Ulrich Wedig

A Piece of the Picture—Misunderstanding of Chemical Concepts

”What is the relationship between static electric charges and oxidation states? None.” This striking claim can be found in a recent issue of one of the most attractive scientific journals and stems from a series of first-principle calculations on the charges of individual transition-metal atoms embedded within an extended solid-state matrix; ionic, covalent, and intermediate bonding situations were considered. A change in the total electron count of the system (compensated for by a universal background charge) is equated with a change in the oxidation state of the transitionmetal atom. It is found that the effective local charge changes only slightly; hence, the usefulness of the term “oxidation state” is called into question. Informed chemists will rub their eyes in astonishment; apparently even in today s world great attention can be attracted when preaching to the saved. At the same time, however, it is particularly strange that the line of argument with which the term “oxidation state” is questioned also rests on somewhat shaky foundations. How could it even come to this? As all so often, there are many reasons. To begin with, the scope of definition of the widely used and welldefined term “oxidation state” is disregarded. However, in this case, the misconception has much deeper roots. It assumes that quantum mechanical calculations (first principle) of the electronic structures of chemical compounds can be transferred to common chemical concepts without bias. Yet such a strategy appears inevitable; a mathematical description or simulation of a natural phenomenon does not automatically give rise to a conceptual structure, nor does it establish “understanding”. Nevertheless, the price to be paid for a conceptual description of the “real” world is high; at the very least, it entails a loss of accuracy and detail; in more extreme situations, it may involve a complete distortion of the subject matter. To minimize these risks, the concepts need to be defined as precisely as possible, and these definitions must always be kept in mind during applications.

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.

Homoatomic stella quadrangula [Tl8]6- in Cs18Tl8O6, interplay of spin-orbit coupling, and Jahn-Teller distortion.

Cs(18)Tl(8)O(6) was synthesized reacting the binary compounds CsTl and Cs(2)O. According to single crystal X-ray analysis, the title compound crystallizes as a novel structure type in the cubic space group I23 and is diamagnetic. The electronic structure of the extended solid and of excised Cs(6)Tl(8) clusters has been examined by relativistic density functional calculations including spin-orbit coupling. Cs(18)Tl(8)O(6) comprises a clusteranion [Tl(8)](6-) in the shape of a tetrahedral star. An isoelectronic cluster was found previously in Cs(8)Tl(8)O, however, with the shape of a parallelepiped. Both clusteranions can be derived from a homocubane unit by displacive distortions. It has been shown by quantum mechanical analyses that the closed-shell electronic structure of the parallelepiped is the result of a Jahn-Teller distortion, while in contrast the tetrahedral star in Cs(18)Tl(8)O(6) would still exhibit an open-shell degenerate HOMO within a scalar relativistic approximation. Only if spin-orbit coupling is considered, a closed-shell electronic system is obtained in accordance with the diamagnetic behavior of Cs(18)Tl(8)O(6).

Geometric variations and electron localizations in intermetallics : PbFCl type compounds

Abstract The structural relations of the intermetallic compounds Cu2Sb, Mn2Sb, Fe2As, Mn2As, Cr2As, Sc2Sb as well as of YTiSi and ZrSiS, all adopting the PbFCl structure, are discussed. In the course of these investigations, the crystal structures of Mn2Sb, Mn2As and Fe2As have been redetermined and refined from single crystal data. Bandstructures have been calculated in the framework of Density Functional Theory. The bonding properties are compared on the basis of partial densities of states, of the Crystal Orbital Hamilton Population (COHP) and of the Electron Localization Function (ELF). The trend of the d electrons to become more localized with increasing number leads to different bonding conditions in the compounds discussed.

