Crystal field model naming

The one-electron crystal field Hamiltonian does not take into account electron correlation effects. For some systems, it has been useful to augment the crystal field Hamiltonian with additional terms representing the two-electron, correlated crystal field. The additional terms most commonly used (see, for example, Peijzel et al., 2005b Wegh et al., 2003) are from the simplified delta-function correlation crystal field model first proposed by Judd (1978) that assumes electron interaction takes place only when two electrons are located at the same position (hence the name delta-function ). This simplified model, developed by Lo and Reid (1993), adds additional terms, given as,... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

In this chapter, we discuss mostly the bonding in mononuclear homoleptic complexes ML using two simple models. The first, called crystal field theory (CFT), assumes that the bonding is ionic i.e., it treats the interaction between the metal ion (or atom) and ligands to be purely electrostatic. In contrast, the second model, namely the molecular orbital theory, assumes the bonding to be covalent. A comparison between these models will be made. 

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... 

This model based on a shortened version of m.o. theory is known as ligand field theory, a name reminiscent of the so-called crystal field theory that approaches the problem by considering the effect of six negative point charges, octahedraUy placed around a metal atom, on the energies of the various d orbitals ... 

The rare earth metals form hydrides readily and a number of studies have been performed on these materials (143). The dihydrides of the rare earths form in CaF2-type structure. The crystal field problem has been applied to characterize the fundamental role of hydrogen in these compounds (144-149). The information accumulated for several dihydrides seems to favor the anionic model, namely, that hydrogen accepts an electron to become negatively charged. We will illustrate the results on PrH2 and ErH2. 

There are two models by means of which the loss of degeneracy of the d orbitals can be explained the electrostatic model, and the molecular orbital model. In the first model, the differentiation of the d orbitals is attributed to the electric field produced by the symmetrical disposition of the attached groups, which may be anions like Cl"" or CN or dipole molecules like H20 or NH3. In a crystal also, the metal ion finds itself in a similar environment and hence the original name Crystal Field Theory. The five d orbitals which may be denoted as dxy, dyz, dxz, dx2-y2 and d7 have the shapes as represented in Figure 12.L The dxy, dxz and dYZ orbitals have their maximum in a diagonal direction between the co-ordinate axes in each of the three planes. The dx2-y2 and d72 orbitals are directed along the co-ordinate axes. Although... 

The name crystal field arose because the theory was first developed to explain the properties of solid, crystalline materials, such as ruby. The same theoretical model apfiies to comfdexes in solution. 

In order to consider the periodic crystal potential in cluster calculations, we developed the "chemically complete cluster model" (MODEL II) [10], which is similar to that proposed by Goodman et al. [11]. In our cluster model, atoms in the cluster are classified into three types. Type I atoms are "seed atoms" of which basis functions are obtained by the self-consistent procedure. The seed atoms are chemically complete. Namely, they are put in a potential environment similar to that in the bulk. Type II atoms are "passive atoms" of which basis functions are solved in the same potential field as for the type I atoms of the same species. Type in atoms have atomic potentials which are the same as in the type I atoms, but their wavefunctions are not included in molecular orbital calculations. The validity of MODEL II is tested for TiC in comparison with the results obtained using MODEL I. 

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