Geometry of the Fluorides, Oxofluorides, Hydrides, and Methanides of Vanadium(V), Chromium(VI), and Molybdenum(VI): Understanding the Geometry of Non-VSEPR Molecules in Terms of Core Distortion

This paper describes a study of the topology of the electron density and its Laplacian for the molecules VF(5), VMe(5), VH(5), CrF(6), CrMe(6), CrOF(4), MoOF(4), CrO(2)F(2,) CrO(2)F(4)(2)(-) and CrOF(5)(-) all of which, except VF(5,) CrF(6), and CrOF(5)(-) have a non-VSEPR geometry. It is shown that in each case the interaction of the ligands with the metal atom core causes it to distort to a nonspherical shape. In particular, the Laplacian of the electron density reveals the formation of local concentrations of electron density in the outer shell of the core, which have a definite geometrical arrangement such as four in a tetrahedral arrangement or five in a square pyramidal or trigonal bipyramidal and six in an octahedral arrangement. Ligands that are predominately covalently bonded are found opposite regions of charge depletion between these core charge concentrations. In VH(5), VMe(5), CrOF(4), and MoOF(4), these core charge concentrations have a square pyramidal arrangement, and the regions of charge depletions have the corresponding inverse square pyramidal arrangement so that these molecules have a square pyramidal geometry rather than a trigonal prism geometry. In CrMe(6), there are five core charge concentrations with a trigonal bipyramidal arrangement so that the regions of charge depletion have a trigonal prismatic arrangement and the molecule has the corresponding trigonal prism geometry rather than an octahedral geometry. In contrast, molecules in which the only ligand is the more ionically bound fluorine are less affected by core distortion and have VSEPR-predicted structures. The unexpected bond angles in CrO(2)F(2) and the preference of CrO(2)F(4)(2)(-) for a cis structure are also discussed in terms of the pattern of core charge concentrations.     

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.     

Comments on the nature of the bonding in oxygenated dinuclear copper enzyme models

The nature of the bonding in model complexes of di-copper metalloenzymes has been analyzed by means of the electronic localization function (ELF) and by the quantum theory of atoms in molecules (QTAIM). The constrained space orbital variations (CSOV) approach has also been used. Density functional theory (DFT) and CASSCF calculations have been carried out on several models of tyrosinase such as the sole Cu2O22+ central core, the Cu2O2(NH3)62+ complex and the Cu2O2(Imidazol)62+ complex. The influence on the central Cu(2)O(2) moiety of both levels of calculation and ligand environment have been discussed. The distinct bonding modes have been characterized for the two major known structures: [Cu(2)(mu-eta(2): eta(2)-O(2))](2+) and [Cu(2)(mu-O(2))](2+). Particular attention has been given to the analysis of the O-O and Cu-O bonds and the nature of the bonding modes has also been analyzed in terms of mesomeric structures. The ELF topological approach shows a significant conservation of the topology between the DFT and CASSCF approaches. Particularly, three-center Cu-O-Cu bonds are observed when the ligands are attached to the central core. At the DFT level, the importance of self interaction effects are emphasized. Although, the DFT approach does not appear to be suitable for the computation of the electronic structure of the isolated Cu(2)O(2) central core, competitive self interaction mechanisms lead to an imperfect but acceptable model when using imidazol ligands. Our results confirm to a certain extent the observations of [M.F. Rode, H.J. Werner, Theoretical Chemistry Accounts 4-5 (2005) 247.] who found a qualitative agreement between B3LYP and localized MRCI calculations when dealing with the Cu(2)O(2) central core with six ammonia ligands.     

Ligand close packing and the geometry of the fluorides of the nonmetals of periods 3, 4, and 5

