Frank R. Wagner

Improving the efficiency of FP-LAPW calculations

Abstract The full-potential linearized augmented-plane wave (FP-LAPW) method is well known to enable most accurate calculations of the electronic structure and magnetic properties of crystals and surfaces. The implementation of atomic forces has greatly increased its applicability, but it is still generally believed that FP-LAPW calculations require substantial higher computational effort compared to the pseudopotential plane wave (PPW) based methods. In the present paper we analyze the FP-LAPW method from a computational point of view. Starting from an existing implementation (WIEN95 code), we identified the time consuming parts and show how some of them can be formulated more efficiently. In this context also the hardware architecture plays a crucial role. The remaining computational effort is mainly determined by the setup and diagonalization of the Hamiltonian matrix. For the latter, two different iterative schemes are compared. The speed-up gained by these optimizations is compared to the runtime of the “original” version of the code, and the PPW approach. We expect that the strategies described here, can also be used to speed up other computer codes, where similar tasks must be performed.

Metal–Metal Distances at the Limit: A Coordination Compound with an Ultrashort Chromium–Chromium Bond

The nature of the chemical bond is of fundamental importance, and has always fascinated scientists. Metal–metal bonds are of particular interest, as bond orders greater than four are known and are of considerable current interest. The quest for the shortest metal–metal bond is strongly linked with the element chromium and has very recently been reinitiated after the first observation of a bond order greater than four for this metal in a stable compound. Soon afterwards, the shortest metal–metal bond with a chromium–chromium distance of 1.80 ( was observed in a dimeric chromium complex with such a high bond order. Detailed studies on ArCrCrAr complexes (Ar= aryl) performed at the same time showed that such small values can be obtained for this class of compounds as well. Some years ago, we started working with aminopyridinato complexes of chromium and herein report the synthesis and the (electronic) structure of a bimetallic Cr2 complex with a drastically shortened metal– metal distance. The very short metal–metal bond of only 1.75 ( results from a combination of Power3s concept for the stabilization of bond orders higher than four, Hein– Cotton3s principles on the realization of extremely short metal–metal bonds with bridging anionic ligands of type XYZ, and a minimization of additional metal–ligand interactions by optimal steric shielding (Scheme 1). The deprotonation of 1 with potassiumhydride leads to potassium [6-(2,4,6-triisopropylphenyl)pyridin-2-yl](2,4,6-trimethylphenyl)amide, which readily reacts with [CrCl3(thf)3] affording complex 2 (Scheme 2). Compound 2 can be isolated as a green crystalline material in good yield. In the H NMR spectrum, only broad signals can be observed, and magnetic susceptibility experiments show a magnetic moment meff(300 K)= 3.2 mB. When 1 is deprotonated with BuLi and allowed to react with CrCl2 in THF, the Cr II 2 complex 3 is obtained in good yield as a green crystalline material after removal of the solvent and subsequent extraction with

Molecules containing rare-earth atoms solely bonded by transition metals

Although metal-metal bonding is important in the chemistry of both solid-state intermetallic compounds and molecular species, the study of this bonding is limited by the compounds available and it is rarely possible to identify connections between these two areas. In this study, molecular intermetalloids [Ln(ReCp(2))(3)] (Ln = Sm, Lu and La) have been synthesized that contain lanthanoid metals bound only to transition metals. Although they are highly reactive species, such lanthanoid-core transition-metal-shell compounds can be stable in solution. They mimic the bonding situation of intermetallic compounds, as revealed by a direct comparison of molecular and solid state lanthanoid-transition metal bonding.

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.

