Use of molecular electrostatic potential for quantitative assessment of inductive effect

Abstract

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 (V_min) and the inductive substituent constant σ _I. All the three model systems show excellent linear correlation between V_min and σ _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 σ _I- 48.867, V_min = 13.444 σ _I- 182.760, and V_min = 18.100 σ _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 σ _I. Further, the additivity effect of σ _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 sI is not well represented in the caged molecular systems.