Orthogonal Analytical Concepts

Analytical strategies ivhich employ combinations of various separation and/or detection methods are called orthogonal analytical concepts . They are an inevitable means for quality control in speciation, and provide the best chances to obtain correcf speciation results and even identification of heretofore unknoivn species. In analytical systems ivith only one separation and one detection system, the risk of coelution, impossibility of species identification or misidentification is high (e.g., McSheehy et al. 2002), but this problem can be solved by employing different systems in various ways. 

A section has been added to Chapter 1 on the distinction between analytic vs. enumerative studies. A section on mixture designs has been added to Chapter 9. A new chapter on the application of linear models and matrix least squares to observational data has been added (Chapter 10). Chapter 13 attempts to give a geometric feel to concepts such as uncertainty, information, orthogonality, rotatability, extrapolation, and rigidity of the design. Finally, Chapter 14 expands on some aspects of factorial-based designs. 

Figure 2.24. The concept of orthogonality as shown by retention plots of two sets of columns for a variety of different analytes. (A) Since the log k data of the two columns (C8 and C18) are well correlated for most analytes, these two columns are expected to yield similar elution profiles. (B) The selectivity differences of a C18 and a polar-embedded phase (amide) column lead to very scattered correlation of their respective retention data. Methods using a C18 and a polar-embedded column are therefore termed orthogonal and expected to yield very dissimilar profiles. Diagram courtesy of Supelco, Inc.

First one can build up other effective Hamiltonians based on hierarchized orthogonalization procedures. The Gram-Schmidt procedure is recommended if one starts from the best projected wavefunctions of the bottom of the spectrum. Thus one can obtain a quite reliable effective Hamiltonian with well behaved wavefunctions and good transferability properties (see Section III.D.2). The main drawback of this approach is that the Gram-Schmidt method, which involves triangular matrices, does not lead to simple analytical expressions for perturbation expansions. A partial solution to these limitations is brought about by the new concept of intermediate Hamiltonian,... 

---