This paper discusses the geometry of the fluorides of the nonmetals of periods 3, 4, and 5 in terms of the ligand close packing (LCP) model according to which molecular geometry is determined primarily by ligand-ligand repulsions (Pauli closed shell repulsions) rather than by the bonding and lone pair Pauli repulsions of the VSEPR model. The LCP model becomes the dominant factor in determing geometry when the ligands are sufficiently crowded that they may be regarded as essentially incompressible. Ligand close packing is a modification of the VSEPR model in which ligand-ligand repulsion (Pauli closed shell repulsion) is given more emphasis than bonding and nonbonding electron pair Pauli repulsion. The nonmetals of period 3 are large enough to form octahedral six coordinated molecules in which the ligands are close packed. The larger nonmetals of period 4 also have a maximum coordination number of six and an octahedral geometry although the ligands are not close packed. Ligand radii derived from the interligand distances in the molecules of period 3 depend only on the charge of the fluorine ligands and are consistent with the previously derived radii obtained from the fluorides of the close packed tetrahedral molecules of the period 2 elements. Although the ligands in the molecules of the period 4 nonmetals are not close packed, these elements are not large enough to form molecules with a higher coordination number. However, the larger period 5 nonmetals may have coordination numbers of seven and eight. The seven coordinated molecules have a pentagonal bipyramidal geometry in which the equatorial ligands are close packed. The eight coordinated molecules have a square antiprism geometry, which is not a close packed geometry although the fluorine interligand distances are only a little larger than expected for close packing. The difference between the axial and equatorial bond lengths in the trigonal bipyramidal pentafluorides and the pentagonal bipyramidal pentafluorides can be understood on the basis of ligand close packing. Ligand packing prevents the lone pair in AF(6)E molecules from fully entering the valence shell and thereby exerting its full stereochemical effect so that these molecules have a C(3)(v)() distorted octahedral geometry rather than a geometry based on pentagonal bipyramidal seven coordination.     

A topological study of the geometry of AF6E molecules: weak and inactive lone pairs

The geometries of AF6E molecules, which may have either an O(h) or a C(3v) geometry, have been studied by means of the electron localization function. Our results show that when the molecule has a C(3v) geometry, there is a valence-shell monosynaptic V(A) basin corresponding to the presence of a lone pair in the valence shell of the central atom A. The population of this basin is, however, extensively delocalized so that the electron density has a core-valence basin character, which is consistent with an earlier suggestion of a weakly active lone pair that gives a C(3v) distorted octahedral molecule rather than the valence-shell electron-pair repulsion predicted pentagonal-pyramid geometry. In contrast, the molecules with O(h) geometry do not have a monosynaptic valence-shell basin, but they have a larger core. These results provide confirmation of a previous suggestion that in AX6E (X = Cl, Br, I) molecules with the O(h) geometry the ligands X are sufficiently closely packed around the central atom A so as to leave no space in the valence shell for the lone pair E, which remains part of the core. Among the corresponding fluorides, only BrF6- has the O(h) geometry, while the others have the C(3v) geometry because there is sufficient space in the valence shell to accommodate the lone pair, the presence of which distorts the O(h) geometry to C(3v). The energies of the O(h) and C(3v) geometries have been shown to be very similar so the observed geometries are a consequence of a very fine balance between ligand-ligand repulsions and the energy gained by the expansion of the two nonbonding electrons into the valence shell.     

Chemical bonding in hypervalent molecules: is the octet rule relevant?

The bonding in a large number of hypervalent molecules of P, As, S, Se, Te, Cl, and Br with the ligands F, Cl, O, CH(3), and CH(2) has been studied using the topological analysis of the electron localization function ELF. This function partitions the electron density of a molecule into core and valence basins and further classifies valence basins according to the number of core basins with which they have a contact. The number and geometry of these basins is generally in accord with the VSEPR model. The population of each basin can be obtained by integration, and so, the total population of the valence shell of an atom can be obtained as the sum of the populations of all the valence basins which share a boundary with its core basin. It was found that the population of the V(A, X) disynaptic basin corresponding to the bond, where A is the central atom and X the ligand, varies with the electronegativity of the ligand from approximately 2.0 for a weakly electronegative ligand such as CH(3) to less than 1.0 for a ligand such as F. We find that the total population of the valence shell of a hypervalent atom may vary from close to 10 for a period 15 element and close to 12 for a group 16 element to considerably less than 8 for an electronegative ligand such as F. For example, the phosphorus atom in PF(5) has a population of 5.37 electrons in its valence shell, whereas the arsenic atom in AsMe5 has a population of 9.68 electrons in its valence shell. By definition, hypervalent atoms do not obey the Lewis octet rule. They may or may not obey a modified octet rule that has taken the place of the Lewis octet rule in many recent discussions and according to which an atom in a molecule always has fewer than 8 electrons in its valence shell. We show that the bonds in hypervalent molecules are very similar to those in corresponding nonhypervalent (Lewis octet) molecules. They are all polar bonds ranging from weakly to strongly polar depending on the electronegativity of the ligands. The term hypervalent therefore has little significance except to indicate that an atom in a molecule is forming more than four electron pair bonds.     

