Transition metal-lanthanides, energy

The Self-Consistent (SfC) (G)RECP version [23, 19, 24, 27] allows one to minimize errors for energies of transitions with the change of the occupation numbers for the OuterMost Core (OMC) shells without extension of space of explicitly treated electrons. It allows one to take account of relaxation of those core shells, which are explicitly excluded from the GRECP calculations, thus going beyond the frozen core approximation. This method is most optimal for studying compounds of transition metals, lanthanides, and actinides. Features of constructing the self-consistent GRECP are ... 

Values in boldface type are from Durwent and represent his estimates of ihc "best value" and uncertainties for the energies required to break the bonds at 0 K. Where values are not available from Darwent. they arc taken from Brewer and coworkers for metal halides and dihaiidcs (boldface italics) or from Feber for transition metal, lanthanide, and actinide halides (italics). These values represent enthalpies of atomization at 298 K. The remaining values are from Cottrell (Arabic numerals) and other sources (Arabic numerals with superscripts keyed to references at end of table). 

Likewise the Hubbard model the periodic Anderson model (PAM) is a basic model in the theory of strongly correlated electron systems. It is destined for the description of the transition metals, lanthanides, actinides and their compositions including the heavy-fermion compounds. The model consists of two groups of electrons itinerant and localized ones (s and d electrons), the hybridization between them is admitted. The model is described by the following parameters the width of the s-electron band W, the energy of the atomic level e, the on-site Coulomb repulsion U of d-electrons with opposite spins, the parameter V of the... 

Energy Transfer in Transition Metal-Lanthanide Systems. 264... 

Some of the earliest experimental studies of neutral transition metal atom reactions in the gas phase focused on reactions with oxidants (OX = O2, NO, N2O, SO2, etc.), using beam-gas,52,53 crossed molecular beam,54,55 and flow-tube techniques.56 A few reactions with halides were also studied. Some of these studies were able to obtain product rovibrational state distributions that could be fairly well simulated using various statistical theories,52,54,55 while others focused on the spectroscopy of the MO products.53 Subsequently, rate constants and activation energies for reactions of nearly all the transition metals and all the lanthanides with various oxidant molecules... 

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). 

The lanthanides have electrons in partly filled 4/orbitals. Many lanthanides show colors due to electron transitions involving the 4/orbitals. However, there is a considerable difference between the lanthanides and the 3d transition-metal ions. The 4/ electrons in the lanthanides are well shielded beneath an outer electron configuration, (5.v2 5p6 6s2) and are little influenced by the crystal surroundings. Hence the important optical and magnetic properties attributed to the 4/ electrons on any particular lanthanide ion are rather unvarying and do not depend significantly upon the host structure. Moreover, the energy levels are sharper than those of transition-metal ions and the spectra resemble those of free ions. 

The colors are characteristic of the ions themselves and are due to transitions between the partly filled d orbitals of transition metals (d-d transitions) or the partly filled / orbitals of lanthanides (f-f transitions). In the 3d transition-metal ions, the 3d orbitals contain one or more electrons. When these ions are introduced into a solid, the orbital energies are split by interactions with the surrounding anions. The color observed is due to transitions between these split energy levels. The color observed varies considerably as the interactions are dependent upon the... 

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