Since the dawn of quantitative structure-properties relationships (QSPR), empirical parameters related to structural, electronic and hydrophobic molecular properties have been used as molecular descriptors to determine such relationships. Among all these parameters, Hammett sigma constants and the logarithm of the octanol-water partition coefficient, log P, have been massively employed in QSPR studies. In the present paper, a new molecular descriptor, based on quantum similarity measures (QSM), is proposed as a general substitute of these empirical parameters. This work continues previous analyses related to the use of QSM to QSPR, introducing molecular quantum self-similarity measures (MQS-SM) as a single working parameter in some cases. The use of MQS-SM as a molecular descriptor is first confirmed from the correlation with the aforementioned empirical parameters. The Hammett equation has been examined using MQS-SM for a series of substituted carboxylic acids. Then, for a series of aliphatic alcohols and acetic acid esters, log P values have been correlated with the self-similarity measure between density functions in water and octanol of a given molecule. And finally, some examples and applications of MQS-SM to determine QSAR are presented. In all studied cases MQS-SM appeared to be excellent molecular descriptors usable in general QSPR applications of chemical interest.