Chemometrics and its Roots in Physical Organic Chemistry.

Linear free energy relationships (LFERs) and extra-thermodynamic relationships (ETRs), i.e., similarity and analogy models of physical organic chemistry, are mathematically and statistically equivalent to the models much used in chemometrics and data analysis, i.e., PCA, PLS, and SIMCA. Examples of early LFERs and ETRs include the Bronsted, Hammett, Taft, and Hansch relationships. Much of the early development of chemometrics derives from this equivalence. Thus, the interpretation and derivation of LFERs and ETRs as the first terms of serial expansions of perturbation theory applied to moderate structural change lead first to the SIMCA method for classification and discriminant analysis (pattern recognition), then to the approach of principal properties for the characterization of structural fragments, compounds, and materials, and finally also strongly influenced the development of PLS and its use in structure-effect relationships such as quantitative structure-activity relationships (QSARs). The interpretation of chemical data by a combination of physical organic chemistry models and chemometric principles often leads to interesting conclusions as illustrated by some examples.