The Hartree-Fock (HF), restricted open shell HF (ROHF), configuration interaction (CI), complete active space (ICASCF), and multiconfiguration self-consistent field (MCSCF) methods provide sophisticated fundamental theory-based, computational tools to study structure, composition,chemistry and electronic properties of small artificial molecules composed of semiconductor compound atoms. These tools are used to synthesize virtually several prismatic In-N and Zn-O artificial molecules whose structure is derived from that of the symmetry elements of the respective wurtzite bulk lattices. Applications of spatial constraints to the atomic coordinates allow modeling molecular synthesis in quantum confinement, to obtain pre-designed molecules with tunable electronic properties. Relaxation of these constraints, or optimization, leads to the corresponding molecules synthesized in “vacuum”. The development of computational templates of the studied artificial molecules synthesized in confinement reflects effects of quantum confinement on the electronic level structure, bonding, the direct optical transition energy, and charge and spin density distributions of the molecules. Comparison of the structure and properties of these molecules to those of their vacuum counterparts leads to a conclusion that a small changes in atomic positions in otherwise structurally similar molecules cause a significant change in their electronic properties. Thus, the electronic properties of artificial molecules can be tuned by changing their synthesis conditions that are defined by atomistic details of quantum confinement where the molecules are synthesized.