Ionization error statistics

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

A third source of error is associated with the fragmentation pattern caused by dissociation of the molecular ions formed in the source region of the spectrometer. Under severe conditions these processes may proceed with substantial isotopic fractionation, and this obscures the measurements of isotopic composition at the collector. To some extent careful standardization of the instrumental conditions may ensure that errors from fragmentation are systematic, and thus cancel (at least to some extent). Alternatively, softer ionization methods can be used to prevent most or all of the fragmentation. The bottom spectrum in Fig. 7.7 illustrates this approach it shows the mass spectrum of chlorobenzene obtained by photoionization. Only the parent molecular ions are observed. It should be kept in mind, however, that softer ionization usually yields smaller ion currents and consequently statistical counting errors increase. 

In summary, the overall error in microanalysis using GELS is a combination of the statistical error in the measurement of Ia (P, A) which for Poisson statistics (applicable in the case of EELS) is given by VIa, the errors in background fitting and extrapolation (-5%) above VlA, and the accuracy of the ionization cross-sections (theory -5-15%, experiments -2-5%). 

Primary a values are obtained from the thermodynamic ionizations of the appropriate benzoic acids at 25°C these are reliable and easily available. Secondary values are obtained by comparison with another series of compoundsand are thus subject to error because they are dependent on the accuracy of a measured series and the development of a regression line using statistical methods. 

Figure 2 Variations of counting statistical error (2cr or 95% confidence) for nuclides of different half-lives using different measurement techniques. Four different scenarios are shown with details listed in legend, aimed to cover a typical range of conditions. The values of ionization efficiencies span a full range of values appropriate for elements difficult (Th) and easy (Ra) to ionize thermally, see text. All scenarios assume a sample with MORB-hke U concentration (50 ngg ), but with all daughter nuclides in secular equilibrium (for illustrative simplicity). Calculations assume (unrealistic) 100% yields for chemical purification of the nuclide of interest and 40% counting...

In both the fast-beam apparatus and the double-focusing mass spectrometer, absolute cross sections can be determined with uncertainties of 15% for the parent ionization cross sections and 18% for the dissociative ionization cross sections. These error margins include statistical and all known systematic uncertainties and are typical for ionization-cross-section measurements carried out with this apparatus (Tamovsky and Becker, 1992 Tamovsky and Becker, 1993). 

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