonds over the breaking of C(3)-C(4) bond process, changing the reaction mechanism from a concerted towards a stepwise, via a cyclohexane biradical intermediate. On the other side, reaction C presents the same type of turning points but two ELF SSD less than A or B; there is an enhancement of the C(3)-C(4) bond breaking process at an earlier stage of the reaction by delocalizing the electrons from the C(3)-C(4) bond among the cyano groups. In the case of competitive effects of cyano subsituents on each moiety, as it is for reaction D, seven different ELF SSDs have been identified separated by eight turning points (two of them occur simultaneously). Both processes, formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, are slightly favored with respect to the parent reaction (A), and the TS presents mixed electronic features of both B and C. The employed methodology provides theoretical support for the centauric nature (half-allyl, half-radical) for the TS of D.     

New insights on the bridge carbon-carbon bond in propellanes: a theoretical study based on the analysis of the electron localization function

The nature of the bonding between bridgehead carbon atoms (Ca, Ca') as well as the ring strain in a family of 10 propellanes formed by three-, four-, or five-member rings: [1.1.1] (I), [2.1.1] (II), [3.1.1] (III), [2.2.1] (IV), [3.2.1] (V), [2.2.2] (VI), [3.3.1] (VII), [3.2.2] (VIII), [3.3.2] (IX), and [3.3.3] (X) are studied by means of the electron localization function (ELF) at the DFT level (B3LYP/cc-pVTZ). The ELF analysis of smaller propellanes (I, II, and III) reveals the coexistence of two resonance forms: one with a nonbonding electron pair partially delocalized between Ca and Ca' atoms outside the cage (ionic) and the other with a bridge bond between the same atoms (covalent). The weights of each form are calculated according to the ELF-basin populations, yielding 94, 88, and 53% for the ionic structure of I, II, and III, respectively, while larger propellanes (IV-X) present only the covalent form. The question of the s-character of the bridge bond is addressed by dissecting the bridge-bond ELF basin into the molecular orbital contributions. Finally, sigma-aromaticity associated to surface electron delocalization has been analyzed by means of nucleus-independent chemical shift (NICS) calculations. The results point out that the stability of the fused ring structure of propellanes I, II, and III, can be assigned to the remarkable sigma-aromaticity of the involved three-member rings.     

Li3[ScN2]: the first nitridoscandate(III)-tetrahedral Sc coordination and unusual MX2 framework

Li(3)[ScN(2)] was prepared from Li(3)N with Sc or ScN in a nitrogen atmosphere at 1020 K as a light yellow powder with an optical band gap of about 2.9 eV. The crystal structure was refined based on X-ray and neutron powder diffraction data (Ia$\bar 3$, Z=16, X-ray diffraction: R(profile)=0.078, R(Bragg)=0.070; Neutron diffraction: R(profile)=0.077, R(Bragg)=0.074; Rietfeld: a=1003.940(8) pm, Guinier: a=1004.50(3) pm). Li(3)[ScN(2)] is an isotype of Li(3)[AlN(2)] and Li(3)[GaN(2)] and crystallizes in an ordered superstructure of the Li(2)O structure type, leading to a three-dimensional framework of all-vertex-sharing tetrahedra 3[infinity[ScN[4/2][3-]]. Li is displaced from the center of a tetrahedron of N atoms in the direction of one trigonal face. Li(3)[ScN(2)] decomposes above 1050 K to form ScN and Li(3)N. Calculations of the periodic nodal surface (PNS) and of the electron localization function (ELF) support the picture of a covalent Sc-N network separated from isolated Li cations, whereby scandium d orbitals are involved in the chemical bonding.     

