Classical Free Wilson model

The Fujita-Ban model is a linear transformation of the classical Free-Wilson model indeed, group contributions of the Free-Wilson model can be transformed to Fujita-Ban group contributions by subtracting the group contributions of the corresponding substituents of the reference compound. 

Different regression coefficients are obtained if any other compound is chosen as the reference compound or if the classical Free Wilson model is applied. However, these values are only linearly shifted to the values of eq. 70 all statistical parameters are identical, with the only exception of the 95% confidence intervals [390, 391,410]. 

QSARs include statistical methods to relate biological activities (most often expressed by logarithms of equipotent molar activities) with structural elements (Free Wilson analysis), physicochemical properties (Hansch analysis), or fields (3D QSAR). The parameters used in a QSAR model are also called (molecular) descriptors. Classical QSAR analyses (Hansch and Free Wilson analyses) consider only 2D structures. Their main field of application is in substituent variation of a common scaffold. 3D-QSAR analysis (CoMFA) has a much broader scope. It starts from 3D structures and correlates biological activities with 3D-property fields (McKinney et al. 2000). 

The classical QSAR methodology started 1964 with the publications of Hansch and Fujita (1964) and Free and Wilson (1964) and the statement of Hansch (1969) resulted from a proposal by Fujita. They proposed to combine several physiochemical parameters (tt, a), also called descriptors, in a quantitative model. This Hansch-type analysis is very flexible and describes many different kinds of biological activities, e.g. in vitro data such as enzyme inhibition (Kubinyi 2002) ... 

The earliest attempt to predict the free energy of a water cluster containing an ion originates from the classical drop model of a small cluster, Eq. (40). Wilson attempted to calculate the free energy of formation of a liquid drop of radius r on an ion of radius ri and charge e. He treated the problem by considering the ion as embedded in a uniform dielectric medium and obtained... 

The thermodynamic state in the Wilson point and the progress of cbndensation in the flow were calculated with a model of the condensation process based on the classical nucleation model and a formulation of droplet growth proposed by Gyarmathy. It is remarkable that the results of the calculation, obtained with a uniform choice of the free parameters of this condensation model, agree well with the experimental results, both for pure COp and for COp/air-mixtures. ... 

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