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 NO2, CN, Cl, Br, CF3, F, CHO, CH2Cl, COOH, COCH3, CONH2, OH, OCH3, C6H5, NH2, H, CH3, CH2CH3, CH(CH3)2, and C(CH3)3 to study the dependencies between molecular electrostatic potential minimum (Vmin) and the inductive substituent constant σI. All the three model systems show excellent linear correlation between Vmin and σI suggesting that the calculation of Vmin 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 Vmin = 12.982 σI− 48.867, Vmin = 13.444 σI− 182.760, and Vmin = 18.100 σI− 65.785, respectively. Considering the simplicity of the quinuclidine model, Vmin value at the nitrogen lone pair region of a 4-substituted quinuclidine system is recommended for the evaluation of σI. Further, the additivity effect of σI is tested on multiply substituted quinuclidine and bicyclo[2.2.2]octane carboxylic acid derivatives using the Vmin 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 Vmin response site. However, the distance relation of σI is not well represented in the caged molecular systems.