Electron Localizability Indicator Research Articles

Structural Topology and Chemical Bonding in Laves Phases

A combined analysis of the electron localizability indicator (ELI; see isosurface ELI for TiBe2) and electron density, the characteristic structural motif of the Laves phases MN2 was shown to be mainly stabilized by charge transfer from M to N. In different groups of Laves phases, the bonding situation ranges from multicenter bonds between M and N atoms to the formation of Nδ− polyanions.

The Electron Localizability Indicator from X‐Ray Diffraction Data—A First Application to a Series of Epoxide Derivatives

No longer hidden! An extension of the capabilities of the X‐ray diffraction experiment is introduced. Locations of electron pairs within a molecule can be measured and made visible (see figure). This is demonstrated on a series of epoxides, for which ring strain, crystal, and substituent effects can be quantified. Comparison with experimental and theoretical electron‐density analyses shows the advantages of the new method.

Charge Transfer via the Dative N−B Bond and Dihydrogen Contacts. Experimental and Theoretical Electron Density Studies of Small Lewis Acid−Base Adducts

The electronic characteristics of the dative N−B bond in three Lewis acid−base adducts, hydrazine borane, hydrazine bisborane, and ammonia trifluoroborane, are analyzed by an approach combining experimental electron density determination with a broad variety of theoretical calculations. Special focus is directed to the weak dihydrogen contacts in hydrazine borane. The Atoms In Molecules partitioning scheme is complemented by additional methods like the Source Function, and the Electron Localizability Indicator. For the multipole-free theoretical models of hydrazine borane and hydrazine bisborane, a weak charge donation from Lewis base to acid of about 0.05 e is found, whereas multipole refinement of theoretical and experimental structure factors resulted in opposite signs for the Lewis acid and base fragments. For ammonia trifluoroborane, the donation from Lewis base to acid is slightly larger (about 0.13 e) in the multipole-free models, and the charges obtained by multipole refinement retain the direction of the charge donation but show quite large variations. The natural population analysis charges predict larger charge donations (0.35 e) from the Lewis bases to the acids for the three title complexes. Although the three compounds exhibit intermolecular interactions of different types and strengths, including classical hydrogen bonds, F···H contacts and the already mentioned dihydrogen bonds, almost no charge transfer is detected between different molecules within the crystal environment. The main electronic effect of the formation of the Lewis acid-base adducts and of the crystallization is an increase in the charge separation within the ammonia/hydrazine fragments, which is supported by all investigated bond and atomic properties. The nature of the dative N-B bond is found to be mainly electrostatic, but with a substantial contribution of covalency. The F-B bonds show similarities and differences from the N-B bonds, which makes a distinction of coordinative (or dative) bonds from polar covalent interactions possible.

Cover Picture: ZAAC ‐ Journal of Inorganic and General Chemistry 9‐10/2010

AbstractThe cover picture shows the complex crystal structure of the stannides RE3Sn7 (RE = Tb, Ho, Er) is isotypic to that of Gd3Sn7 and can be described as being constituted by condensed fragments of simple parent structures. Shown here are AlB2‐, AuCu3‐ and CaF2‐type motifs of the atomic arrangement. A sequence of CaF2, AuCu3 and CaF2 segments corresponds to the slightly more complex TiAl3‐type assembly (lower left) which is also found as a constituting segment of the Gd3Sn7 pattern. The background shows the electron localizability indicator values in an AuCu3‐type layer of Er3Sn7. The magnitudes are represented by a colour code and visualize erbium‐tin interactions.

Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB 2, CaTiO 3, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.

The high stability of boron-doped lithium clusters Li 5B, Li 6B +/− and Li 7B: A case of the phenomenological shell model

A quantum chemical investigation of the clusters Li 5B, Li 6B +, Li 6B − and Li 7B was performed using the DFT, MP2 and CCSD(T) methods. The high symmetry structures ( C 4v, 1A 1), ( O h, 1A 1g) and ( D 5h, 1 A 1 ′ ) turnout to be the global minima for Li 5B, Li 6B + and Li 7B, respectively. These clusters are predicted to be highly stable species with large vertical ionization energies, and large HOMO–LUMO gaps. Chemical bonding of clusters was probed using an electron localizability indicator (ELI) which indicates a large aromatic character. The high stability of these clusters can be accounted for by the phenomenological shell model.

