Hierarchy of methods

With regard to the hierarchy of methods, primary methods or definitive methods frequently represent the highest level of reliability. Such concepts, coming from fundamental physical metrology, may find their interest in particular within discussions on traceability concepts (see section 2.1.3). In chapter 5, on the certification of RMs, these aspects are discussed in some more detail (section 5.1.4.1). 

Definitive method method with a high scientific status applied in a laboratory of high proven quality [10]. In brief it means that only negligible systematic errors may remain compared to the precision and trueness required for the final result. Isotope Dilution Mass Spectrometry (IDMS), in its thermo-ionisation mode, for the determination 

The ISO Guide 32 on calibration of chemical analysis and the use of certified reference materials [11] classifies chemical methods into three categories with regards to the calibration procedure. 

Calibration the set of operations which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system, or values represented by a material measure, and the corresponding known values of a measurand [Ij. 

Type III or comparative method a method where the sample to be analysed is compared to a set of calibration samples, using a detection system which has to be recognised to be sensitive not only to the content of elements or molecules to be analysed but also to differences of matrix [11], Ignoring any difference in the matrix will lead to errors. Calibration of such methods requires (Certified) Reference Materials ((C)RMs) with a known matrix composition similar to the matrix of the sample. Such methods are rapid and are often used in monitoring of manufacturing processes (e.g. WDXRF in the production of metals, alloys, coal, cement, powdered oxides, etc.) or for the determination of basic parameters (e.g. viscosity, particle size distribution etc.). 

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Recently a hierarchy of methods has been developed which covers the mapping of polymers to a mesoscopic level as well as the reintroduction of the atomistic structure [43-45]. Section 6 (Kremer, Murat, Hahn) gives some very first attempts to bridge the gap from microscopic to mesoscopic [43,44] and thereafter to the semi-macroscopic regime [45] within a simulation scheme. 

A second fundamental classification of quantum chemistry calculations can be made according to the quantity that is being calculated. Our introduction to DFT in the previous sections has emphasized that in DFT the aim is to compute the electron density, not the electron wave function. There are many methods, however, where the object of the calculation is to compute the full electron wave function. These wave-function-based methods hold a crucial advantage over DFT calculations in that there is a well-defined hierarchy of methods that, given infinite computer time, can converge to the exact solution of the Schrodinger equation. We cannot do justice to the breadth of this field in just a few paragraphs, but several excellent introductory texts are available... 

We note the following papers that chronicle a hierarchy of methods for estimating enthalpies of vaporization ... 

The OFFC Regulation establishes a hierarchy of methods used for sampling and analysis in applying official controls. First priority is given to methods laid down in Community legislation. If these do not exist, methods according to internationally established rules such as those of CEN or those in national legislation should be applied. In the absence of these methods other methods fit for the purpose or developed in accordance with scientific protocols shall be used. In the area of food contact materials analytical methods are laid... 

In considering the solution of the approximate problem, a number of points are evident. It is highly desirable to tackle the problem with a hierarchy of methods and models. The design process can be likened to a mixture of broad and deep searches over the space of design options. The search has two main mechanisms ... 

It is an attractive feature of ab initio wave function theory that there is a clear hierarchy of methods leading from Hartree-Fock to the exact solution of the Schrodinger equation. Post-Hartree-Fock methods can be divided into three main categories [88]. The first is based on (Mqller-Plesset) perturbation theory [89] and referred to as MPn where n is the order of the perturbation. MPn is excellent when Hartree-Fock already is giving a reasonable description, as is often the case for complexes involving Ad and 5d elements. Otherwise, it fails or might only converge slowly with the order n. MP2 can be used for medium size systems of 100-200 atoms. 

The following hierarchy of methods of use goes from the ones with the most waste to the ones producing the least waste (An example is given in most cases.)... 

A very important observation at this point is that an IDMS assay is in principle a physical measurement since it is a measurement of ratio of isotopes and not of a ratio of elements (as in classical analytical chemistry). Indeed two numbers of atoms are compared in a ratio determination and these atoms belong to the same element. Hence ail the chemical interferences, normal in a chemical assay, do not affect the result anymore. Combined with the fact that the requirement of being quantitative - essential and difficult in classical chemistry assay - must not be fulfilled (after spiking), this means that IDMS ranks higher in the hierarchy of methods than normal elemental assay methods since it is far less subject to potential chemical error sources. In other words its inherent potential for good precision and accuracy (i.e. small overall uncertainty) and - at least as important -the transparency of the uncertainty propagation in (Eqs. 4 and 5) give it the character of what some have called a "reference method" or even a definitive method". 

With the workplace hazards identified and defined, the next logical step is to eliminate or control them. Historically, there have been two predominant concepts about hazard controls. The first concept is to think of hazard control as a hierarchy of methods of control. In the hierarchy, the best control method is to eliminate the hazard through redesign or substitution. If elimination or substitution cannot be achieved, then the next-best approach is to block employee access to the hazard. Fintilly, if blocking cannot be achieved, then a last approach would be to warn the employees of the hazard and train them how to avoid the hazard. 

The disparate time and length scales that control heterogeneous catalytic processes make it essentially impossible to arrive at a single method to treat the complex structural behavior, reactivity and dynamics. Instead, a hierarchy of methods have been developed which can can be used to model different time and length scales. Molecular modeling of catalysis covers a broad spectrum of different methods but can be roughly categorized into either quantum-mechanical methods which track the electronic structure or molecular simulations which track the atomic structme (see the Appendix). 

By choosing one arrives at MR-CC methods that are currently an active field of research, but that are not applied routinely except for benchmark systems. Similar to the Cl method, truncation of the excitation operator then leads to a hierarchy of methods termed CCS (which is equivalent to CIS for energies), CCSD, CCSDT, and so on. 

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