Synthesis, Characterization, and Bonding Properties of Polymeric Fullerides AC70⋅nNH3 (A=Ca, Sr, Ba, Eu, Yb)

Reduction of C70 with alkaline earth and rare earth metals dissolved in liquid ammonia results in metal fulleride solvates AC70.nNH3 (A = Ca, Sr, Ba, Eu, Yb) containing linear polymeric, anionic chains infinity 1 [C70(2-)]. The compounds were characterised by means of Raman spectroscopy and single-crystal structure determination. The accurate crystal structure of [Sr(NH3)8]C70.3NH3, determined with atomic resolution, allowed for a comparison with results of quantum chemical calculations. The nature of the C-C bonds in the fulleride is analysed in detail leading to a model explaining the unexpected polymerisation of C70(2-).

HB9X9˙ and H2B9X9 (X = Cl, Br, I): Neutral closo‐Nonaboranes in the Novel Series BnHn+1, and BnHn+2 – Syntheses, Ab Initio Calculations, and Electronic Structures

Chemical reduction of B9X9 (X = Cl, Br, I) with gaseous HI proceeds stepwise to give the neutral paramagnetic clusters HB9X9·, and the corresponding diamagnetic clusters H2B9X9. Together they comprise the first neutral derivatives in the series BnHn+1 and BnHn+2 with n = 9. The EPR spectra of the paramagnetic HB9X9· (X = Cl, Br, I) in glassy frozen CH2Cl2 solutions showed increasing g anisotropy for the heavier halogen derivatives, illustrating significant halogen participation at the singly occupied MO due to the larger spin-orbit coupling contributions. Temperature dependent 1H NMR spectra of H2B9X9 (in CD3CN, X = Cl, Br) indicate the presence of H2B9X9, [HB9X9]–, and [CD3CNH]+ with H2B9X9 acting as a Bronsted acid. The corresponding 11B NMR spectra (in CD3CN) show the presence of the dianions [B9X9]2– as a result of the protonation of CD3CN. The 11B resonances of the species H2B9X9 and [HB9X9]– are obscured by superimposition of the two resonance lines of the dianions [B9X9]2–. Temperature dependent 11B{1H} MAS-NMR spectra of H2B9Br9 show coalescence at 410 K and hence dynamic behaviour of the neutral B9-cluster in the solid. Cyclic voltammetry experiments of H2B9Br9 in CH3CN solvent) are compatible with the redox sequence [B9Br9]2––[B9Br9]· ––B9Br9. Quantum chemical calculations with the electron localization function (ELF) are described. HB9X9˙ und H2B9X9 (X = Cl, Br, I): Neutrale closo-Nonaborane aus der neuartigen Reihe BnHn+1 und BnHn+2 – Synthesen, ab initio Rechnungen und elektronische Strukturen Die chemische Reduktion von B9X9 (X = Cl, Br, I) mit gasformigem HI verlauft stufenweise, wobei die neutralen paramagnetischen Cluster HB9X9· sowie die diamagnetischen Cluster H2B9X9 gebildet werden. Beide Verbindungstypen sind die ersten neutralen Vertreter der Serien BnHn+1 und BnHn+2 mit n = 9. Die EPR-Spektren der paramagnetischen Verbindungen HB9X9· (X = Cl, Br, I) in glasartig gefrorenen CH2Cl2-Losungen zeigen fur die schwereren Halogenide zunehmende g-Anisotropie, was auf signifikante Halogen-Beteiligung am einfach besetzten MO hinweist, (zunehmende Spin-Bahn-Kopplungsbeitrage). Temperaturabhangige 1H-NMR-Spektren von H2B9X9 (in CD3CN, X = Cl, Br) zeigen die Anwesenheit von H2B9X9, [HB9X9]– neben [CD3CNH]+, die H2B9X9 als Bronsted-Saure ausweisen. Die entsprechenden 11B-NMR-Spektren zeigen die Anwesenheit der Dianionen [B9X9]2– als Resultat der Protonierung von CD3CN. Die 11B-NMR-Resonanzlinien von H2B9X9 und [HB9X9]– sind von den beiden Linien des Dianions [B9X9]2– uberlagert und somit nicht nachweisbar. Temperaturabhangige 11B{1H}-MAS-NMR-Spektren von H2B9Br9 zeigen bei 410 K Koaleszenz und beweisen damit das dynamische Verhalten des H2B9Br9-Clusters im festen Zustand. Cyclovoltammetrische Untersuchungen von H2B9Br9 in CH3CN sind in Ubereinstimmung mit der Redox-Sequenz [B9Br9]2–[B9Br9]· ––B9Br9. Quantenmechanische Rechnungen sowie Elektronen-Lokalisierungs-Funktionen (ELF) werden beschrieben.

