Crystal field theory adjusted

The basic difficulty with the CFT treatment is that it takes no account of the partly covalent nature of the metal-ligand bonds, and therefore whatever effects and phenomena stem directly from covalence are entirely inexplicable in simple CFT. On the other hand, CFT provides a very simple and easy way of treating numerically many aspects of the electronic structures of complexes. MO theory, in contrast, does not provide numerical results in such an easy way. Therefore, a kind of modified CFT has been devised in which certain parameters are empirically adjusted to allow for the effects of covalence without explicitly introducing covalence into the CFT formalism. This modified CFT is often called ligand field theory, LFT. However, LFT is sometimes also used as a general name for the whole gradation of theories from the electrostatic CFT to the MO formulation. We shall use LFT in the latter sense in this Chapter, and we introduce the name adjusted crystal field theory, ACFT, to specify the form of CFT in which some parameters are empirically altered to allow for covalence without explicitly introducing it. 

Let us now look at the center of the MO diagram, where we see the T2g orbitals and, somewhat higher in energy, the E orbitals. The latter, as noted, are predominantly of metal-ion d orbital character though with some ligand orbital character mixed in. Is this not the same situation, qualitatively speaking, as we obtained from the electrostatic arguments of crystal field theory Indeed it is, and, moreover, it is the same result we get from the adjusted crystal field theory, where we allow for the occurrence of orbital overlap that destroys to some extent the purity of the metal-ion d orbitals. 

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. ... 

The model just described, which is derived on the basis of pure crystal field theory, can be modified rather simply to include the effects of electron delocalization. Since the ab initio calculation of crystal field terms is at best totally unreliable, we follow the usual practice of treating these terms simply as adjustable parameters. Thus the question of paramount importance is how the spin-orbit coupling constant i is affected by covalent bond formation. 

Richard Fenske arrived as Assistant Professor at the University of Wisconsin in 1961 after having completed his PhD, with Donald Martin at Iowa State University on applying crystal-field theory to square-planar platinum complexes [19]. Fenske was interested in developing a method more closely tied to the ab initio molecular orbital method described so beautifully by Roothaan [20]. Building on some previous suggestions [21], he and his first students, especially Ken Caulton and Doug Radtke, developed an approximate self-consistent field method that had no empirical or adjustable parameters. With some later refinements by this author, the method became widely known as the Fenske-Hall method [22], and in this form it is still being used today [23]. 

The Akm can be calculated from a model such as the modified point-charge model presented in section 3.2.4, the Rt l) can be calculated as well, and matrix elements of ju, can be computed between crystal-field split sublevels for a particular lanthanide ion in a particular host crystal a priori, without fitting experimental intensity measurements (Esterowitz et al., 1979a Leavitt and Morrison, 1980). However, this method is not prevalent in the literature rather, usually the theory is expressed in terms of a few adjustable parameters and a fit is made to intensity data. To this end, we consider the line strength, defined by (Condon and Shortley, 1959)... 

Polymer phase separation and crystallization, as introduced separately in the previous two chapters, have different molecular driving forces that can be simultaneously expressed by the use of the lattice model. Adjusting the corresponding driving forces, the mean-field theory can predict the phase diagrams, and at the meanwhile molecular simulations can demonstrate the complex phase transition behaviors of polymers in the multi-component miscible systems. 

The superiority of using lasers for material studies often lies in its spatial and temporal flexibilities, that is, the material can selectively excited and probed in space and time. These qualities may allow us to elucidate fundamental material properties not accessible to conventional techniques. The location, dimension, direction, and duration of the material excitation can be readily controlled through adjustment of the beam spot, direction, polarization, and pulse width of the exciting laser field. The flexibilities can be further enhanced when two or more light waves are used to induce excitations. Such a technique, however, has not yet been fully explored in liquid-crystal research. Although the recent studies of optical-field-induced molecular reorientation in nematic liquid-crystal films have demonstrated the ability of the technique to resolve spatial variation of excitations, corresponding transient phenomena induced by pulsed optical fields have not yet been reported in the literature. Because of the possibility of using lasers to induce excitations on a very short time scale, such studies could provide rare opportunities to test the applicability of the continuum theory in the extreme cases. 

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