Crystal electrostatic model

Wood and Blundy (2001) developed an electrostatic model to describe this process. In essence this is a continuum approach, analogous to the lattice strain model, wherein the crystal lattice is viewed as an isotropic dielectric medium. For a series of ions with the optimum ionic radius at site M, (A(m))> partitioning is then controlled by the charge on the substituent (Z ) relative to the optimum charge at the site of interest, (Fig. 10) ... 

How to Determine the Crystal-Field Parameters 2. The Point Charge Electrostatic Model... 

Edvarsson, S. and Klintenberg, M. (1998) Role of the electrostatic model in calculating rare-earth crystal-field parameter. 

Classical electrostatic modeling based on the Coulomb equation demonstrated that the model system chosen could account for as much as 85% of the effect of the protein electric field on the reactants. Several preliminary computations were, moreover, required to establish the correct H-bond pattern of the catalytic water molecule (WAT in Fig. 2.6). Actually, in the crystal structure of Cdc42-GAP complex [60] the resolution of 2.10 A did not enable determination of the positions of the hydrogen atoms. Thus, in principle, the catalytic water molecule could establish several different H-bond patterns with the amino acids of the protein-active site. Both classical and quantum mechanical calculations showed that WAT, in its minimum-energy conformation,... 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

It is quite remarkable that electrostatic calculations based on a simple model of integral point charges at the nuclear positions of ionic crystals have produced good agreement with values of the cohesive energy as determined experimentally with use of the Born-Haber cycle. The point-charge model is a purely electrostatic model, which expresses the energy of a crystal relative to the assembly of isolated ions in terms of the Coulombic interactions between the ions. 

Conclusion Ionic crystals may be viewed quite simply in terms of an electrostatic model of lattices... 

The crystal lattice energy can be estimated from a simple electrostatic model When this model is applied to an ionic crystal only the electrostatic charges and the shortest anion-cation intermiclear distance need be considered. The summation of all the geometrical interactions be/Kveeti the ions is called the Madelung constant. From this model an equatitWjor the crystal lattice energy is derived ... 

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin-orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius Rs which is embedded into an infinite medium with dielectric constant e. This leads to a reduction AFk of the Slater parameters (Newman, 1973) ... 

The terms in the Hamiltonian that represent the non-spherical part of the interaction with the crystal are modeled using the so-called crystal-field Hamiltonian. It is important to recognize that this Hamiltonian is not restricted to electrostatic effects, which form a minor part of the total crystal-field effect (Ng and Newman, 1987). When the parameters are fitted to experimental energies, their values reflect all one-electron non-spherical interactions. The crystal-field Hamiltonian is expressed in Wyboume (1965) notation as,... 

According to the crystal field model, the crystalline electrostatic field of ligands in a crystal structure influences the 3d orbital energy levels of a central transition metal ion in a coordination site. There is a two-fold influence of temperature on a crystal structure. First, increased thermal motion results in increased amplitudes of atoms vibrating about their crystallographic positions. Second, thermal expansion causes small increases in interatomic distances, so that according to eq. 

The phenomenon of the nephelauxetic effect cannot be interpreted in the framework of an electrostatic model which considers exclusively first-order crystal field effects. The observed band shifts could be due to second-order crystal field effects. However, the theoretical values of the second-order crystal field effects are of the order of 10 cm-1 or so [40,41] and cannot account for the experimentally observed band shifts, which in some cases are as high as 100 to 1000 cm 1. 

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