SCF calculations on MIMD type parallel computers

SummaryOne of the key methods in quantum chemistry, the Hartree-Fock SCF method, is performing poorly on typical vector supercomputers. A significant acceleration of calculations of this type requires the development and implementation of a parallel SCF algorithm. In this paper various parallelization strategies are discussed comparing local and global communication management as well as sequential and distributed Fock-matrix updates. Programs based on these algorithms are bench marked on transputer networks and two IBM MIMD prototypes. The portability of the code is demonstrated with the portation of the initial Helios version to other operating systems like Parallel VM/SP and PARIX. Based on the PVM libraries, a platform-independent version has been developed for heterogeneous workstation clusters as well as for massively parallel computers.

Computational chemistry with transputers: a direct SCF program

By using transputers it is possible to build up networks of parallel processors with varying topology. Due to the architecture of the processors it is appropriate to use the MIMD (multiple instruction multiple data) concept of parallel computing. The most suitable programming language is OCCAM. We investigate the use of transputer networks in computational chemistry, starting with the direct SCF method. The most time consuming step, the calculation of the two electron integrals is executed parallelly. Each node in the network calculates whole batches of integrals. The main program is written in OCCAM. For some large-scale arithmetic processes running on a single node, however, we used FORTRAN subroutines out of standard ab-initio programs to reduce the programming effort. Test calculations show, that the integral calculation step can be parallelized very efficiently. We observe a speed-up of almost 8 using eight network processors. Even in consideration of the scalar part of the SCF iteration, the speed-up is not less than 7.1.

Structural ordering principles in quasi one-dimensional Wigner crystals of the series Na1+xCuO2 (0 ≤ x ≤ 1)

Abstract The general building principle of the commensurate subset of mixed valent sodium cuprates Na1+xCuO2 (0 ≤ x ≤ 1) has been revealed. Starting from parent NaCuO2, spin doping of the chain of edge sharing CuO4 plaquettes requires to incorporate further sodium ions for charge compensation. The accessible space needed for this purpose is generated by elongating the NaO6 octahedra present in NaCuO2. In this way, from one octahedron two square pyramidal and two tetrahedral sites result, out of which at best one each tetrahedral and square pyramidal site per original octahedron can be occupied, excluding combinations of electrostatically blocked sites. This general building principle has been employed to predict further structure candidates of this series (x = 1/4, 1/3, 2/3, 5/7, 3/4, 1). Density functional calculations (x = 0, 5/7, 3/4, 1) confirm the predicted charge ordering as well as the related structural features. The structure candidates are identified as local minima on the energy landscape.

The Use of Transputers in Quantum Chemistry

Quantum chemistry is one of the areas in natural sciences that is most closely related to the development of computers. The several methods to approximately solve the basic equations describing the electronic structure of atoms, molecules and solids (e.g. the Schrodinger equation), all have in common the large amount of computational expense. For ab-initio methods, that is for methods that do not use parameters fitted to experimental data, this expense is proportional to about n 3 (density functionals), n 4 (Hartree-Fock) or even n 5 (configuration interaction (CI)), where n is a quantity related to the accuracy of the calculation and to the size of the problem treated. Looking at this n dependency we understand, why very powerful computers are necessary to envisage reasonable problems.