Preparation, crystal structure and physical properties of ternary compounds (R3N)In, R = rare-earth metal

Abstract The compounds (R3N)In (R=Sc, La–Nd, Sm, Gd–Tm, Lu) were synthesized by arc melting and sintering reactions from the binaries RN and R2In. Combined Rietveld refinements on X-ray and neutron powder diffraction data on the Ce-phase and X-ray diffraction for the other phases reveal the compounds (R3N)In to crystallize in the perovskite structure ((Ce3N)In: Pm 3 m , a=504.89(2) pm; Rietveld: neutron powder diffraction: RF=0.056, RBragg=0.104, X-ray powder diffraction: RF=0.069, RBragg=0.115; refined composition Ce3InN0.92(1), chemical analysis Ce3InN0.91(2)O0.05(1)). Compounds R3In (AuCu3 structure type) are known for R=La–Sm. Nitrogen is able to stabilize this AuCu3-substructure with R=Gd–Tm, Lu and Sc. In measurements of the magnetic susceptibility (Ce, Pr, Nd, Sm, Tb: antiferromagnetic ordering at low temperature) and X-ray absorption spectroscopy at the R-LIII-edges the rare-earth atoms behave like R3+ species in insulating compounds. The electrical resistivity of the Sc, Ce and Nd compounds shows metallic temperature dependence. Chemical bonding was analyzed via LDA-COHP calculations for (La3N)In showing ionic polyhedra NLa6/2 embedded in a metallic matrix.

The analysis of “empty space” in the PdGa5 structure

Abstract The structure of PdGa 5 is characterized by a framework of condensed bicapped tetragonal antiprisms [PdGa 10 ]. The appropriate symmetry governed periodic nodal surface (PNS) divides the space into two labyrinths. The atoms of the coordination polyhedra are located in one labyrinth or are close to the surface. The second labyrinth seems to be “empty”. The electron localization function (ELF) calculated by the TB-LMTO method, shows that the “empty” labyrinth contains the regions with high ELF values. These regions are related to inter-polyhedral GaGa bonds forming Ga 4 squares. The vertices of eight covalently bonded Ga 4 squares build tetragonal antiprisms which are centered by Pd atoms. High electron density but low ELF values inside these coordination polyhedra of Pd represent regions of delocalized (metal-like) electrons. Thus, the PNS separates the regions of different bonding character. Some relations to stuffed derivatives of the PdGa 5 structure are discussed.

Synthesis, Crystal Structure, and Physical Properties of (Ca3N)TI

Single crystals of (Ca3N)Tl (Pm 3 m, No. 221, a = 4.9851(3) A; Z = 1) with a metallic luster and black single phase powders of the ternary nitride were obtained from reactions of the respective metals with nitrogen at maximum temperatures of 950 °C. (Ca3N)Tl crystallizes in an antiperovskite-type arrangement. The magnetic susceptibility is nearly temperature independent (+170(10) · 10–6 emu/mol). Metallic behavior is supported by band structure calculations on the LDA LMTO-ASA level of theory. Chemical bonding is analyzed and the results are compared with the isotypic nitrides (Ca3N)Pb and (Ca3N)Bi. Synthese, Kristallstruktur und physikalische Eigenschaften von (Ca3N)Tl Bei Temperaturen von 950 °C bilden sich schwarz-metallisch glanzende Einkristalle und schwarze, phasenreine Pulver von (Ca3N)Tl (Pm 3 m, Nr. 221, a = 4,9851(3) A; Z = 1) aus den Elementen. (Ca3N)Tl kristallisiert im anti-Typ des Perowskits. Messungen der magnetischen Suszeptibilitat ergeben ein nahezu temperaturunabhangiges Verhalten (+170(10) · 10–6 emu/mol). Bandstrukturrechnungen mit der LDA LMTO-ASA Methode stutzen die Annahme von metallischem Verhalten. Chemische Bindungswechselwirkungen werden analysiert und mit denen der isotypen Nitride (Ca3N)Pb und (Ca3N)Bi verglichen.

