The design of solvents for solutes typically found in the pharmaceutical and agrochemical industries is considered. These solutes are usually aromatic, with several heteroatoms, and they therefore exhibit complex interactions with solvents. As a result, detailed models are often needed to predict the behavior of solute/solvent systems. The use of the SM5.42 continuum model of solvation(1-4) in solvent design is investigated. This model is based on a quantum mechanical representation of the solute. An optimization-based molecular design problem is formulated with the simple objective of minimizing the free energy of solvation. The solvent properties needed to calculate the free energy of solvation are obtained using group contribution methods. The resulting problem is a nonconvex mixed-integer nonlinear program with mixed-integer algebraic constraints. The outer-approximation algorithm is implemented to solve this optimization problem, using a combination of analytical and numerical gradients. Several case studies are solved, based on HF/6-31G* quantum calculations. Monofunctional and bifunctional aromatic compounds are used as test solutes. The design of the solvent is based on combinations of up to 41 different atom groups. In all cases, the algorithm identifies the best solvent in a small number of iterations. The required CPU time is up to 9 times smaller than that needed to evaluate all possible solvent structures.