Influence of substituent on rate and equilibrium constants by means of spectral-isolation factor analysis

Abstract

The key set and spectral isolation methods of factor analysis suggested by Malinowski have been applied to a chemical reactivity data matrix in order to obtain substituent constant scales as orthogonal as possible for the given set of data. The data matrix used consisted of equilibrium and rate constants (24 substituents in the aromatic ring and 10 reaction series). Principal component analysis (p.c.a.) yielded four factors by the indicator function method. The key set method identified the following reaction series: pK values of benzoic acids in water, pK values of phenols in water, pK values of phenols in ethanol–water (23.68 vol.% EtOH), and rate constants for solvolyses of substituted diphenylmethane in ethanol for use as substituent constant scales in correlation analysis of the remaining reaction series. The results of the respective correlation analysis were found to be unsatisfactory: the root mean square error S is 0.23 in logarithmic units. The spectral isolation method enabled us to isolate substituent constant scales whose application to correlation analysis yielded s 0.12, close to the experimental error in the data used, estimated by p.c.a. The first scale is well correlated with the σ° and Hammett σ scales indicating that it reflects the influence of the inductive effect of substituents. The second scale obtained is shown to be related to the resonance effect of substituents because it correlates with σ⁺_R values. It was concluded that the application of the spectral isolation method of factor analysis leads to meaningful substituent constant scales.