Transition metals band structure

Much insight in the transition metal band structure is provided by the LMTO method (Andersen 1975, Andersen and Jepsen 1977, Andersen et al. 1985, Skriver 1983a), which gives a very useful approximate description of narrow transition-metal bands when they hybridize little with s and p bands. The unhybridized energy band eigenvalues given by eq. (22) become particularly simple when y, is small. Then... 

R. L. Jacobs, The theory of transition metal band structures, J. Phys. C1,492-506 (1968). 

Electron transitions in transition-metal ions usually involve electron movement between the d orbitals (d-d transitions) and in lanthanides between the / orbitals (/-/ transitions). The band structure of the solid plays only a small part in the energy of these transitions, and, when these atoms are introduced into crystals, they can be represented as a set of levels within the wide band gap of the oxide (Fig. 9.15). 

United Kingdom, 1969, pp. 340-408, Transition Metals. Electronic Structure of the d-Band. Its Role in the Crystalline and Magnetic Structures. 

The dissociation of water was examined over a range of different close-packed transition-metal surface structures in order to establish periodic trends. The results shown in Fig. 6.5 indicate that it becomes easier to activate water over metals that lie to the left of the periodic table which have more vacancies in the d-band. 

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. 

Terakura K, Qguchi T, Williams A R and Kubler J 1984 Band theory of insulating transition-metal monoxides Band-structure calculations Phys. Rev. B 30 4734... 

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

Equation (6.20) and the semiquantitative trends it conveys, can be rationalized not only on the basis of lateral coadsorbate interactions (section 4.5.9.2) and rigorous quantum mechanical calculations on clusters89 (which have shown that 80% of the repulsive O2 - O interaction is indeed an electrostatic (Stark) through-the-vacuum interaction) but also by considering the band structure of a transition metal (Fig. 6.14) and the changes induced by varying O (or EF) on the chemisorption of a molecule such as CO which exhibits both electron acceptor and electron donor characteristics. This example has been adapted from some rigorous recent quantum mechanical calculations of Koper and van Santen.98... 

Each energy level in the band is called a state. The important quantity to look at is the density of states (DOS), i.e. the number of states at a given energy. The DOS of transition metals are often depicted as smooth curves (Fig. 6.10), but in reality DOS curves show complicated structure, due to crystal structure and symmetry. The bands are filled with valence electrons of the atoms up to the Fermi level. In a molecule one would call this level the highest occupied molecular orbital or HOMO. 

Figure 6.28. Schematic illustration of the change in local electronic structure of an oxygen atom adsorbing on the late transition metal rhodium, the DOS of which is shown on the right-hand side. The interaction of the oxygen 2p orbital with the sp band of the transition metal is illustrated through interaction with the idealized free-electron...

Mercuric sulfide (HgS) is dimorphic. The more common form, cinnabar (red a-form), has a distorted RS, trigonal structure which is unique among the monosulfides, for the crystal is built of helical chains in which Hg has two nearest neighbors at 2.36 A, two more at 3.10 A, and two at 3.30 A. Bulk a-HgS is a large-gap semiconductor (2.1 eV), transparent in the red and near IR bands. The rare, black mineral metacinnabarite is the 3-HgS polymorph with a ZB structure, in which Hg forms tetrahedral bonds. Upon heating, 3-HgS is converted to the stable a-form. The ZB structure of HgS is stabilized under a few percent admixture of transition metals, which replace Hg ions in the lattice. 

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