Hydrogen bonding has a great impact on the partitioning of organic compounds in biological and environmental systems as well as on the shape and functionality of macromolecules. Electronic characteristics of single molecules, localized at the H-bond (HB) donor site, are able to estimate the donor strength in terms of the Abraham parameter A. The quantum chemically calculated properties encode electrostatic, polarizability, and charge-transfer contributions to hydrogen bonding. A recently introduced respective approach is extended to amides with more than one H atom per donor site, and adapted to the semi-empirical AM1 scheme. For 451 organic compounds covering acidic CH, NH, and OH groups, the squared correlation coefficient is 0.95 for the Hartree–Fock and density functional theory (B3LYP) level of calculation, and 0.84 with AM1. The discussion includes separate analyses for weak, moderate, and strong HB donors, a comparison with the performance of increment methods, and opportunities for consensus modeling through the combined use of increment and quantum chemical methods.