The number of chemical species of modest molecular weight that can be accessed with known synthetic methods is astronomical. An open challenge is to explore this space in a manner that will enable the discovery of molecular species and materials with optimized properties. Recently, an inverse molecular design strategy, the linear combination of atomic potentials (LCAP) approach [J. Am. Chem. Soc. 128, 3228 (2006)] was developed to optimize electronic polarizabilities and first hyperpolarizabilities. Here, using a simple tight-binding (TB) approach, we show that continuous optimization can be carried out on the LCAP surface successfully to explore vast chemical libraries of 10(2) to 10(16) extended aromatic compounds. We show that the TB-LCAP optimization is not only effective in locating globally optimal structures based on their electronic polarizabilities and first hyperpolarizabilities, but also is straightforwardly extended to optimize transition dipole moments and HOMO-LUMO energy gaps. This approach finds optimal structures among 10(4) candidates with about 40 individual molecular property calculations. As such, for structurally similar molecular candidates, the TB-LCAP approach may provide an effective means to identify structures with optimal properties.