In this study, various ways of calculating electronegativity are analyzed after a brief summary of the evolution of this concept. We point out that some commonly used basis sets to calculate this parameter, such as 6-311G(d), provide results with an extraordinarily high margin of error. Therefore, a correction to the 6-311G(d) basis set is proposed that leads to calculations of electronegativity and hardness with a quality similar to those obtained with much broader basis sets, such as Aug-cc-pVQZ and Aug-cc-pV5Z. Since the calculation effort of the proposed basis is small, it can be applied to the accurate calculation of electronegativity and hardness in relatively large systems. It has also been tested in the calculation of reactivity indices and we have obtained results similar to those of the Aug-cc-pV5Z basis set. Finally, we have studied the densities corresponding to the frontier molecular orbitals in a representative sample set of molecules, using both the improved and other standard basis sets, and we have verified that the quality level of the proposed basis set is clearly better than that of standard basis sets with a similar calculation effort.