Theoretical Calculation of Hammett Constants for Benzoic Acid and Its Derivatives Using AM1-DFT Method

The Hammett equation constants were calculated theoretically by statistically correlating the practical Hammett equation constants for these compounds with several theoretically calculated structural properties. Two quantum-mechanical methods were used to calculate the structural properties. The experimental method (AM1) used the basic process (DFT), and the calculated structural variables were divided into two types. The first is the inductive, the energies of bond and charge distributions on atoms. In contrast, the second type includes the energy variables, which include the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), hardness (ŋ), and total energy (E). The single- and double-regression analyses were performed using the statistical analysis program (SPSS). The relationship between the theoretically calculated variables and the practical Hammett equation constants was evaluated through the correlation coefficients (R2). In a single regression analysis, several variables were found to strongly correlate with the practical Hammett equation constants, with the strongest being the charge on the oxygen atom at position 9 adjacent to the carbonyl group (C=O). By conducting the double regression analysis, we obtained the best correlation strength of the theoretically calculated variables with the values of the practical Hammett equation constants and the values of the correlation coefficients (R2) for the best two variables for each of the four methods gave the highest value of the correlation coefficient R2 = 1 through the variables (C6 + C7) because they are among the factors affecting the values of (σ).