Filled platinum germanium skutterudites MPt4Ge12 (M = Sr, Ba, La—Nd, Sm, Eu): crystal structure and chemical bonding

The crystal structures of filled skutterudite compounds MPt 4 Ge 12 (M = Sr, Ba, La—Nd, Sm, Eu) with LaFe 4 P 12 type structure were refined from single crystal data. Depending on the size of the M species, displacement parameters of filler atoms M can be similar or much larger than those of Pt and Ge. We discuss the MPt 4 Ge 12 skutterudites in a crystal chemical framework of related structure types. Electronic structure calculations and chemical bonding analysis by the electron localizability indicator describe the MPt 4 Ge l2 compounds as covalently bonded polyanionic [Pt 4 Ge 12 ] framework structures which are stabilized by electron transfer from the filler metal-ions M. In case of 3d metal containing filled skutterudite compounds the DOS at the Fermi level is dominated by contributions of 3d metal states. In contrast, for the MPt 4 Ge 12 compounds, it is essentially composed of Ge p states with Pt 5d contributions at significantly lower energies.

Quantum chemical topology: The electronic structure of the alkaline nitrites MONO (M = Li, Na, K) studied by means of topological analysis of the electron localization function

AbstractIn the search of the protocovalent bonding, previously recognized in the nitrous acid (HONO), a nature of the chemical bonds in the alkaline nitrites MONO (M = Li, Na, K) has been studied by means of the topological analysis of the Electron Localization Function (ELF) and Electron Localizability Indicator (ELI‐D). Calculations carried out with the B3LYP and MP2(full) methods, in conjunction with the aug‐cc‐pVTZ and 6‐311++G(3df,3pd) basis sets, revealed the cis (C2v, more stable) and trans (Cs) isomers as minima on PES. Alkaline nitrites consist of the alkali metal cation Mδ+ interacting, mainly via electrostatic forces, with the nitrite anion [ONO]δ− (δ ≈ 1e). The covalent NO bonds are characterized by disynaptic basins V(N,O) with the basin populations: 1.58÷1.62e for cis‐Mδ+[ONO]δ− but 1.39÷1.49e for single NO bond and 1.81÷1.87e for formally double NO bond in trans Mδ+[ONO]δ−. The protocovalent nitrogen–oxygen bond has not been observed. The NO bonds are slightly polarized towards the nitrogen atom with the polarity index pNO ≤ 0.12. Two different sets of the hybrid (Lewis) structures are compared leading to different pictures of the bonding. According to NBO data there is a delocalization between the single NO and double NO type bonds, meanwhile results of the ELF analysis emphasize an electron delocalization between the single NO and ionic O−N+ hybrids. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Electron Densities of Three B12 Vitamins

The electron densities of the three natural B(12)-vitamins, two of them being essential cofactors for animal life, were determined in a procedure combining high-order X-ray data collection at low to very low temperatures with high-level density functional calculations. In a series of extensive experimental attempts, a high-order data set of adenosylcobalamin (AdoCbl) could be collected to a resolution of sin theta/lambda = 1.00 A(-1) at 25 K. This modification contains only minor disorder at the solvent bulk. For methylcobalamin (MeCbl), only a severely disordered modification was found (sin theta/lambda = 1.00 A(-1), 100 K, measured with synchrotron radiation). The already published data set of cyanocobalamin (CNCbl) (sin theta/lambda = 1.25 A(-1), 100 K) was reintegrated to guarantee similar treatment of the three compounds and cut to sin theta/lambda = 1.11 A(-1) to obtain a higher degree of completeness and redundancy. On the basis of these accurate experimental geometries of AdoCbl, MeCbl, and CNCbl, state-of-the-art density functional calculations, single-point calculations, and geometry optimizations were performed on model compounds at the BP86/TZVP level of theory to evaluate the electronic differences of the three compounds. AdoCbl and MeCbl are known to undergo different reaction paths in the body. Thus, the focus was directed toward the characterization of the dative Co-C(ax) and Co-N(ax) bonds, which were quantifed by topological parameters, including energy densities; the source function including local source; and the electron localizability indicator (ELI-D), respectively. The source function reveals the existence of delocalized interactions between the corrin macrocycle and the axial ligands. The ELI-D indicates unsaturated Co-C(ax) bonding basins for the two biochemically active cofactors, but not for CNCbl, where a population of 2.2e is found. This may be related to significant pi-backbonding, which is supported by the delocalization index, delta, of 0.15 between the Co atom and the N atom of the cyano ligand. Considering all results, the inherent electronic differences between AdoCbl and MeCbl are found to be small thus, supporting earlier findings that the interaction with the protein site mainly controls the type of Co-C(ax) bond cleavage.

