Discrete levels parameterization

A real advancement in the development of Z-N catalysts came when metallocene catalysts were discovered.91 Now discrete, single-site complexes of early-transition metal metallocenes could be synthesized and characterized. These not only were potentially useful on an industrial scale, but also served as useful model systems for studying the mechanism and stereochemistry of Z-N catalysis. With the advent of high-level DFT-MO methods that were parameterized for all transition metals, metallocene catalysts and the attendant polymerization processes could be easily modeled to help understand the stereochemical outcomes of Z-N... 

The parameterization of the particle collision densities was obviously performed emplo3ung elementary concepts from the kinetic theory of gases, thus the derivation of the source term closures at the microscopic level have been followed by some kind of averaging and numerical discretization by a discrete numerical scheme [f6, 92, 118]. 

From the several continuum solvation methods available in the literature, the PCM model and its derivatives seem to be most used for pK calculations. In fact, the best pK results reported so far have been obtained with one of the PCM-based methods. Nevertheless, the fact that these calculations differ in many respects precludes any comparative evaluation of the different solvation models employed. More systematic studies are needed, taking into consideration the level of theory (method and basis sets) employed, the various continuum solvation models, and different classes of compounds. The introduction of solvent molecules into the solute cavity, in order to better represent the short-range solute-solvent interactions, must also be carefully examined. There is no apparent relationship between the structure of the solute and the number of intracavity solvent molecules that best reproduces the solvation energy. Hence, this best number is generally established on a trial-and-error basis. Also, the use of a such hybrid (discrete -I- continuum) description of the solvent molecules seems to be inconsistent with the fact that for some of the solvation models employed, the effects of the first solvation shell have been already incorporated when parameterizing the cavity. 

Erosion in SEDZLJ is parameterized based on data collected using Sedflume, which directly measures erosion rates at various depths within a sediment core as a function of applied shear stress. Rates of erosion, typically expressed in units of cm/s, obtained via Sedflume experiments are used in combination with estimates of sediment dry bulk density, particle size distribution, and critical shear stress to specify the properties of discrete sediment layers in the model simulation. Because erosion rates are measured for discrete shear stresses and sediment depths, interpolation is required to develop continuous functions. Linear interpolation is used between discrete shear stress levels, while logarithmic interpolation is used to specify the erosion as a function of depth. 

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