Crystal field theory numbers

In the case of covalent compounds, crystal-field theory is a poor model for estimating electric field gradients because of the extensive participation of ligand atomic orbitals in the chemical bonds. MO calculations are a much better choice, since the corresponding interactions are considered, and realistic (noninteger) population numbers are obtained for the central metal as well as the ligand atomic orbitals. 

All materials in the Lai- r ,Coi- Fe/)3-(5 (LSCF) family of materials have electronic transference numbers approaching unity. The electronic structure LSC and LSF has often been described in terms of partially delocalized O p—Co band states based on the tg and e levels of crystal-field theory. In... 

Symmetry considerations derived from group theory predict three main absorption-bands for Cr + in an octahedral environment and a number of low-intensity quartet-doublet-transitions in addition. The energies of the corresponding levels are calculated by means of crystal-field theory to be those of table 2 for the special choices AjB = 20 and 30 respectively ). 

As a number of excellent books and review articles have been written on the topic of crystal-field theory (10-14) and the general aspects of luminescence (75-79), these subjects are not considered per se. 

Describe the bonding in [Mn(CN)g]3-, using both crystal field theory and valence bond theory. Include the appropriate crystal field d orbital energy-level diagram and the valence bond orbital diagram. Which model allows you to predict the number of unpaired electrons How many do you expect ... 

Another possibility to address the problem of the correlation crystal fields is an approach based on different wavefunctions for the spin-up and spin-down electrons. This spin-correlated crystal-field model merely doubles the number of crystal-field parameters and thus can be applied in most cases. Shen and Holzapfel (1995c) presented a high pressure study on spin-correlated crystal fields in MFCl Sm2+ (M = Ba, Sr, Ca). In particular, they considered the splitting ratio R of the 5Di and 7Fi multiplets, which should be equal to 0.298 within the conventional one-electron crystal-field theory and independent of the host crystal. In a first step, Shen and Holzapfel (1995c) considered ambient pressure as well as high pressure data of the isoelectronic Eu3+ ion. In this case they found a ratio of R = 0.238, which could be explained by taking into account a spin-correlated crystal-field parameter C2 = —0.007(3). 

Almost any theory correctly predicts the octahedral and tetrahedral structures of 6- and 4-coordinated molecules. Thus, a simple ionic model in which a central positive ion attracts a number of negative ions gives these structures because, for a given central atom to ligand distance, they maximize the distance between the ligands and hence minimize their repulsive interactions. For this reason, the octahedron is more stable than the trigonal prism, and the tetrahedron is more stable than the square plane. An extension of this model, namely crystal field theory, explains... 

Among the early successes of crystal field theory was its ability to account for magnetic and spectral properties of complexes. In addition, it provided a basis for understanding and predicting a number of their structural and thermodynamic properties. Several such properties are described in this section from the crystal field point of view. Certainly other bonding models, such as molecular orbital theory, can also be used to interpret these observations. Even when they are, however, concepts from crystal field theory, such as crystal (or ligand) field stabilization energy, are often invoked within the discussion. 

At the same time as Ballhausen cultivated the scientific activity at FKI did he also found time to write his influential books. Apart from the dissertation, the first of these was Introduction to Ligand Field Theory [16]. It is probably the publication for which he is best known to the broad audience of chemists. It is a classic in the world of inorganic chemistry. It contains chapters on atomic theory and group theory, crystal-field theory, molecular orbitals, spin-orbit coupling, and vibronic interactions. Last, but not least, it also contains an actual discussion of the properties of a number of inorganic complexes. In the preface, he writes, inter alia ... 

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