Metallic-covalent bonding conversion in boron icosahedral cluster solids studied using electron localizability indicator

The metallic-covalent bonding conversion of clusters in boron icosahedral cluster solids was studied using the electron density and electron localizability indicator (ELI). The comparison of B12 and B13 clusters revealed that the bonding conversion from covalent to metallic one involved a decrease in both the electron density and ELI between two boron atoms in the clusters. On the other hand, in the case of vanadium doping into the B48 cluster surrounding the vanadium doping site in β-rhombohedral boron, the electron density increased in some parts of the cluster and decreased in other parts. This uncertainty regarding the bonding conversion was clarified by the use of the ELI. The ELI analysis clearly revealed that bonding conversion occurs in the cluster surrounding the vanadium doping site.

SnxPt4SnySb12−y: A Skutterudite with Covalently Bonded Filler

A new phase, Sn(x)Pt4Sb(12-y)Sn(y), has been prepared from the elements. It exhibits a wide range of homogeneity with 0.3(2) < or = x < or = 1.0(2) and 4.2(2) < or = y < or = 7.0(2). The crystal structure and the composition were established by single-crystal and powder X-ray diffraction as well as wavelength-dispersive X-ray analysis measurements and were supported by nuclear magnetic resonance experiments. The compound is the first representative of the filled-skutterudite family with the filler atoms not located at the center of the cavity but covalently bonded to the cavity's wall, as confirmed by the analysis of chemical bonding with the electron localizability indicator. The Sn and Sb atoms share the framework site with different coordinate parameters caused by the difference in atomic size; additional tin atoms are located in the cavities of the framework. The material is a diamagnet in the whole composition range. In agreement with the calculated electronic density of states, the material reveals a metallic behavior in electronic transport. The absolute values of electrical resistivity vary with the tin-to-antimony ratio.

Direct Space Decomposition of ELI-D: Interplay of Charge Density and Pair-Volume Function for Different Bonding Situations

The topological features, i.e., gradients and curvatures of the same-spin electron pair restricted electron localizability indicator (ELI-D) in position space are analyzed in terms of those of the electron density and the pair-volume function. The analysis of the topology of these constituent functions and their interplay on ELI-D attractor formation for a number of molecules representing chemically different bonding situations allows distinguishing between different chemical bonding scenarios on a quantum mechanical basis without the recourse to orbitals. The occurrence of the Laplacian of the electron density in the expression for the Laplacian of ELI-D allows us to establish a physical link between electron localizability and electron pairing as displayed by ELI-D and the role of Laplacian of the density in this context.

Crystal Structure and Chemical Bonding of Mg3Ru2

Mg 3Ru 2 was prepared by a reaction between the elements in the ideal ratio in a sealed tantalum ampule. Its beta-manganese type crystal structure was refined on the basis of the single-crystal data: space group P4 132, a = 693.52(6) pm, wR2 = 0.024, 168 F (2) values, and 10 parameters. The magnesium (CN = 14) and ruthenium (CN = 12) atoms are completely ordered on the 12d and 8c sites of the crystal structure of beta-manganese. Both environments can be considered as Frank-Kasper related polyhedra. A periodic nodal surface P4 132(110) pi (1) P4 132 separates the magnesium and ruthenium positions in two different labyrinths, suggesting different chemical interactions within different parts of the structural motif. Analysis of the chemical bonding with the electron localizability indicator (ELI-D) reveals covalently interacting three-bonded ruthenium atoms, forming a 3D network. The network interacts with the magnesium substructure by multicenter bonds.

