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Table 5.4 Taft steric parameters'1.

Substituent

Substituent

CHj-

CTfjCOCHj-

CHj-

CTfjCOCHj-

aTaft, R.W. (1956) Separation of polar, steric and resonance effects. In Steric Effects in Organic Chemistry, edited by M.S.Newman, pp. 559-675. New York: John Wiley.

More comprehensive lists of Taft steric parameters can be found in: Tute, M.S. (1971) Principles and practice of Hansch analysis: A guide to structure activity correlation for the medicinal chemist. In Advances in Drug Research, edited by N.J.Harper and A.B.Simmonds, Vol. 6, pp. 1-77. London: Academic Press. Hansch, C. and Leo, A. (1979) Substituent Constants for Correlation Analysis in Chemistry and Biology. New York: John Wiley.

Van der Waals volume (Vw) and radius (rv) represent the actual dimensions of the group. Since chemical groups are rarely symmetrical, the van der Waals radius depends on the axis along which it is measured, and three types are defined, rv(min), the minimum radius, rv(max), the maximum radius, and rv , which is the distance the group protrudes from the bulk of the parent molecule. Van der Waals radii can be correlated with biological results in the same ways as Es, to which they are linearly related. rv(min) is usually preferred because groups are expected to take up positions which will minimize the degree of steric interaction. Sometimes the mean of the three radii (rv(av)) is used. McGowan and Mellors introduced the characteristic volume Vx, the molar volume at absolute zero, and provided atomic and bond contributions for its evaluation (see Section 5.4.2.2).

The principal problem with van der Waals radii and Taft's Es values is the limited number of groups for which these constants have been determined. Charton introduced a corrected van der Waals radius U, in which the minimum value of van der Waals radius of the substituent group (rv(min)) is corrected for the corresponding radius for hydrogen (rvH), as defined by Equation [5.18].

5.41.2 Van der Waals dimensions

5.41.3 Charton's steric constants

They were shown to be a good measure of steric effect by correlation with Es values, and were also found to be rectilinearly related to the rates of esterification of substituted carboxylic acids with methanol and ethanol. Since there were ample data for these reactions, Charton was able to extend his list of constants to 62, by substituting rate constants into the regression equations linking esterification rates to U. The large number of constants available makes this a useful source of steric parameters for QSAR studies.

### 5.4.1.4 Sterimol parameters

A criticism of the steric parameters described so far is that they represent only one aspect of the shape of the group. Thus for example, van der Waals volume represents the total volume of the group, and rv the width along one plane. Sterimol parameters were developed to overcome this weakness. Each chemical group is allocated 5 Sterimol parameters: L, which is the distance the group protrudes from the parent molecule, and B1-B4, which give the widths of the group in four directions, 90° to each other and perpendicular to the axis along which L is measured. Cross sectional dimensions increase from B1 to B4. The procedure is shown diagrammatically in Figure 5.3.

5.4.1.5 Molar refractivity Molar refractivitiy (MR) is defined as:

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