Georg Eickerling

Topological analysis of electron densities from Kohn-Sham and subsystem density functional theory

In this study, we compare the electron densities for a set of hydrogen-bonded complexes obtained with either conventional Kohn-Sham density functional theory (DFT) calculations or with the frozen-density embedding (FDE) method, which is a subsystem approach to DFT. For a detailed analysis of the differences between these two methods, we compare the topology of the electron densities obtained from Kohn-Sham DFT and FDE in terms of deformation densities, bond critical points, and the negative Laplacian of the electron density. Different kinetic-energy functionals as needed for the frozen-density embedding method are tested and compared to a purely electrostatic embedding. It is shown that FDE is able to reproduce the characteristics of the density in the bonding region even in systems such as the F-H-F(-) molecule, which contains one of the strongest hydrogen bonds. Basis functions on the frozen system are usually required to accurately reproduce the electron densities of supermolecular calculations. However, it is shown here that it is in general sufficient to provide just a few basis functions in the boundary region between the two subsystems so that the use of the full supermolecular basis set can be avoided. It also turns out that electron-density deformations upon bonding predicted by FDE lack directionality with currently available functionals for the nonadditive kinetic-energy contribution.

Valence shell charge concentrations and the Dewar–Chatt–Duncanson bonding model

Combined experimental and theoretical charge density studies of the complex [Ni(η2-C2H4)dbpe] (dbpe = But2PCH2CH2PBut2), 1, reveal how the location and magnitude of charge concentrations in the valence shell of the metal atom influence the σ- and π-components of the metal–olefin interaction.

Relativistic Effects on the Topology of the Electron Density

The topological analysis of electron densities obtained either from X-ray diffraction experiments or from quantum chemical calculations provides detailed insight into the electronic structure of atoms and molecules. Of particular interest is the study of compounds containing (heavy) transition-metal elements, which is still a challenge for experiment as well as from a quantum-chemical point of view. Accurate calculations need to take relativistic effects into account explicitly. Regarding the valence electron density distribution, these effects are often only included indirectly through relativistic effective core potentials. But as different variants of relativistic Hamiltonians have been developed all-electron calculations of heavy elements in combination with various electronic structure methods are feasible. Yet, there exists no systematic study of the topology of the total electron density distribution calculated in different relativistic approximations. In this work we therefore compare relativistic Hamiltonians with respect to their effect on the electron density in terms of a topological analysis. The Hamiltonians chosen are the four-component Dirac-Coulomb, the quasi-relativistic two-component zeroth-order regular approximation, and the scalar-relativistic Douglas-Kroll-Hess operators.

Anagostic Interactions under Pressure: Attractive or Repulsive?

Square-planar d(8)-ML4 complexes might display subtle but noticeable local Lewis acidic sites in axial direction in the valence shell of the metal atom. These sites of local charge depletion provide the electronic prerequisites to establish weakly attractive 3c-2e M⋅⋅⋅H-C agostic interactions, in contrast to earlier assumptions. Furthermore, we show that the use of the sign of the (1)H NMR shifts as major criterion to classify M⋅⋅⋅H-C interactions as attractive (agostic) or repulsive (anagostic) can be dubious. We therefore suggest a new characterization method to probe the response of these M⋅⋅⋅H-C interactions under pressure by combined high pressure IR and diffraction studies.

The Shell Structure of Atoms

The total electron density distribution of an isolated atom or an atom in a molecule does not reveal an atomic shell structure. Many localization functions, such as the radial averaged electron density, the Laplacian of the electron density, or the electron localization function have been proposed to visualize and analyze the shell structure of atoms. It was found that for light main group elements the correct number of shells is revealed by such functions. Later it was recognized that for heavy main group elements and for transition metals many of these diagnostic tools fail to reveal the full set of electronic shells as expected from the periodic table. In this work we focus on the radial structure of isolated atoms as revealed by the Laplacian of the electron density. We will demonstrate that it is the nodal structure of the orbitals of the inner shells which is responsible for the diminishing of at least one valence shell of third row transition metal atoms. Particular attention is paid to the effect of different electronic configurations on the shell structure of atoms and the question if the changes observed in the Laplacian of the radial density are sufficiently large for experimental studies on the topology of the electron density. Our presentation is as general as possible and, hence, employs a fully relativistic, i.e., four-component picture and a multiconfigurational ansatz for the wave function, which is thus valid for the whole periodic table of elements.

Elucidation of the bonding in Mn(η2-SiH) complexes by charge density analysis and T1 NMR measurements: asymmetric oxidative addition and anomeric effects at silicon

The bonding in Mn(eta2-SiH) complexes is interpreted in terms of an asymmetric oxidative addition whose extent is controlled by the substitution pattern at the hypercoordinate silicon centre, and especially by the ligand trans to the eta2-coordinating SiH moiety.

