Crystal field theory advantages

E. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd ed., John Wiley Sons, Inc., New York, 1967. An excellent volume that stresses the reactions of complexes ia solution a background and a detailed theory section is iacluded that is largely crystal field theory, but some advantages and disadvantages of molecular orbital theory are iacluded. 

Thus in order to calculate an energy-level diagram and/or details of magnetic behavior in ligand field theory, one proceeds in the same manner as in crystal field theory except that, instead of assuming the free-ion values for A, B and C, one either assumes somewhat smaller ones or leaves them as parameters to be evaluated from the experimental observations. In this way all the computational and conceptual advantages of the simple electrostatic theory are preserved while allowance is made—in an indirect and admittedly artificial way—for the consequences of finite orbital overlap. One also bears in mind that there are other consequences of the overlap, for example, electron delocalization. 

It seems that, in its most widely used forms at any rate, the AOM involves such severe approximations and draws on empirical information to such an extent that it cannot be regarded as a proper implementation of quantum mechanics. Nevertheless, as a form of ligand field theory, it possesses distinct advantages and leads to a novel parameterization scheme which promises some degree of transferability of parameters with a metal-ligand bond. This last feature is entirely lacking, at least outside cubic symmetry, in crystal or ordinary ligand field treatments. 

The mean-polarizability approximation, discussed in detail by Agranovitch,16 presents the same advantages (simplicity, arbitrary concentrations, etc.), and the same limitations as the average-locator approximation in particular, this theory provides two bands of persistence behavior for all values of the parameters. This may be checked on the example of a cubic crystal, where the local field has a very simple form The modes of the mixed crystal are given by... 

A. V. Kiselev Zeolites are porous crystals. This means that we can find the molecular field distribution in their channels. The advantage of describing the adsorption on zeolites using the molecular theory consists in obtaining the constants which have a definite physical meaning (for example, the Henry constant and second virial coefficient). Further development of the theory needs a further improvement of the model based on the investigation of the adsorbate-zeolite systems by the use of modern physical methods. 

A large part of the theory of the effect of an external magnetic field on lanthanide ions in crystals was developed in the context of paramagnetic resonance (Bleaney and Stevens 1953). It is that field that bequeathed optical spectroscopists the spin Hamiltonian and its various elaborations. This is not to say that such devices have ever been taken much advantage of. After all, the perturbation Hamiltonian m-(L + 2S), where P is the Bohr magneton and H the applied magnetic field, is particularly simple to evaluate, since the quantum number S and L are used in defining all lanthanide states. 

In the theory of electronic structure of crystals, we also use the molecrdar-cluster model being based on physical reasons we choose a molecular fragment of a crystal and somehow try to model the influence of the rest of a crystal on the cluster chosen (for example, by means of the potential of point charges or a field of atomic cores). Prom the point of view of symmetry such a model possesses only the symmetry of point group due to which it becomes impossible to estabhsh a connection of molecular-cluster electronic states with those of a boundless crystal. At the same time, with a reasonable molecular-cluster choice it is possible to describe well enough the local properties of a crystal (for example, the electronic structure of impurity or crystal imperfections). As an advantage of this model it may also be mentioned an opportunity of application to crystals of those methods of the account of electronic correlation that are developed for molecules (see Chap. 5). 

We present a derivation of the broadening due to the solvent according to a system/ bath quantum approach, originally worked out in the field of solid-state physics to treat the effect of electron/phonon couplings in the electronic transitions of electron traps in crystals [67, 68]. This approach has the advantage to treat all the nuclear degrees of freedom of the system solute/medium on the same foot, namely as coupled oscillators. The same type of approach has been adopted by Jortner and co-workers [69] to derive a quantum theory of thermal electron transfer in polar solvents. In that case, the solvent outside the first solvation shell was treated as a dielectric continuum and, in the frame of the polaron theory, the vibrational modes of the outer medium, that is, the polar modes, play the same role as the lattice optical modes of the crystal investigated elsewhere [67,68]. The total Hamiltonian of the solute (5) and the medium (m) can be formally written as... 

Polymers and liquid ciystals are important materials for various research fields. If the two substances are mixed, novel materials which combine the advantageous properties of both may be formed. 1 began to think about this around 1994. Already at that time, this mixed system had attracted attention as an electro-optical material, but from the perspective of basic physical properties, the center of the liquid crystal research up to that point was the phase transition and Uquid crystal stracture of novel low molecular weight liquid crystals. The physics of liquid crystals was based on the Onsager theory, the Maier-Saupe theory, and the elastic theory by Frank. However, the theoretical study of a liquid crystal mixed with other substances had not yet been developed. So, 1 began to think to build theories of phase separations and phase transitions in mixtures of liquid crystals and other substances. Our first paper on the theory of phase separations in the mixture of a polymer and a liquid crystal was published in 1996 [41]. 1 found at a later date that a paper on the same topic by Prof. Kyu of Akron University had been presented already in 1995 [42]. However, there was a difference between the two theories. Kyu s theory has dealt with low molecular weight liquid crystals in an attractive model, whereas our model considered both attractive and repulsive interactions between rodlike liquid crystal molecules and can handle also long rodlike molecules. After that, I had a variety of discussions with Kyu and it was a valuable experience for my research. 

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