Interatomic distances, transition metal

In order to perform the calculation., of the conductivity shown here we first performed a calculation of the electronic structure of the material using first-principles techniques. The problem of many electrons interacting with each other was treated in a mean field approximation using the Local Spin Density Approximation (LSDA) which has been shown to be quite accurate for determining electronic densities and interatomic distances and forces. It is also known to reliably describe the magnetic structure of transition metal systems. 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

Strong boron-transition metal interaction interatomic distances are shorter by 5-10%, as compared to the sum of the metal radii. 

The potential maps were remarkably clear (Figs. 5a and b) with most of the peaks perfectly round and well resolved. 63 and 68 peaks were peak found from the density maps in the flat (Fig. 5a) and puckered layers (Fig. 5b), respectively. Out of the 131 peaks, 7 were removed due to too short interatomic distances. It was possible to distinquish Al and transition metal atoms according to the peak height and chemical knowledge. There are in total 129 unique atoms in the unit cell, 62 atoms in the flat layer and 67 atoms in the puckered layer. The structure model and the potential map are superimposed in Fig. 5. 

Table I. Interatomic distances, shrinkages, and bending vibrational frequencies of first row transition metal dihalides...

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

Mean cobalt-cobalt and nickel-nickel distances observed in these complexes are very close to interatomic distances determined at ambient temperatures in cobalt and nickel metals (Co-Co 2.489(7) A vs. 2.507 A in a-cobalt (33) Ni-Ni 2.469(6) A vs. 2.492 A in the metal (39)). The mean M-H bond lengths, as well as hydride displacements from M3 faces, are less for nickel in H3Ni4(Cp)4 than for cobalt in HFeCo3(CO)9(P(OMe)3)3. Although the differences are marginally significant within error limits (Ni-H 1.691(8) A vs. Co-H 1.734(4) A displacements from plane Ni3 0.90(3) A vs. Co3 0.978(3) A), they are in the expected direction since the covalent radius should vary inversely with atomic number within a transition series. However, other effects such as the number of electrons in the cluster also can influence these dimensions. 

The crystal chemistry of many transition metal compounds, including several minerals, display unusual periodic features which can be elegantly explained by crystal field theory. These features relate to the sizes of cations, distortions of coordination sites and distributions of transition elements within the crystal structures. This chapter discusses interatomic distances in transition metal-bearing minerals, origins and consequences of distortions of cation coordination sites, and factors influencing site occupancies and cation ordering of transition metals in oxide and silicate structures, which include crystal field stabilization energies... 

One property of a transition metal ion that is particularly sensitive to crystal field interactions is the ionic radius and its influence on interatomic distances in a crystal structure. Within a row of elements in the periodic table in which cations possess completely filled or efficiently screened inner orbitals, there should be a decrease of interatomic distances with increasing atomic number for cations possessing the same valence. The ionic radii of trivalent cations of the lanthanide series for example, plotted in fig. 6.1, show a relatively smooth contraction from lanthanum to lutecium. Such a trend is determined by the... 

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