Relationship between the critical points found by the electron localization function and atoms in molecules approaches in adducts with hydrogen bonds

In this work, 11 adducts with hydrogen bonds were studied by using the B3LYP exchange-correlation functional of the Kohn-Sham approach and the M?ller-Plesset second-order perturbation theory MP2. With both approaches, the geometry of each adduct was optimized with the aug-cc-pVTZ basis set. The binding energies of the considered systems, found by the MP2 method, range from 1.2 to 8.3 kcal/mol. By using the atoms in molecules (AIM) analysis and the electron localization function (ELF) we found that the critical points positions characteristic of hydrogen bonds obtained by AIM and ELF are very similar each other. Besides, we found a linear correlation between the critical points positions found by AIM and those obtained by ELF with the B3LYP method and also with the MP2 method. The slope of such a linear relationship was close to 1 and the y-intercept close to 0.     

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.     

Comparative study of the bonding in the first series of transition metal 1:1 complexes M-L (M = Sc, ..., Cu; L = CO, N(2), C(2)H(2), CN(-), NH(3), H(2)O, and F(-))

The nature of the chemical bonding in the 1:1 complexes formed by the fourth period transition metals (Sc, ..., Cu) with 14 electrons (N(2), CN(-), C(2)H(2)) and 10 electrons (NH(3), H(2)O, F(-)) ligands has been investigated at the ROB3LYP/6-311+G(2d) level by the ELF topological approach. The bonding is ruled by the nature of the ligand. The 10 electrons and anionic ligands are very poor electron acceptors and therefore the interaction with the metal is mostly electrostatic and for all metal except Cr the multiplicity is given by the [Ar]c(n)() configuration of the metallic core (n = Z - 20). The electron acceptor ligands which have at least a lone pair form linear or bent complexes involving a dative bond with the metal and the rules proposed previously for monocarbonyls hold. In the case of ethyne, it is not possible to form a linear complex and the cyclic C(2)(v)() structure imposed by symmetry possesses two covalent M-C bonds, therefore the multiplicity is given by the local core configuration [Ar]c(n)() for all metals except Mn and Ni.     

Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin‐polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 2016 Wiley Periodicals, Inc.     

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     

Electron Domains and the VSEPR Model of Molecular Geometry

The valence shell electron pair repulsion (VSEPR) model—also known as the Gillespie–Nyholm rules—has for many years provided a useful basis for understanding and rationalizing molecular geometry, and because of its simplicity it has gained widespread acceptance as a pedagogical tool. In its original formulation the model was based on the concept that the valence shell electron pairs behave as if they repel each other and thus keep as far apart as possible. But in recent years more emphasis has been placed on the space occupied by a valence shell electron pair, called the domain of the electron pair, and on the relative sizes and shapes of these domains. This reformulated version of the model is simpler to apply, and it shows more clearly that the Pauli principle provides the physical basis of the model. Moreover, Bader and his co-workers' analysis of the electron density distribution of many covalent molecules have shown that the local concentrations of electron density (charge concentrations) in the valence shells of the atoms in a molecule have the same relative locations and sizes as have been assumed for the electron pair domains in the VSEPR model, thus providing further support for the model. This increased understanding of the model has inspired efforts to examine the electron density distribution in molecules that have long been regarded as exceptions to the VSEPR model to try to understand these exceptions better. This work has shown that it is often important to consider not only the relative locations and sizes, but also the shapes, of both bonding and lone pair domains in accounting for the details of molecular geometry. It has also been shown that a basic assumption of the VSEPR model, namely that the core of an atom underlying its valence shell is spherical and has no influence on the geometry of a molecule, is normally valid for the nonmetals but often not valid for the metals, including the transition metals. The cores of polarizable metal atoms may be nonspherical because they include nonbonding electrons or because they are distorted by the ligands, and these nonspherical cores may have an important influence on the geometry of a molecule.     