Synthesis, chemical bonding and physical properties of RERhB 4 ( RE=Y, Dy–Lu)

The compounds of rare-earth metals with rhodium and boron RERhB 4 ( RE=Y, Dy–Lu) crystallize with the orthorhombic structure type YCrB 4 (space group Pbam, Pearson symbol oP24). The crystal structures of the compounds with RE=Y, Er, Tm and Yb were refined by using single-crystal diffraction data. Analysis of chemical bonding for YRhB 4 and YbRhB 4 was performed by electron localizability indicator and by calculation of quantum chemical charges (quantum theory of atoms in molecules). Boron and rhodium form the 3-D polyanion containing planar nets of three-bonded boron atoms interconnected by rhodium along [001]. The interaction of the RE species with the rhodium–boron polyanion is predominantly ionic. Magnetic susceptibility data of TmRhB 4 and YbRhB 4 showed that the RE species are in 4 f 12 (Tm) and 4 f 13 (Yb) electronic states, respectively. In the low-temperature region, the specific heat revealed a Schottky anomaly for TmRhB 4 while an antiferromagnetic transition is observed at 3.5 K for YbRhB 4. X-ray absorption measurement at the Yb L III edge for YbRhB 4 reveals the 4 f 13 state of ytterbium.

Electron localizability for hexagonal element structures

For 21 elements crystallizing in hexagonal structure density functional calculations were performed. The topology of the electron localizability indicator (ELI) allows classifying the elements as appertaining to one of six patterns. The bifurcation diagrams as well as the electron populations in ELI basins for each pattern are discussed.

The Cu7Sc Cluster is a Stable σ‐Aromatic Seven‐Membered Ring

Density functional theory calculations demonstrate that the global minimum of the Cu(7)Sc potential energy surface is a seven-membered ring of copper atoms with scandium in its center, yielding a planar D(7) (h) structure. Nucleus-independent chemical shifts [NICS(1)(zz) and NICS(2)(zz)] show that this cluster has aromatic character, which is consistent with the number of 4s electrons of copper and scandium plus the 3d electrons of scandium satisfying Hückel's rule. According to a canonical MO decomposition of NICS(1)(zz) and NICS(2)(zz), the MOs consisting of the 4s atomic orbitals are mainly responsible for the aromatic behavior of the cluster. The electron localizability indicator (ELI-D) and its canonical MO decomposition (partial ELI-D) suggest that a localized basin is formed in Cu(7)Sc by the copper atoms whereas the two circular localized domains are situated below and above the ring. The planar Cu(7)Sc cluster can thus be considered as a sigma-aromatic species. These findings agree with the phenomenological shell model.

Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs

The electron pair density can be decomposed into the symmetric and antisymmetric parts. The antisymmetric component is connected with the probability that two electrons are coupled to a triplet. On the basis of triplet-coupled electrons the electron localizability indicator is defined, describing the correlation of motion of electrons forming a triplet pair. In case of spin-polarized systems the electron localizability indicator for triplet pairs combines the two spin channels together into a single functional.

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.

Atomic shells from the electron localizability in momentum space

AbstractThe electron localizability indicator in momentum space is proposed as a functional of the same‐spin momentum pair density. This functional yields a discrete distribution of values, which are proportional to the charge needed to form a fixed very small fraction of a same‐spin electron pair. It resolves all atomic shells for the examined atoms (Li–Kr) with reasonable occupation numbers, especially in the valence region. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Electron localizability indicator for correlated wavefunctions. II Antiparallel-spin pairs

The electron localizability indicator (ELI) is based on a functional of the same-spin pair density. It reflects the correlation of the motion of same-spin electrons. In the Hartree–Fock approximation the ELI can be related to the electron localization function (ELF). For correlated wavefunctions the ELI formula differs from the one for the ELF.