Crystal field theory shapes

The VSEPR approach is largely restricted to Main Group species (as is Lewis theory). It can be applied to compounds of the transition elements where the nd subshell is either empty or filled, but a partly-filled nd subshell exerts an influence on stereochemistry which can often be interpreted satisfactorily by means of crystal field theory. Even in Main Group chemistry, VSEPR is by no means infallible. It remains, however, the simplest means of rationalising molecular shapes. In the absence of experimental data, it makes a reasonably reliable prediction of molecular geometry, an essential preliminary to a detailed description of bonding within a more elaborate, quantum-mechanical model such as valence bond or molecular orbital theory. 

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... 

Crystal field theory assumes that all M-L interactions are purely electrostatic in nature. More specifically, it considers the electrostatic effect of a field of ligands on the energies of a metals valence-shell orbitals. To discuss CFT, we need only be aware of two fundamental concepts (1) the coulombic theory of electrostatic interactions and (2) the shapes of the valence orbitals of transition metals—that is, the nd orbitals ( = 3 for the first row of transition metals, etc.). The first concept involves only the familiar ideas of the repulsion of like and the attraction of dislike electrical charges. Quantitatively, Coulomb s law states that the potential energy of two charges Qj and Q2 separated by a distance r is given by the formula shown in Equation (4.3) ... 

The most remarkable aspect of Eq. (14-10) is that the dependence upon bond length and therefore, the dependence upon which alkali halide is being considered—has cancelled out. Another consequence is that the ion. softening does not depend upon pre.ssurc. This explains why theories of the crystal-field splitting and its pressure dependence that arc based upon hard ions have been successful the 0.51 factor can be absorbed in an undetermined scale parameter, depending upon the shape of the orbitals being split, since the factor 0.51 does not change with distortion. 

During recent decades the molecular theory of flexoelectricity in nematic liquid crystals was developed further by various authors. " In particular, explicit expressions for the flexocoefiicients were obtained using the molecular-field approximation taking into account both steric repulsion and attraction between the molecules of polar shape. The influence of dipole-dipole correlations and molecular flexibility was later considered. Recently flexoelectric coefficients have been calculated numerically using the mean-field theory based on a simple surface intermolecular interaction model. This approach allows us to take into consideration the real molecular shape and to evaluate the flexocoefiicients for mesogenic molecules of different structures including dimers with flexible spacers. 

There are several different theoretical approaches to the problem. The Landau molecular field theory was applied by de Gennes to liquid-crystal phase transitions. (89) The Maier-Saupe theory focuses attention on the role of intermolecular attractive forces.(90) Onsager s classical theory is based on the analysis of the second virial coefficient of very long rodlike particles.(91) This theory was the first to show that a solution of rigid, asymmetric molecules should separate into two phases above a critical concentration that depends on the axial ratio of the solute. One of these phases is isotropic, the other anisotropic. The phase separation is, according to this theory, solely a consequence of shape asymmetry. There is no need to involve the intervention of intermolecular attractive forces. Lattice methods are also well suited for treating solutions, and phase behavior, of asymmetric shaped molecules.(80,92,93)... 

CICP pigments contain transition metals, and the absorptions that provide color are due to ligand field theory [9], In these pigments optical absorptions tend to be broad with the maximum in the middle of the band. This shape is due to vibrational interactions and crystal field irregularities. 

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