Principal component analysis of solvent effects on equilibria and kinetics — A hemisphere model

Principal Component Analysis (PCA) was applied to 17 selected properties relating to the properties of solvents and their effect on solute spectra and equilibria and rates of reactions in solution. The analysis showed affinities and contrasts among the parameters. Using the first three principal components (PC's) as unit vectors in the Cartesian directions, the properties were represented as vectors in this space with their directions being represented as points on the unit hemisphere; their magnitudes are lost in the process of correlation. Properties that fell into recognizable groups included the following: (i) those purporting to measure acidity (A) (α, AN, SA, and A j ), closely associated with E T N , Z, S, and A( 14 N), which are usually considered to be measures of polarity; (ii) properties supposed to measure basicity (B) (β, SB, and DN); (iii) polarity group (P), including pure (di-)polarity properties (β µ 1/2 and Q v ) and those measuring some combinations of polarity and polarizability (π*, π azo , SPP, and –χ R ). The space spanned by the three PCs of the properties provided a frame in which solvent effects on equilibria and on rates of reactions could be represented. Eight equilibria, represented by log 10 (K) measured in different solvents, and 10 reaction rates, similarly represented by log 10 (k), were correlated with the three PCs of the solvent properties. This enabled plotting of their directions in the hemisphere to show which groups of properties were most strongly correlated with the rate of each reaction. A separate plot showed the magnitudes and sense of the effects. These finding are considered in the light of the mechanisms proposed for the reactions.