Computational determination of p Ka values. A comparison of different theoretical approaches and a novel procedure

Abstract

We have estimated the p K a values of different series of imidazol-1-ylalcanoic acid derivatives using combinations of semiempirical or ab initio methods and two semiempirical solvation models SM2 and SM5.4. None of these procedures was able to describe the zwitterionic structure of the carboxylic monoacids series as their most stable form determined experimentally in solution. Under these conditions, a comparison of the theoretical and experimental p K a values showed RMS differences ranging from 1.43 to 3.04 p K a units. As an alternative strategy we describe here a mathematical model for p K a determination based on quantitative structure–property relationships. The model uses two quantum chemical descriptors, the natural atomic charge on the N3 proton ( q H +) and the frontier orbital energy ( ε L), allowing the determination of p K a values for every compound of a given series with a reasonable computational effort. A linear relationship is described among p K a, q H +, ε L and the number of ester groups in the molecule n. Multiple linear regression analysis of the available series of imidazol-1-ylalcanoic compounds allowed to obtain the expression p K a = − 119.435 × q H + + 0.612 × ε L − 1.043 × n + 65.204 which reproduced the experimental values within 0.1 p K a units.