Mulliken population analysis based evaluation of condensed Fukui function indices using fractional molecular charge

A thorough study on the nature of Mulliken population analysis (MPA) based condensed Fukui function (FF) indices has been performed. It is claimed analytically that nothing can be predicted about the sign of condensed FF indices, even when evaluated by using very small fractional molecular charge (i.e., approximately following the analytical definition of FF indices). The corresponding numerical demonstrations on different chemical systems confirm our claim.