Empirical scaling procedure

The above discussion neglects polarization effects. In part, these are taken into account by the empirical scaling procedures (e.g., the dipole moment of the water molecule in condensed-phase models is chosen to be larger than the gas-phase value).12 Internal charge rearrangements due to conformational... 

Experimental work has not validated the scaling procedure above with respect to scale-up of blending processes. Since this approach also relies on empirical work, this model should not be favored over other approaches currently in use, though it may provide additional insights. 

There is some evidence to suggest that, depending upon the phase volume ratios employed, the emulsification technique used can be of greater importance in determining the final emulsion type than the H LB values of the surfactants themselves [434], As an empirical scale the HLB values are determined by a standardized test procedure. However, the HLB classification for oil phases in terms of the required HLB values is apparently greatly dependent on the emulsification conditions and process for some phase-volume ratios. When an emulsification procedure involves high shear, or when a 50/50 phase volume ratio is used, interpretations based on the classical HLB system appear to remain valid. However, at other phase-volume ratios and especially under low shear emulsification conditions, inverted, concentrated emulsions may form at unexpected HLB values [434]. This is illustrated in Figures 7.4 and 7.5. 

Rationalization of these discrepancies between calculated and observed molecular properties has been achieved by recognizing that the accuracy problems tend to be systematic for the computational methods [726], For the same levels of theory, the errors in molecular parameters tend to be similar [79] for molecules if a variety of types and size. Building on the ideas of similarities between similar chemical functional groups in different molecules, the SQM procedure develops empirical scaling factors to correct the overestimated harmonic force constants from the computations [77], These scale factors form a diagonal matrix C which modified the calculated force matrix Fcalc according to the relationship [727] ... 

Biochemical impurities originate from the media components, antifoams, oils, and metal ions, and may include metabolites closely related to the compound of interest they can all affect empirical isolation procedures. It is therefore essential to maintain close liaison between the fermentation and extraction scientists during all aspects of scale-up to ensure that fermentation developments are not adversely affecting isolation procedures. The inevitably changing nature of the feedstock further highlights the requirement for a quantitative specific assay for the product and an assessment of product purity throughout the isolation process. 

More sophisticated models employ molecular shaped cavities, but there is again no consensus on the exact procedure. The cavity is often defined based on van der Waals radii of the atoms in the molecule multiplied with an empirical scale factor. Alternatively, the molecular volume may be calculated directly from the electronic wave function, for example by using a contour surface corresponding to an electron density of 0.001. 

As defined in this manner, the natural electronegativity scale agrees closely with empirical Pauling, MulUken, or Allred-Rochow scales (as closely as any of these scales agree with one another). Such namral scale is based on a more methodical and firmly grounded theoretical procedure than the empirical scales, and can be... 

Implementation Issues A critical factor in the successful application of any model-based technique is the availability of a suitaole dynamic model. In typical MPC applications, an empirical model is identified from data acquired during extensive plant tests. The experiments generally consist of a series of bump tests in the manipulated variables. Typically, the manipulated variables are adjusted one at a time and the plant tests require a period of one to three weeks. The step or impulse response coefficients are then calculated using linear-regression techniques such as least-sqiiares methods. However, details concerning the procedures utihzed in the plant tests and subsequent model identification are considered to be proprietary information. The scaling and conditioning of plant data for use in model identification and control calculations can be key factors in the success of the apphcation. 

Vibrational Spectra Many of the papers quoted below deal with the determination of vibrational spectra. The method of choice is B3-LYP density functional theory. In most cases, MP2 vibrational spectra are less accurate. In order to allow for a comparison between computed frequencies within the harmonic approximation and anharmonic experimental fundamentals, calculated frequencies should be scaled by an empirical factor. This procedure accounts for systematic errors and improves the results considerably. The easiest procedure is to scale all frequencies by the same factor, e.g., 0.963 for B3-LYP/6-31G computed frequencies [95JPC3093]. A more sophisticated but still pragmatic approach is the SQM method [83JA7073], in which the underlying force constants (in internal coordinates) are scaled by different scaling factors. 

A less rigorous approach to modeling than the one described above is an empirical procedure whereby water data for a given geometry may be linked with that of another fluid by numerical scaling factors without actually... 

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