The acid dissociation constant (pKa) has an important influence on molecular properties crucial to compound development in synthesis, formulation, and optimization of absorption, distribution, metabolism, and excretion properties. We will present a method that combines quantum mechanical calculations, at a semi-empirical level of theory, with machine learning to accurately predict pKa for a diverse range of mono- and polyprotic compounds. The resulting model has been tested on two external data sets, one specifically used to test pKa prediction methods (SAMPL6) and the second covering known drugs containing basic functionalities. Both sets were predicted with excellent accuracy (root-mean-square errors of 0.7-1.0 log units), comparable to other methodologies using a much higher level of theory and computational cost.