A theoretical study on the reaction mechanism for the bergman cyclization from the perspective of the electron localization function and catastrophe theory

The reaction mechanism associated with the Bergman cyclization of the (Z)-hexa-1,5-diyne-3-ene to render p-benzyne has been analyzed by means of a combined use of the electron localization function (ELF) and the catastrophe theory on the basis of density functional theory (DFT) calculations (B3LYP/6-31G(d)). The complex electronic rearrangements of this reaction can be highlighted using this novel quantum mechanical perspective. Five domains of structural stability of the ELF occurring along the intrinsic reaction path as well as four catastrophes (fold-cusp-fold-cusp) responsible for the changes in the topology of the system have been identified. The multiple factors that occur along the intrinsic reaction coordinate path are presented and discussed in a consistent way. The topological analysis of ELF and catastrophe theory reveals that mechanical deformation of the C1-C2-C3 unit and closed-shell repulsion between terminal acetylene groups lead to an early formation of diradicaloid character at C2 and C5 atoms. Immediately after the transition structure (TS) is reached, the open-shell-singlet biradical becomes stable. Meanwhile, C1 and C6 atoms are preparing to be covalently bonded; that will finally occur at a distance of 1.791 A. In addition, a separation of the ELF into in-plane (sigma) and out-of-plane (pi) contributions allows us to discuss the aromaticity profiles; sigma-aromaticity appears in the vicinities of the TS, while pi-aromaticity takes place in the final stage of the reaction path, once the ring has been formed.     

电子定域化函数的含义与函数形式

电子定域化函数(ELF)是研究电子结构的重要工具.本文介绍了电子定域性的概念,从电子对密度和动能密度两个角度详细讨论了ELF的物理意义与其函数形式的联系,并将ELF推广到自旋极化形式.通过实例分析,指出了参考项在ELF 中起到了关键性作用.对两种自旋极化形式的ELF 的比较发现:CheckDen 和TopMoD程序中使用的形式并不合理,明显低估了单电子区域的定域性.最后指出了一些文献由于对ELF函数的错误理解而在引用时出现的错误.     

Evidence of an unexpectedly long C-C bond (>2.7 A) in 1,3-metalladiyne complexes [Cp2MCCR]2 (M = Ti, Zr): QTAIM and ELF analyses

Topological analyses of the electron density using the quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) have been carried out, at the B3LYP/DGVZVP and MP2/DGVZVP theoretical levels, on different 1,3-metalladiyne cyclic compounds [Cp2M(CCR)]2, (M = Ti, Zr; R = F, CH3, H, SiH3). The QTAIM results indicate the presence of an extraordinarily long C-C bond (in a 2.7-3.0 A range) connecting the CCR moieties, contrary to the common geometrical assumption of a M-M bond in similar metallacycles. The existence of this C-C bond is also supported by the distinct consequences on the reaction profiles for the Ti and Zr complexes, the CC oxidative coupling reactions being favored only for the Ti complexes. Moreover, the consequences of this bonding in the coupling/cleavage reactions of these metallacyclic complexes are reported and analyzed, revealing the transcendence of these long-range bonds in the overall behavior of these compounds.     

Nature of chemical bonding and metalloaromaticity of Na2[(MArx')3] (M = B, Al, Ga; Arx' = C6H3-2,6-(C6H5)2)

The nature of chemical bonding and metalloaromaticity of Na(2)[(MArx')(3)] (M = B, Al, Ga) have been studied within the framework of the atoms in molecules (AIM) theory and using electron localization function (ELF) analysis. The π electrons of the studied systems were separated from the total electron density and analyzed. The calculated results indicate that there are closed-shell weak interactions between the sodium atom and the M(3) (M = B, Al, Ga) ring, between the sodium atom and the terminal phenyl group on each Arx', and between the terminal phenyl groups on Arx' in Na(2)[(MArx')(3)]. The Na(2)[(MArx')(3)] has metalloaromatic nature, and the sodium atoms have an active role in determining the computed aromatic properties of the three-numbered cycle.     

Electron localization function as information measure

The conditional two-electron probability function, which defines the electron localization function (ELF) of Becke and Edgecombe in the Kohn-Sham theory, is interpreted as the nonadditive (interorbital) Fisher information contained in the electron distribution. The probability normalization considerations suggest a use of the related information measure defined in terms of the unity-normalized probability distributions (shape factors of the electron densities), as the key ingredient of the modified information-theoretic ELF. This modified Fisher information density is validated by a comparison with the original two-electron probability function. Illustrative applications to typical molecular systems demonstrate the adequacy of the modified information-theoretic ELF in extracting the key features of the electron distributions in molecules. The overall Fisher information itself and the associated information-distance quantities are also proposed as complementary localization functions.