Configuration coordinate approach

In the present chapter we focus on the optical spectra of the transitional metal ion impurities, as the point defects in insulating crystals. The reasons are because the JT effect is most often encountered in the transitional metal complexes, and very common in the octahedral complexes. We shall make use of the configuration coordinate approach [12], which enables one to apply much of the theory developed for molecules to the case of an isolated impurity in a crystal. 

Dolan et al. [ 176] and Rinzler et al. [ 142] presented a semi-empirical approach based on a single configuration coordinate model (see Sect. 3.1) for separating the effects of local compressibihty and crystal field strength on pressure-induced changes in the T2 energy of Cr + in several fluoride elpasohte systems. Their approach is based on an empirical form, motivated by the Born-Mayer potential, for the local compressibility k(P) ... 

The conceptually simplest approach to solve for the -matrix elements is to require the wavefimction to have the fonn of equation (B3.4.4). supplemented by a bound function which vanishes in the asymptote [32, 33, 34 and 35] This approach is analogous to the fiill configuration-mteraction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefimction. While successfiti for intennediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this type of method is prohibitively expensive for diatom-diatom reactions at high energies. 

Atoms not explicitly included in the trajectory must be generated. The position at which an atom may be placed is in some sense arbitrary, the approach being analogous to the insertion of a test particle. Chemically meaningful end states may be generated by placing atoms based on internal coordinates. It is required, however, that an atom be sampled in the same relative location in every configuration. An isolated molecule can, for example, be inserted into... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

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