Aromaticity and electron affinity of Carbo(k)-[3]radialenes, k=0, 1, 2

Aromaticity enhancement is a possible driving force for the low reduction potentials of buta-1,3-diynediyl-expanded [N]radialenes: this hypothesis is theoretically analyzed for the expanded [3]radialene prototype. This study is undertaken within a more general prospect, namely the evaluation of the variation of aromaticity with endocyclic and peripheral carbomeric expansion of [3]radialene and its mono- and dianions. The structures, denoted as [C-H](6) (h)[C-C](3) (k)carbo-[3]radialene(q) (h=0, 1; k=0, 1, 2; q=0, -1, -2), were optimized in relevant singlet, doublet, or triplet spin states at the B3PW91/6-31G** level. They were found to be all planar. The structural aromaticity was measured through the average bond length d(av) over the [C-C](3) (k)carbo-[3]radialene core, and by the corresponding bond-length equalization parameter sigma(d), related to Krygowski's GEO. The magnetic aromaticity was measured by Schleyer's NICS values at the center of the rings. Regarding the relative variation of NICS and sigma(d), two classes of species can be distinguished according to their endocyclic expansion level. The species with a nonexpanded (k=0) or doubly expanded (k=2) ring constitute the first class: they exhibit D(3h) symmetry and a strong correlation of NICS with sigma(d). The species with a singly expanded ring (k=1) fall far from the correlation line, and constitute the second class. This class distinction is related to the degeneracy scheme of the frontier orbitals of the neutral representative. A finer appraisal of the electron (de)localization is brought by the ELF (Electron Localization Function) analysis of the electron density. It allows for a weighting of relevant resonance forms. Unsubstituted species are well described by the superimposition of two or three resonance forms. For (doublet spin state) monoanionic species, their respective weights are validated by comparison with AIM spin density. The weighted mean, n, of the formal numbers of paired pi(z) electrons in the resonance forms was calculated and compared with the closest even integer of either forms 4m+2 or 4m. A density-based continuous generalization of the orbital-based discrete Hückel rule is then heuristically proposed through an analytical correlation of NICS versus sigma(d), n, and S, the spin of the species. The frontier-orbital-degeneracy pattern of neutral species is discussed with respect to structural and magnetic aromaticity criteria. A decreasing HOMO-LUMO gap versus endocyclic expansion is obtained, but [C-C](3) (1)carbo-[3]radialene possesses the highest HOMO and LUMO energies. Vertical and adiabatic electron affinities of neutral and monoanionic species were also computed and compared with related experimental data.     

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.     

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 interplay of inverted redox potentials and aromaticity in the oxidized states of new pi-electron donors: 9-(1,3-dithiol-2-ylidene)fluorene and 9-(1,3-dithiol-2-ylidene)thioxanthene derivatives

Derivatives of 9-(1,3-dithiol-2-ylidene)fluorene (9) and 9-(1,3-dithiol-2-ylidene)thioxanthene (10) have been synthesised using Horner-Wadsworth-Emmons reactions of (1,3-dithiol-2-yl)phosphonate reagents with fluorenone and thioxanthen-9-one. X-ray crystallography, solution electrochemistry, optical spectroscopy, spectroelectrochemistry and simultaneous electrochemistry and electron paramagnetic resonance (SEEPR), combined with theoretical calculations performed at the B3P86/6-31G** level, elucidate the interplay of the electronic and structural properties in these molecules. These compounds are strong two-electron donors, and the oxidation potentials depend on the electronic structure of the oxidised state. Two, single-electron oxidations (E(1)ox < E(1)ox) were observed for 9-(1,3-dithiol-2-ylidene)fluorene systems (9). In contrast, derivatives of 9-(1,3-dithiol-2-ylidene)thioxanthene (10) display the unusual phenomenon of inverted potentials (E(1)ox > E(1)ox) resulting in a single, two-electron oxidation process. The latter is due to the aromatic structure of the thioxanthenium cation (formed on the loss of a second electron), which stabilises the dication state (10(2+)) compared with the radical cation. This contrasts with the nonaromatic structure of the fluorenium cation of system 9. The two-electron oxidation wave in the thioxanthene derivatives is split into two separate one-electron waves in the corresponding sulfoxide and sulfone derivatives 27-29 owing to destabilisation of the dication state.