Use of molecular electrostatic potential for quantitative assessment of inductive effect

Density functional theory computations at the B3LYP/6-31G(d,p) level have been carried out for three types of model compounds, viz. (i) 4-substituted bicyclo[2.2.2]octane carboxylic acids, (ii) anions of 4-substituted bicyclo[2.2.2]octane carboxylic acids and (iii) 4-substituted quinuclidines where the substituents are NO(2), CN, Cl, Br, CF(3), F, CHO, CH(2)Cl, COOH, COCH(3), CONH(2), OH, OCH(3), C(6)H(5), NH(2), H, CH(3), CH(2)CH(3), CH(CH(3))(2), and C(CH(3))(3) to study the dependencies between molecular electrostatic potential minimum (V(min)) and the inductive substituent constant sigma(I). All the three model systems show excellent linear correlation between V(min) and sigma(I) suggesting that the calculation of V(min) parameter in these systems offers a simple and efficient computational approach for the evaluation of inductive substituent constants. The calculated linear equation for the models (i), (ii), and (iii) are V(min) = 12.982 sigma(I)- 48.867, V(min) = 13.444 sigma(I)- 182.760, and V(min) = 18.100 sigma(I)- 65.785, respectively. Considering the simplicity of the quinuclidine model, V(min) value at the nitrogen lone pair region of a 4-substituted quinuclidine system is recommended for the evaluation of sigma(I). Further, the additivity effect of sigma(I) is tested on multiply substituted quinuclidine and bicyclo[2.2.2]octane carboxylic acid derivatives using the V(min) approach and the results firmly supported the additivity rule of inductive effect. The systems showing considerable deviations from the additivity rule are easily recognized as those showing either steric effect or intramolecular hydrogen bond interactions at the V(min) response site. However, the distance relation of sigma(I) is not well represented in the caged molecular systems.