Predictions using crystal field theory

We used crystal field theory to order the energy-level splittings induced in the five d orbitals. The same procedure could be applied to p orbitals. Predict the level splittings (if any) induced in the three p orbitals by octahedral and square-planar crystal fields. 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

There are two major theories of bonding in d-metal complexes. Crystal field theory was first devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions, and then adapted to individual complexes. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory (Section 16.12), is based on molecular orbital theory. 

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 ... 

All the off-diagonal matrix elements of the spin-orbit coupling in the >, Tl> [ basis are thus reduced by the factor y, and we use the experimentally observed quenching to calculate Ej j and the corresponding geometrical distortion (14). In the Cs2NaYClg host lattice the total spread of the four spin-orbit components of T2 is 32 cm whereas crystal field theory without considering a Jahn-Teller effect predicts a total spread of approximately 107 cm-. ... 

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. 

The spin-orbit coupling constant plays a considerable role in determining the detailed magnetic properties of many ions in their complexes, for example, the deviations of some actual magnetic moments from spin-only values and inherent temperature-dependence of some moments. All studies to date show that in ordinary complexes the values of A are 70-85% of those for the free ions. It is possible to get excellent agreement between crystal field theory predictions and experimental observations simply by using these smaller A values. 

Bethe (1929) initiated the crystal field theory with which van Vleck, Use, and Hartman explained the color and magnetic properties of metal complexes. The crystal field theory (CFT) constitutes a fonndation for predicting the structure, stability, kinetic lability, and redox properties, and of metal complexes. It also accounts for certain trends in the physicochemical properties of metal complexes (Orgel 1952). 

The last determination to make is the d electron count. The number of electrons in the metal s d orbitals is the number that the metal starts with, based on its position in the periodic table, minus the number of electrons that are considered to be removed by oxidation. The count is designated as d", where n is the number of electrons in the d orbitals. This number is not used as often as the full metal electron count and the oxidation state when predicting reactivity, but it is quite useful when coupled with crystal field theory to predict the spectroscopy and spin state of the organometallic complex. Once again. Figure 12.2 shows a series of examples. 

The crystals of simple salts such as NaCl and ZnS have lattices which are often regarded as ionic. That this is a plausible approximation is indicated by, amongst other things, the fact that it is possible to assign ionic radii and to use the approximate additivity of these radii to predict interatomic distances. Crystal field theory similarly assumes that the forces between a... 

The question may now arise whether it is possible to use the crystal field theory for mechanistic predictions. It is taken that the answer is positive, assuming that the degree of orbital overlap is not too large. Experience shows that the orbital overlap is often small, which leads to the modified (adjusted) crystal field theory. However, if the orbital overlap is large, then the molecular orbital approach is the only solution. On the other hand, molecular orbital overlap calculations are not easy to perform. ... 

Using the Crystal Field Theory to Predict the Structure of a Complex from Its Magnetic Properties... 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

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