Errors in Hellmann-Feynman forces due to occupation-number broadening and how they can be corrected

necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a broadening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics ~MD! calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the ~111! surfaces of aluminum and platinum. The second, more general, scheme employs linearresponse theory and is applied to the calculation of the surface relaxation of Al ~111!. We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton. @S0163-1829~97!04647-X#

Characterization of 2,2′-bi-(1,4,8,11-tetra-azacyclotetradecane): X-ray structure and properties of the dinuclear complex [Ni2(C20H46N8)][ClO4]4

2,2′-Bi-(1,4,8,11-tetra-azacyclotetradecane) has been isolated as a minor product from the nickel (II)-assisted synthesis of 1,4,8,11-tetra-azacyclotetradecane (cyclam) and its structure confirmed by X-ray structural analysis of the dinuclear complex [Ni2(C20H46N8)][ClO4]4.

Molecular Lanthanoid–Transition-Metal Cluster through CH Bond Activation by Polar Metal–Metal Bonds

Metal–metal bonds have been fascinating scientists for long time and nowadays a lot of enthusiasm is devoted to unsupported metal–metal bonds. Until now unsupported Ln–TM bonds (Ln = lanthanoid, TM = transition metal) could only be found in a few compounds. These bonds are rather polar 11] and are important for the fundamental understanding of bonding phenomena between these metals. An improved understanding of a Ln–TM bond is important because intermetallic compounds of these metals play an important role in everyday life. The high bond polarity should allow a systematic approach towards highly aggregated systems. 15] To date there has been little exploration of the reactivity of such Ln–TM bonds. Herein we show how metal clusters can be prepared by multiple C H bond activations at Ln–TM bonds, which leads to the formation of doubly deprotonated Cp ligands. (Cp = cyclopentadienyl). The starting point of this reaction sequence is the fourcoordinate rare-earth-metal compound 2 which has a chiral lanthanoid atom. We recently explored the reaction of tris(alkyl) Ln compounds with [Cp2ReH] and ascertained that in addition to triply Re-bonded Ln complexes, polymeric insoluble byproducts are formed in bulk (66–99 %). Since the reaction of [Cp2Y(thf)(CH2SiMe3)] (Me = methyl) with the above-mentioned rhenium hydride proceeds in very good yields, it was suspected, that the presence of one Ln–carbon bond brings about side reactions of the Ln–TM bond leading to those polymeric materials. Now, if one wants to understand and to use such (side) reactions purposefully, a bis(alkyl) Ln compound which allows the substitution of one of the two alkyl ligands by Cp2Re-ligands should be exploited. The reaction of [Lu(thf)2(CH2SiMe3)3] [16] with one equivalent of 2,6-di-tertbutylphenol affords bis(alkyl) 1 in high yields (Scheme 1). The new complex reacts selectively with one equivalent of [Cp2ReH] to yield compound 2 (Scheme 1). The molecular structure of 2 as determined by X-ray structural analysis is shown in Figure 1. The lutetium ion in 2 is four-coordinated, in a tetrahedral environment, and is chiral owing to the different substituents. The selective introduction of four different substituents appears to be complicated for rare earth ions, which have a tendency for very high coordination numbers. The Lu–Re distance is 2.8498(6) and is significantly shorter than the Lu–Ru distance of 2.955(2) in [Cp2(thf)Lu-Ru(CO)2Cp] [6] and almost identical with the average value of the Lu–Re bonding distances in [Lu(ReCp2)3] [9] [2.886(1)]. The Lu C bond in 2 is 2.359(10) and complies with the expected value for such a bond (2.3781 ). The H NMR spectrum of 2 shows strong temperature dependence (at 188–295 K; see the Supporting Information). By virtue of the chirality, the signal belonging to the protons of the CH2-group of the alkyl ligand appears as AB spin system. By analogy the protons of the coordinated THF ligand should display more than two groups of signals. At room temperature, however, only two broad signals are observed for the H atoms of THF ligand and for the CH2 group merely one broad signal. Upon cooling to 253 K signal separation occurs and for the CH2 group (typical) geminal Scheme 1. Synthesis of 2.