Pragmatic Approximations

As the dynamics of the system are removed from the model, it is no longer necessary to allow the molecules to live in a continuous space. Instead, the use of lattices - discrete sets of coordinates on to which the molecules are restricted - is popular. Digital computers are of course much more efficient with discrete space than with continuum space. The use of a lattice implies that one removes all properties that occur on shorter length scales than the lattice spacing from the model. This is no problem if the main interest is in phenomena that are larger than this length scale. 

With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Muller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, realistic moves are incorporated, such that the number of MC steps can be linked to a simulated time. 

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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. 

The validity of this approximation can be justified only pragmatically, although some qualitative conditions for it can be stated, as will be seen. Assuming the legitimacy of Eq. (7-70), and substituting into (7-69), which is now to be solved in successive orders of smallness of its terms, we obtain... 

Fortunately, as shown by Lee, Handy, and Colwell, 1995, it seems that the consequences of this approximation with regard to the accuracy of the computed chemical shifts are rather modest and are of less significance than the general shortcomings inherent in the functionals used. Hence, from an application-oriented, pragmatic point of view one does not need to worry too much about using functionals which are formally inadequate because they neglect the required dependence on j(r). 

II electronic states, 634-640 theoretical background, 625-626 triatomic molecules, 611-615 pragmatic models, 620-621 Ab initio multiple spawning (AIMS) conical intersection location, 491-492 direct molecular dynamics, 411-414 theoretical background, 360-361 Adiabatic approximation geometric phase theory ... 

Being a pragmatic, adopting sometimes very rough approximations, required simplicity, efficacy, rapidity, but that does not mean that Barriol sacrificed the scientist s principles on the altar of the results. On the contrary, one finds here the occasion to point out that this theoretical chemist at work was theoretical in the most classical sense of the word The one who thinks about the bases, who works on the foundations. Every time Barriol followed his intuition, every time he adopted a rough, simple, and far-from-reality model, he justified his choice and showed, a posteriori, why it worked. It has been shown above how the non-acceptable results for polarizability, when extended from methane to hydrochloric acid, constituted an occasion to reexamine the precedently admitted hypothesis and more precisely, the theoretical significance of what was considered as a charge. Let us examine two other examples. 

The preceding behavior, which, for simplicity, has been described pragmatically in terms of equations such as eq. (9), reflects the dependence of the relative volume of the momentum-coordinate hyperspace spanned by the respective complexes and molecules as a function of momentum (energy). The classical approximation to the reaction coordinate and momentum eigenvalues has been employed, but otherwise the quantum formulation was used. 

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