The current availability of cheap computer power enables the construction of QSARs from modern ab initio quantum chemical data. Multivariate models for three classes of compounds are developed by means of the quantum topological molecular similarity (QTMS) tool, which incorporates descriptors originating from the "Atoms in Molecules" (AIM) theory. Correlations obtained outperform the Hammett and other traditional parameters. The advantage of QTMS over semiempirical and empirical descriptors is demonstrated by the following r(2)/q(2) values: 0.920/0.891 (acids), 0.974/0.953 (anilines), and 0.952/0.884 (phenols).