Atomistic details of matter determine physical and chemical properties. Much research has been carried out in order to understand and model this relationship using quantum mechanical (QM) first principles, statistical mechanics, and the ever increasing role of the computational sciences. Employed methods are based on a physico-chemical framework that nowadays permits to routinely compute relevant properties for any combinations of atomic configurations and composition, also called chemical compound space (CCS). The task of using QM for the discovery of novel compounds with improved properties is therefore equivalent to a combinatorial optimization problem in CCS. Tackling this task through QM based high-throughput screening, albeit straight-forward, is the least efficient way. The overall goal of this proposal is to make a comprehensive exploration of CCS possible by developing QM based rational compound design (QM-RCD) schemes that are drastically more efficient than screening. The proposed QM-RCD approach is based on two of the most fundamental and complementary strategies in numerical optimization theory, namely variational and correlational methods. For the former, differential, response-like, QM predictions of properties will be studied for compounds that are ``close'' in CCS. For the latter, intelligent data analysis methods (machine learning) will be applied to exploit complex correlations. Such models promise to dramatically accelerate the estimation of QM properties, enabling the modeling of massive numbers of compounds within discrete combinatorial optimization implementations, e.g. evolutionary or Monte Carlo based. While many QM properties are amenable to such efforts, the focus of this proposal lies on the archetypical problem of ligand design. The usefulness of this highly interdisciplinary endeavor, tightly linking theoretical physics with computational chemistry and biochemistry, and with computer sciences, will be exemplified for realistic and relevant ligand leads, such as DNA intercalating drugs (dominated by pi-pi-interactions) and ligand-protein (dominated by hydrogen bonding and polarization) interactions.