Empiric pragmatic approach

Figure 2.2. Process development involving no mathematical models the empirical pragmatic approach. X, biomass Sj, substrate, Pj, products P/K power/ volume H TR, volumetric heat rate.

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. 

Almost all contemporary ab initio molecular electronic structure calculations employ basis sets of Gaussian-type functions in a pragmatic approach in which no error bounds are determined but the accuracy of a calculation is assessed by comparison with quantities derived from experiment[l] [2]. In this quasi-empirical[3] approach each basis set is calibrated [4] for the treatment of a particular range of atoms, for a particular range of properties, and for a particular range of methods. Molecular basis sets are almost invariably constructed from atomic basis sets. In 1960, Nesbet[5] pointed out that molecular basis sets containing only basis sets necessary to reach to atomic Hartree-Fock limit, the isotropic basis set, cannot possibly account for polarization in molecular interactions. Two approaches to the problem of constructing molecular basis sets can be identified ... 

Johannes Hunger (Chapter 7) takes on another of the standard topics in the philosophy of science, explanation. Hunger examines, in detail, various ways that chemists explain and predict the structural properties of molecules. We learn about ab initio methods, empirical force field models and neural network models, each of which have been used to explain and predict molecular structure. And we learn that none of these approaches can be subsumed under either hypothetico-deductive or causal models of explanation. Either chemistry does not offer proper explanations (the normative option) or our philosophical models for explanation are inadequate to cover explanation in chemistry (the descriptive option). Hunger takes the descriptive option and sketches a more pragmatic approach to the explanation that develops Bas van Fraassen s approach to explanation for chemistry. Once again, we find that the philosophy of science has much to learn from the philosophy of chemistry. 

A pragmatic approach to developing density functional approximations is to expand the post-LDA correction in a set of suitably chosen parametrized functions and optimize the parameters by training the functional to reproduce certain calibration data as accurately as possible. Of course, fitted parameters appear in many of the previously discussed functionals, but there they were used only to clean up the constmction. In this survey, we call empirical or optimized only those functionals whose design is avowedly empirical. 

We come to reach the conclusion that it is wiser not to load the additive function of the glass transition with quasi-theoretical assumptions and to use a pragmatic, empirical approach. 

Empirical Prediction. To this point, surface tension has been described in terms of an operational definition, a thermodynamic definition, and through its molecular origin. In practice, however, these three approaches do not constitute any pragmatic means for estimating usable values for the surface tension of... 

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