Transition metals geometrical properties

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

It must be emphasized that the duodectet rule (4.6) initially has no structural connotation, but is based on composition only. Indeed, the compositional regularity expressed by (4.6) encompasses both molecular species (such as the metal alkyls) and extended lattices (such as the oxides and halides) and therefore appears to transcend important structural classifications. Nevertheless, we expect (following Lewis) that such a rule of 12 may be associated with specific electronic configurations, bond connectivities, and geometrical propensities (perhaps quite different from those of octet-rule-conforming main-group atoms) that provide a useful qualitative model of the chemical and structural properties of transition metals. 

The description of bonding at transition metal surfaces presented here has been based on a combination of detailed experiments and quantitative theoretical treatments. Adsorption of simple molecules on transition metal surfaces has been extremely well characterized experimentally both in terms of geometrical structure, vibrational properties, electronic structure, kinetics, and thermo-chemistry [1-3]. The wealth of high-quality experimental data forms a unique basis for the testing of theoretical methods, and it has become clear that density functional theory calculations, using a semi-local description of exchange and correlation effects, can provide a semi-quantitative description of surface adsorption phenomena [4-6]. Given that the DFT calculations describe reality semi-quantitatively, we can use them as a basis for the analysis of catalytic processes at surfaces. 

The underlying motivation of the work presented in this paper is to provide a theoretical understanding of basic physical and chemical properties and processes of relevance in photoelectrochemical devices based on nanostructured transition metal oxides. In this context, fundamental problems concerning the binding of adsorbed molecules to complex surfaces, electron transfer between adsorbate and solid, effects of intercalated ions and defects on electronic and geometric structure, etc., must be addressed, as well as methodological aspects, such as efficiency and reliability of different computational schemes, cluster models versus periodic ones, etc.. 

Another useful feature of transition metals in biological systems is the unique battery of physical techniques that can be used to study their structural and electronic properties (electronic properties of transition-metal centers and allow for study of the metal ion without interference from other material in the system. 

Exercise 1.3. Consider a coordination compound formed from BH3 and C2H4. From the HOMO-LUMO properties of each species predict the geometric structure of the Lewis acid-base adduct. Now predict the structure of a compound formed by replacing one CO ligand of Fe(CO)5 with C2H4. Note the parallelism between the main group and transition metal examples. The second compound is a stable and isolatable compound, whereas the first is a transient intermediate in the hydro-boration of ethylene to ethyl borane and has only been characterized as a transient intermediate in a fast-flow system by modulated mass spectrometry. 

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