Borane and Borohydride Complexes of the Rare‐Earth Elements: Synthesis, Structures, and Butadiene Polymerization Catalysis

The reaction of potassium 2,5-bis[N-(2,6-diisopropylphenyl)iminomethyl]pyrrolyl [(dip(2)-pyr)K] with the borohydrides of the larger rare-earth metals, [Ln(BH(4))(3)(thf)(3)] (Ln=La, Nd), afforded the expected products [Ln(BH(4))(2)(dip(2)-pyr)(thf)(2)]. As usual, the trisborohydrides reacted like pseudohalide compounds forming KBH(4) as a by-product. To compare the reactivity with the analogous halides, the dimeric neodymium complex [NdCl(2)(dip(2)-pyr)(thf)](2) was prepared by reaction of [(dip(2)-pyr)K] with anhydrous NdCl(3). Reaction of [(dip(2)-pyr)K] with the borohydrides of the smaller rare-earth metals, [Sc(BH(4))(3)(thf)(2)] and [Lu(BH(4))(3)(thf)(3)], resulted in a redox reaction of the BH(4) (-) group with one of the Schiff base functions of the ligand. In the resulting products, [Ln(BH(4)){(dip)(dip-BH(3))-pyr}(thf)(2)] (Ln=Sc, Lu), a dinegatively charged ligand with a new amido function, a Schiff base, and the pyrrolyl function is bound to the metal atom. The by-product of the reaction of the BH(4) (-) anion with the Schiff base function (a BH(3) molecule) is trapped in a unique reaction mode in the coordination sphere of the metal complex. The BH(3) molecule coordinates in an eta(2) fashion to the metal atom. The rare-earth-metal atoms are surrounded by the eta(2)-coordinated BH(3) molecule, the eta(3)-coordinated BH(4) (-) anion, two THF molecules, and the nitrogen atoms from the Schiff base and the pyrrolyl function. All new compounds were characterized by single-crystal X-ray diffraction. Low-temperature X-ray diffraction data at 6 K were collected to locate the hydrogen atoms of [Lu(BH(4)){(dip)(dip-BH(3))-pyr}(thf)(2)]. The (DIP(2)-pyr)(-) borohydride and chloride complexes of neodymium, [Nd(BH(4))(2)(dip(2)-pyr)(thf)(2)] and [NdCl(2)(dip(2)-pyr)(thf)](2), were also used as Ziegler-Natta catalysts for the polymerization of 1,3-butadiene to yield poly(cis-1,4-butadiene). Very high activities and good cis selectivities were observed by using each of these complexes as a catalyst in the presence of various cocatalyst mixtures.

High- and low-temperature modifications of Sc3RuC4 and Sc3OsC4--relativistic effects, structure, and chemical bonding.

Sc(3)RuC(4) and Sc(3)OsC(4) were synthesized by arc-melting and subsequent annealing. At room temperature, they crystallize with the Sc(3)CoC(4) structure, space group Immm. At 223 and 255 K, Sc(3)RuC(4) and Sc(3)OsC(4), respectively, show a monoclinic distortion caused by a pair-wise displacement of the one-dimensional [Ru(C(2))(2)](delta-) and [Os(C(2))(2)](delta-) polyanions, which are embedded in a scandium matrix. Superstructure formation leads to shorter Ru-Ru and Os-Os distances of 316 pm between adjacent [Ru(C(2))(2)](delta-) and [Os(C(2))(2)](delta-) polyanions. Each ruthenium (osmium) atom is covalently bonded to four C(2) pairs with Ru-C (Os-C) distances of 220-222 pm. A comparison of the C-C bond distances at room temperature in Sc(3)TC(4) with T representing a group 8 transition metal (Fe, Ru, Os) reveals a minimum in the case of the 4d metal Ru: 144.98(11) pm (Fe), 142.8(7) pm (Ru), and 144.6(4) pm (Os). Analysis of the local electronic structure of the [T(C(2))(2)] moieties hints at a complex interplay between chemical bonding and relativistic effects, which is responsible for the V-shaped pattern of the C-C bond distances (long, short, and long for T = Fe, Ru, and Os, respectively). Relativistic effects lead to a strengthening of covalent T-C bonding. This is shown on the basis of periodic DFT calculations by a significant increase of the charge density at the T-C bond critical points (0.55 < 0.57 < 0.64 eA(-3)) down the row of group 8 elements. These structural characteristics and topological features do not change in the corresponding low-temperature phases of Sc(3)RuC(4) and Sc(3)OsC(4). However, topological analyses of theoretical charge density distributions reveal distinct changes of the valence shell charge concentrations at the transition metal centers due to the monoclinic distortions. Presumably, the local electronic situation at the transition metals reflects the origin and extent of these monoclinic distortions.

Probing the Zintl-Klemm concept: a combined experimental and theoretical charge density study of the Zintl phase CaSi.

The nature of the chemical bonds in CaSi, a textbook example of a Zintl phase, was investigated for the first time by means of a combined experimental and theoretical charge density analysis to test the validity of the Zintl-Klemm concept. The presence of covalent Si-Si interactions, which were shown by QTAIM analysis, supports this fundamental bonding concept. However, the use of an experimental charge density study and theoretical band structure analyses give clear evidence that the cation-anion interaction cannot be described as purely ionic, but also has partially covalent character. Integrated QTAIM atomic charges of the atoms contradict the original Zintl-Klemm concept and deliver a possible explanation for the unexpected metallic behavior of CaSi.

Topology of the electron density of d0 transition metal compounds at subatomic resolution.

Accurate X-ray diffraction experiments allow for a reconstruction of the electron density distribution of solids and molecules in a crystal. The basis for the reconstruction of the electron density is in many cases a multipolar expansion of the X-ray scattering factors in terms of spherical harmonics, a so-called multipolar model. This commonly used ansatz splits the total electron density of each pseudoatom in the crystal into (i) a spherical core, (ii) a spherical valence, and (iii) a nonspherical valence contribution. Previous studies, for example, on diamond and α-silicon have already shown that this approximation is no longer valid when ultrahigh-resolution diffraction data is taken into account. We report here the results of an analysis of the calculated electron density distribution in the d(0) transition metal compounds [TMCH3](2+) (TM = Sc, Y, and La) at subatomic resolution. By a detailed molecular orbital analysis, it is demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the TM-C bond formation a significant polarization of the electron density in the inner electronic shells of the TM atoms is observed. We further show that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for the title compounds.