Number system comparison test

The sum of all points scored eventually represents a laboratory s performance in a single proficiency test. The maximum achievable points, however, depends on the total number of spiking chemicals used. As this number varies from test to test, the points scored cannot be used to compare performances between laboratories participating in different proficiency tests. This comparison is achieved with the final letter scoring system, and is shown in Table 9. 

The idea of benchmarking quantum chemical methods by introducing databases covering a wide variety of different properties, for example, atomization energies, spectroscopic properties, barrier heights and reaction energies of diverse reactions, proton affinities, interaction energies of noncovalent bond systems, transition metal systems, and catalytic processes, was extended by Truhlar and coworkers [51]. They were the first to carry out overall statistical analyses of combinations of different test sets to obtain an overall mean absolute deviation (MAD) number for each tested quantum chemical method, which made a comparison with other approaches more feasible. 

In comparisons of eqnilibrium constants collected from the literature (e.g.. Fig. 4.22 or [47]), or correlations of data for a large number of systems (e.g.. Figs. 4.20-4.23), it is desirable to present both the statistical uncertainty of each point which is often given by the standard deviation (one or several a s) of the point, and the general reliability (statistical significance) of the whole correlation [76], for which the chi-square test offers a deeper insight into the reliability of the experimental results [77]. More advanced statistical tests for systems of our kind have been described by Ekberg [78]. 

A proposal for the comprehensive study of chemical processes in a variety of important condensed-phase systems using modern theoretical methodology has been presented. The primary goals of the research are to provide microscopic information on the mechanisms and structural and dynamical properties of the chemical systems proposed for investigation, to test the applicability of modern ab initio molecular dynamics (MD) by comparison with experiment, and to develop and apply novel ab initio MD techniques in simulating complex chemical systems. The proposed research will contribute to the forefront of modern theoretical chemistry and address a number of important technological issues. The PI has carefully attempted to demonstrate his knowledge, ability, and resources to carry out the proposed research projects. 

The model for ionic retention and ion-pair chromatography that are discussed in Sections 15.2 and 15.3 has been tested and applied to a number of different systems and works very well in most of the cases. From colloid and surface chemistry is known that the model has its limitations, and under certain chromatographic conditions, the presented model will not be valid. The limitations of the model when applied to reversed-phase chromatography of ions still need to be found. Some are self-evident, such as if the pairing-ion concentration is close or above the CMC or when the retention factor is very low so that the accumulation in the double layer is important in comparison to the adsorption, see Ref. [7] for a discussion concerning the accumulation in the double layer. 

A different way, developed extensively by Schwartz and his coworkeis, - is to use approximate quantum propagators, based on expansions of the exponential operators. These approximations have been tested for a number of systems, including comparison with the numerically exact results of Ref 38 for the rate in a double well potential, with satisfying results. 

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